WHEN YOU CANNOT MAkE IT TO AN SOA CONFERENCE: … · 2013. 3. 18. · CONTINUED ON PAGE 5 JApANESE EqUITIES AND BUll MARkET ECONOMICS By Steve Scoles Rewards s s& J apan’s financial

ISSUE 61 MARCH 2013

CONTINUED ON PAGE 5

JApANESE EqUITIES AND BUll MARkET ECONOMICSBy Steve Scoles

Rewards&ss

J apan’s financial markets are great examples of the kinds of powerful trends that can develop in markets. Japan’s broad equity market index, the TOPIX, had a 40-year bull market that saw the index grow almost 30 times in value by the late 1980s. However, since 1989, the TOPIX has lost

over 75 percent of its value in a brutal bear market. Furthermore, the index hit a new bear market low in 2012, almost 23 years after its peak.

Moving to fixed income, Japan’s bond market has shown a very strong bull market since 1990. Bond prices have risen steadily as 10-year Japanese government bond yields have fallen from 8 percent to less than 1 percent. As I write this arti-cle in November of 2012, Japan’s 10-year bond futures are just less than their all-time high price.

In my investing career, Japan’s recent financial market trends (bear market in equities and bull market in bonds) have been blamed on something specific to the Japanese culture or government policies. However, looking at the last 10

TOPIX Index 1949 to 2012

Source: Bloomberg

1 Japanese Equities And Bull Market EconomicsBy Steve Scoles

2 Chairperson’s Corner When You Cannot Make It To An SOA ConferenceBy Thomas Anichini

8 Stable Value: Is There Really A Problem?By paul J. Donahue

16 Taking Stock: Revisiting The Loser’s GameBy Nino Boezio

20 Why U.S. Insurers Fared Better Than Banks Did By Max J. Rudolph & Rick Beard

24 Announcing The SOA Investment Section’s 2013 Investment ContestBy Tom Anichini & Frank Grossman

25 Why Are Corporate Pension Plans Reducing Risk Now?By Evan Inglis

27 Pricing And Hedging Financial And Insurance Products Part 2: Black-Scholes’ Model And BeyondBy Mathieu Boudreault

39 SOA 2013 Life & Annuity SymposiumBy Frank Grossman

Rewards&ss

2013 SECTION LEADERSHIP

OfficersThomas Anichini, Chairpersonlarry Zhao, Vice ChairpersonThomas Egan, SecretaryDeep patel, Treasurer Council MembersMartin BelangerSteven Chenpaul DonahueJames GannonFrank Grossman Board PartnerEvan Inglis

Website CoordinatorThomas Anichini Other RepresentativesChad Hueffmeier, Vol. Work Group Coordinatorlarry Zhao, Risks & Rewards liaisonpaul Donahue, Redington prize CoordinatorEd Martin, 2013 Investment Symposium RepFrank Grossman, 2013 life & Annuity Symposium RepRyan Stowe, 2013 life & Annuity Symposium Co-Rep Steven Chen, 2013 Annual Meeting Rep

Nino A. Boezio, Newsletter Editor (Chief Editor of this issue) Segal Rogerscasey Canada 65 queen St. West, Suite 2020 Toronto, ON M5H 2M5ph: 416.642.7790 f: 416.304.0570

Joseph Koltisko, Newsletter Editor (Chief Editor of next issue) New York life Insurance Co51 Madison Avenue rm 1113New York, NY 10010ph: 212.576.5625 f: 212.447.4251

SOA STAFFSam phillips, Staff Editore: [email protected]

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Jill leprich, Section Specialiste: [email protected]

Julissa Sweeney, Graphic Designere: [email protected]

ISSUE 61 MARCH 2013

CHAIRpERSON’S CORNER WHEN YOU CANNOT MAkE IT TO AN SOA CONFERENCE: SOURCES TO SUpplEMENT YOUR INVESTMENT-RElATED CONTINUING EDUCATION

By Thomas Anichini

Among the SOA’s 19 sections, the Investment Section ranks near the top in terms of how widely its members’ job functions, career paths, and interests vary. Investment related topics of interest include generating economic scenarios, modeling asset

returns, transferring pension risk, managing portfolio risk, designing and hedging variable annuities, and otherwise keeping abreast of new quantitative methods. Which topic is most relevant may be unique to each member’s job, experience and interests.

Regardless of how many webcasts and conference sessions our section produces and how well we execute them, in a given year we know few of our members have the chance to access this content. Cost and time are the likeliest barriers, although whether the topics covered in any year match member needs could be another factor. Thus when it comes to investment education, chances are our typical member relies heavily on outside content for investment-related continuing education.

SOA CONfeReNCe SeSSiON ARChiveS: eASily ACCeSSiBle ANd veRy iNexPeNSiveI did not begin consuming these until last fall. What a bargain! You may view or down-load past conference presentations at any time, and for a period of one year after the conference SOA members may purchase the audio recordings for a nominal fee of $10. After one year, the SOA member price is $0. So even if you cannot make it to any of this year’s conferences, chances are sessions from 2009–2011 have enough shelf life that you will find them relevant and educational. Just prior to writing this I downloaded Zvi Bodie’s and William Sohn’s 2009 session on “Impact of the Financial Crisis on Pensions and Investments” to my iPod. (Visit http://www.soa.org/baaudio/).

NON-SOA CONteNt ABOuNdS: CReAte yOuR OWN CuRRiCuluMThe Internet and proliferation of digitized media liberate us from having to depend only on bundled content. They afford us the ability to curate our own continuing education. Aside from obvious sources of investment related content such as academic and practitio-ner journals (e.g., Journal of Portfolio Management, Journal of Finance, and Financial Analysts Journal), below are some of my favorite sources.

eCONOMiCS, fiNANCe, ANd iNveStMeNt BlOgSFor curating blogs I rely on Google Reader to organize, update and improve the library of blog feeds I’ve selected. Google Reader learns from your blog reading activity (including clicks, emails, likes, and +1s) and suggests other blogs you might not have discovered on your own. I have employed Reader in the past to get up to speed on various specific topics and discover topic experts. Two of the Investment Section’s best-rated speakers among our 2011 sessions were experts I found thanks to Google Reader.

published by the Investment Section of the Society of Actuaries

published by the Investment Section of the Society of Actuaries

This newsletter is free to section members. Current issues are available on the SOA website (www.soa.org).

To join the section, SOA members and non-members can locate a membership form on the Investment Section Web page at www.soa.org/investment

This publication is provided for informational and educational purposes only. The Society of Actuaries makes no endorsement, representation or guarantee with regard to any content, and disclaims any liability in connection with the use or misuse of any information provided herein. This publication should not be construed as professional or financial advice. Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries.

© 2013 Society of Actuaries. All rights reserved.

2 | RISKS AND REWARDS MARCH 2013

Next Submission

deadlineMay 15

MARCH 2013 RISKS AND REWARDS | 3

iNveStMeNt CONfeReNCe PReSeNtAtiONS ANd PAPeRSWhile such sites can be inconsistent in terms of how easily available they make their pre-senters’ presentations, at least you can typically discover who’s speaking and on what topic. A little searching can typically scare up the speakers’ earlier working papers or presentations on those topics. Three of my favorites are the Chicago Quantitative Alliance (cqa.org), the Society of Quantitative Analysts (sqa-us.org), and the Q Group (q-group.org).

SOCiAl SCieNCe ReSeARCh NetWORK (SSRN.com) Current and former academics likely know SSRN better than I do, but if you are not familiar with SSRN you owe it to yourself to explore. SSRN is my primary go-to place for academic working papers. Rarely have I found academic papers cited in the media, at conferences, or in the financial press that do not also reside in some incarnation on SSRN. Even if you find an article behind a pay wall, visit SSRN and you might find a related paper or an earlier version by the same authors available at no cost. SSRN allows you to bookmark papers and download/print most as pdfs.

SSRN’s search engine allows you to search papers by title, author, subject, and keywords, and to sort results by date posted, date updated, number of downloads, and number of citations. SSRN also includes citation links, which point to other papers that cite the paper you found, and reference links, which take you to the ones mentioned in the paper’s reference section. These features come in especially handy when you identify a topic you would like to produce as a conference session and you need to identify other possible presenters either as a backup to the author or as opposing speakers on a panel.

Further, SSRN allows you to receive lists of new papers instead of having to search for them. You may subscribe to content produced within multiple research networks and sub-networks; should you subscribe you will receive email updates periodically with links to new research within that network. For example, within the Financial Economics Network you could subscribe to eight different global conference series, over a dozen subject mat-ter eJournals including Pension Risk Management, and several top academic financial research centers including some by Chicago Booth and Harvard Business School.

POdCAStSCFA Institute (CFAI) These podcasts are freely available to all in iTunes and they are a gold mine. Many are audio recordings of global CFA conference sessions; a few are recordings of local CFA society conference sessions.

CONTINUED ON PAGE 4


CHAIRpERSON’S CORNER … | FROM pAGE 3

EconTalkWith archives available since 2006, this weekly podcast series can help you brush up on topics in economics you might have forgotten or never understood in the first place. The topics focus more on economics than on finance or investing.

Vendor PodcastsWhile asset managers might be constrained by FINRA in terms of what is advisable for them to produce in the form of podcasts or blog posts, other types of vendors pro-duce informative content that can be quite advanced. Vendors of return databases (e.g., IndexUniverse, Morningstar), indexes (e.g., EDHEC, S&P), and risk management models (e.g., Axioma, MSCIBarra, Northfield, Sungard) often produce webcasts with high qual-ity practitioner research that might not reach practitioner journals for several months.

WealthTrackA podcast version of the show, these typically involve interviews with investment manag-ers (often with firms that sponsor the show), but I find the interviews to have longer shelf life than those on popular chart-watching shows. Discussions focus on the managers’ views on the current climate, with an emphasis on what they believe is sound advice to individual investors.

What Did I Miss? Tell Me On Our LinkedIn Sub-GroupNo one has a monopoly on interesting material, so share your suggestions. Post your thoughts on the SOA Investment Section’s LinkedIn group. If you are not a member yet, join the LinkedIn SOA group, and then join the Investment Section sub-group. On our discussion board you’ll be able to join over 300 of your colleagues where you may share links to papers and presentations you find provocative or enlightening.

Thomas M. Anichini, ASA, CFA, is a Senior Investment Strategist at GuidedChoice. He may be reached at [email protected].


years, North American stock and bond markets have shown many similarities to what Japan has experienced. Perhaps it is now becoming apparent that what has happened to Japan’s markets are more due to natural market dynamics than the nation itself.

Before pursuing the future of Japan’s financial market per-formance, we need to look at what some of those natural market dynamics are.

Bull MARKet eCONOMiCS – RiSiNg PRiCeS iNCReASe deMANdA basic principle of economics is the law of supply and demand. As prices rise, demand drops and supply increases. The price of a product therefore adjusts and eventually settles at the point where supply equals demand.

There are a couple of problems with applying this idea to financial assets. First of all, people do not really demand financial assets. Instead, what they really demand are future investment returns.

Second, future investment returns are a very tricky thing. Often, to figure out what future returns will be, people look to past returns. For example, anyone who advises “stocks for the long run” typically highlights stocks’ past returns as proof of their future return potential. But note that past returns depend on past price changes.

With these two problems, you start to get a circular loop between demand and price. Demand for financial assets depends on future expected returns, which often depends on past returns, which depends on past price changes.

With stocks and bonds, the laws of supply and demand become warped and prone to these positive feedback loops. As prices rise, demand rises, which increase prices further, which then further increases demand, and so on. To put it simply, rising prices creates an increase in demand.

At a moderate level, these positive feedback loops help create powerful financial market trends or bull markets. On an extreme level, you get bubbles. As well, these feedback loops can operate the other way where falling prices reduce demand, creating bear markets.

When it comes to financial markets, these “bull market economics” often overwhelm the normal law of supply and demand.

the WeAK gRAvitAtiONAl Pull Of fuNdAMeNtAl vAlueSIt is important to note that working as an opposing force to these positive feedback loops for financial asset prices is the gravitational pull of a fundamental value for the asset. The fundamental value is supposed to be the ratio-nally determined price that should be paid for the asset. However, this gravitational pull of fundamental values is often weak for several reasons.

First, when it comes to long-term assets, even just small changes in discount rates and growth rates can result in very different “fundamental” values. Bull markets often are simply the move from the low end of reasonable values to the high end.

Second, as financial speculator George Soros has pointed out, an asset’s fundamentals can be influenced by changing asset prices as well. For example, a company’s rising stock price can allow the company to use its stock as currency to buy out competitors. So fundamentals are often not simply a given fact, but also change as market prices change.

Third, current fundamentals can be misleading, because it’s difficult to imagine how much those fundamentals can change in the future. Not to pick on former U.S. Treasury Secretary Hank Paulson too much, but his quote in July of 2007 that “this is far and away the strongest global economy I’ve seen in my business lifetime” was not very predictive of where the world economy was going.

JApANESE EqUITIES AND BUll MARkET ECONOMICS | FROM pAGE 1

CONTINUED ON PAGE 6


To combine all of the above comments on bull markets and psychology, I would say bull markets are great, but at times of extreme or sustained market sentiment, it’s time to invest in the other direction.

JAPAN equitieS tOdAyThis brings me to where Japanese equities stand today. The following sample of evidence suggests there is some sustained pessimism towards Japanese equities, which may signal the end of its long bear market and the start of a new bull market.

First, In July of 2011, I noticed a long article in The New York Times titled “This Time, Japan’s Gloom Runs Deeper.” The article highlighted the “… aging population, a lack of jobs for college graduates and persistent deflation.” Talking to many people in the investment business, this is very much the strong consensus on Japan’s fundamentals. This is a far cry from the view commonly presented in the 1980s of the “Japanese economic miracle.”

Second, Tower Watson’s recent survey of Japanese pen-sion plan asset allocations have noted a steady decline in allocations to equity assets and within the equity allocation, a steady decline in the allocation to domestic equities. At a recent pension conference it was announced that, “Toyota has moved to get better returns from its domestic equity allocations, shifting 10 billion yen in May away from the long-suffering TOPIX index. …”

Furthermore, I see that Japan’s Government Pension Investment Fund, the largest pension fund in the world, has publicly proclaimed it is reducing exposure to domestic equities in favor of international equities.

While on the one hand, it may appear that these large pen-sion plans allocating funds away from traditional Japanese domestic equities may be a bad thing for the asset class, instead, it is likely a good thing. When a large pension plan

JApANESE EqUITIES AND BUll MARkET … | FROM pAGE 5

Because of these reasons, fundamental values often only provide a weak gravitational pull on asset prices. However, in any market, there are only so many investors and so much leverage that can be applied to the asset before the bull mar-ket ends. Or there are so many people who become negative in a bear market, that there is no one left to be negative. As Soros also points out, what was once self-fulfilling becomes self-defeating.

PSyChOlOgiCAl fACtORSWhile fundamental value considerations are not to be ignored, psychological factors can often be more useful in identifying the various stages of bull and bear markets and more predictive of what is going to happen in the future for those markets.

Famous investor, Sir John Templeton, who happened to make a name for himself by investing early in the Japan’s last bull market, gave a simple outline of a bull market. He said, “Bull-markets are born on pessimism, grow on skepti-cism, mature on optimism, and die on euphoria.”

That’s nice advice, but buying at times of pessimism is difficult by definition—you have to be a very rare person and the odds are very small that you will be that person! As well, it takes a lot of experience and a good memory to know what pessimism really looks like.

I would add to Templeton’s comments above that bull markets tend to end with sustained optimism and bear mar-kets end with sustained pessimism. As an example of this, Business Week had a famous cover story in 1979 highlight-ing the “Death of Equities.” While this is often pointed out as signaling the start of the great bull market in U.S. stocks in the later part of the 20th century, what people miss is that it was almost three years later that the bull market started. On the other side of that bull market, in 1996 and 1997, Business Week had cover stories pointing out “Our love Affair with Stocks” and “The New Business Cycle,” a few years before the bull market ended.

“OR THERE ARE SO MANY pEOplE WHO BECOME NEGATIVE IN A BEAR MARkET, THAT THERE IS NO ONE lEFT TO BE NEGATIVE.


RefeReNCeS:Giant Japan pension fund to dip toe in emerging mar-kets, reuters.com, July 2, 2012

Global Pension Assets Study 2012, Towers Watson, January 2012

Japan sets example in dealing with low bond, equity returns, pionline.com, November 21, 2012

The Greatest Economic Boom Ever, Fortune Magazine, July 23, 2007

This Time, Japan`s Gloom Runs Deeper, New York Times, July 9, 2011

makes a significant change to its asset allocation, it typi-cally needs the agreement of many parties—consultants, committees, and, in the case of government plans, agree-ment by government officials. When so many people agree on an investment strategy it can signal the end of a long trend is near. In the case of Japanese equities, this means it is starting to appear that all those who are going to sell have sold, which is what is needed for its bear market to end and a new bull market to begin.

While this is just a sprinkling of evidence around Japanese equities, it seems now is the time to take a good look at them as an investment option. To use a baseball analogy, while there are certainly other bull markets in play cur-rently, Japan equities appear to be one of the few in the on-deck circle.

DISCLAIMER: This article is for informational purposes and is not intended as a recommendation to buy securities. In fact, it is entirely possible that the author has a large position in Japanese equities that he is desperately trying to sell.

Steve Scoles, FSA, formerly worked as an actuary in asset/liability management. He is now a private investor and is slowly working away on the forthcoming book, Fooled by the Market. He can be reached at [email protected].


STABlE VAlUE: IS THERE REAllY A pROBlEM?

By Paul J. Donahue1

ending on or after Dec. 15, 2006. I am including the condi-tions for an investment contract to qualify as fully-benefit responsive in the footnote to this paragraph. However, the most important point is that they have not changed since promulgated before the financial crisis.3

It is critically important in evaluating significant recent developments, to recall what stable value was designed to be and what it was not designed to be: stable value was designed to provide contract value for participant-directed transactions. It was not designed to provide contract value for plan-directed transactions. To quote AAG INV-1, “Contract value is considered the relevant measurement attribute because that is the amount participants in the fund would receive if they were to initiate permitted transactions (for example, withdrawals) under the terms of the underly-ing defined-contribution plan.” [emphasis added.]

As we shall discuss further below, in the case of individu-ally-managed stable value options, the plan has never had a right to contract value. Some collective investment funds, but not all, have given plans the right to a contract value exit.

StABle vAlue WAS deSigNed tO Be A defiNed CONtRiButiON PlAN SAfe OPtiON4

Stable value is a triumph of financial engineering, designed to offer DC plan participants the greatest yield consistent with protection of principal in the benefit plan environment. A DC pension plan’s provisions will itself restrict a partici-pant’s access to funds, and withdrawals from the plan incurs tax liabilities and sometimes tax penalties. These features mean that a stable value manager can safely invest at longer durations than money market. The fully-benefit responsive contracts5 required for contract value accounting assure that any required liquidity will be available. These features mean that stable value returns will normally exceed those for options that might also qualify as “income-producing, low-risk, liquid.”

S table value has been in the news far more than the facts warrant, and not for the reason that deserves highlighting: stable value continues to

deliver returns far superior to other options that qualify as a defined contribution plan’s “safe option.”2 The long-time motto of the Society of Actuaries, “The work of science is to substitute facts for appearances and demonstrations for impressions,” is more than ever worth recalling, when self-interested spin has become so sophisticated, and so often aims at obscuring the facts rather than at bringing them to light. This article will set out the facts about stable value returns versus those of other options that can qualify as a plan’s “safe option”: a money market fund, some version of an FDIC insured account, and a short bond fund. It will then discuss various issues raised to cast doubt on the continued value offered by stable value options: alleged restrictions on participant rights and the lack of availability of stable value investment contracts. It will conclude that stable value remains as outstanding a value for participants seeking safety as it has ever been, and that the doubts raised about it are generated by self-interested parties whose revenues have been threatened by the risk revaluation that followed the 2008 financial crisis.

WhAt iS StABle vAlue?The defining feature of stable value is principal preserva-tion: in normal circumstances, participants are able to exer-cise all rights available under the plan to transfer among options to make withdrawals at values that never decrease. Like money market, stable value is able to maintain non-decreasing values because, in what is an increasingly rare exception, participant-directed defined contribution plans are able to account for “fully benefit responsive investment contracts” at contract value, which is equal to the purchase price of the investment contract plus contributions less withdrawals plus credited interest.

The accounting guidance that confers this right is FASB’s Staff Position AAG INV-1/SOP 94-4-1, which was posted on Dec. 29, 2005, and effective for accounting periods


RetuRN ANd ACCuMulAtiON COMPARiSONS

Average Returns6

5 Yr Ave % Std. Dev. 10 Yr Ave. Std. Dev. 15 Yr Ave. Std. Dev.

Stable Value

3.03 0.83 3.65 0.88 4.39 1.28

Money Market7

0.73 1.07 1.70 1.65 2.59 1.97

FDIC8 Model

1.48 1.07 2.45 1.65 3.34 1.97

Short9 Bond

3.20 2.31 2.94 2.10 4.07 2.53

Accumulations and Payouts

15 year accumulation of $1000 per year Years to Depletion at $2000 payout per year

Stable Value

$20,516.11 14

Money Market

$17,455.31 10

FDIC Model $18,590.37 11

Short Bond $19,841.87 13

CONTINUED ON PAGE 10


STABlE VAlUE … | FROM pAGE 9

late ‘90s and early 2000s, and with the complete dominance of wrap contracts which transferred the risk of participant withdrawals to other participants rather than to issuers,11 wrap issuers did begin to compete entirely on price, and major stable value managers were able to purchase wrap contracts for fees in the single digits.

Further, competition among stable value managers increased as well, and some managers began to compete on yield, rather than on the soundness of their overall stable value management philosophy. Some stable value managers kept their eye on the principal protection ball, but suffered losses in market share as a result of the focus on yield.

the eCONOMiC CRiSiS Of 2008I have discussed previously in Risks and Rewards how well stable value weathered the crisis overall.12 However, a peri-od when the market value of the underlying assets was in some cases more than 10 percent below the contract value, and in many cases 7 percent to 10 percent below, led to a re-evaluation of the stable value risk. In the case of some of the large banks that had become major writers of synthetic GICs, those contracts were written on derivatives desks that had fallen overall in disfavor. Some of those banks sought to withdraw from the wrap market, and it is certainly true that capacity for “blank check” synthetic GICs declined.

However, other forms of stable value contracts remained available. Many insurance companies of varying sizes con-tinue to offer traditional GICs. MetLife, for example, which had withdrawn from the synthetic GIC market because it judged the fees inadequate, continued to sell its separate account product, as well as traditional GICs. Several com-panies expanded their presence in the market or re-entered the market, although often with offerings limited in various ways. For example, some major insurers will only sell wrap contracts when the assets are managed by affiliated asset managers. Further, many issuers of synthetic or separate account contracts did restrict guidelines in various ways so as to reduce the volatility that led to deep declines in portfolio market values in the crisis, and to take account of

The tables demonstrate the clear superiority of stable value not only to its traditional competitor, money market funds, but also to potential new competitors. Stable value has high-er returns with less volatility than its current and potential competitors for the low risk DC option. Only the return for a short bond fund, an option longer than any unwrapped fund of which I am aware, comes close to that of stable value, with much higher volatility.

Let’s turn to the arguments that some use to attempt to undercut what the return analysis shows.

the AvAilABility Of StABle vAlue iNveStMeNt CONtRACtSA fair evaluation of the availability of stable value invest-ment contracts requires that one look back further into the history of stable value contracts than simply to the period immediately predating the financial crisis. It is worth remembering that a little more than 20 years ago the most prevalent form of stable value contract was an insurance company general account Guaranteed Interest Contract. A stable value option’s portfolio would consist of a ladder of GICs from different issuers. The insurance company offered a rate out of its black box, and the plan sponsor, or, ever increasingly, a stable value manager on behalf of the plan, took it or went elsewhere.10 There was no transparency about the charge for the wrap, for the management of assets supporting the GIC, for insurance company expenses and risk charges, or for profit.

The insolvencies of Confederated Life and Mutual Benefit Life sharply reduced the appeal of GICs, and insurance company separate account backed contracts, and contracts that provided the required AAG INV-1 guarantees disag-gregated from the underlying assets (synthetic GICs), which could then remain in the plan trust, came to dominate the stable value field.

When these contracts first emerged in the early ‘90s, wrap charges of 27 basis points and above were common. In the long period of relative economic tranquility that marked the


of the assets to that manager, the manager could collect a higher fee than would generally be available to stable value managers.

Such a manager could face a loss of revenues if the manager could not obtain stable value contracts and also retain man-agement of the underlying assets.

“hyBRid” StABle vAlue fuNdSA manager as described above, would certainly have an economic incentive to attempt to persuade a plan sponsor to move to a structure that would allow the manager to retain management of all the underlying assets. Plan sponsors would do well to look at the economic motivations of the manager should their manager be touting the advantages of a partially unwrapped fund, a so-called “hybrid.” We have set out above the return characteristics of stable value and the alternatives to it. Based on this analysis, it is difficult to see what case a fiduciary could build for choosing a hybrid fund.13 Such a fund, if meeting the criteria for an income-producing, low-risk, liquid option would likely have lower expected yield and higher volatility than stable value, since any combination of the options listed above with stable value would have that effect.

the StABle vAlue SuRPluSIt may be somewhat more complicated to assess the “stable value surplus” compared to when the safe options of all plans were stable value or money market or both. For the purpose of this discussion, I define “stable value surplus” to be the excess return of stable value over the next best stable net asset product. Using the information from the return comparisons above, that option would be some form of FDIC-insured account.

A reassessment of risk and changes in the stable value investment contract marketplace may both have reduced somewhat the overall stable value surplus and changed

the prolonged and to some extent artificial low interest rate environment.

In short, stable value investment contracts remain plentiful, but choice with respect to the manager of the underlying assets is meaningfully reduced. In order to obtain wrap cov-erage, a manager might be forced to buy an insurance com-pany GIC where the manager would choose a comparably rated bond where wrap coverage for the bond was available. A stable value manager might need to incur the additional due diligence expense of an insurer-affiliated manager, and perhaps adjust more than the stable value manager would like to that manager’s style in order to obtain wrap cover-age. A stable value manager might be forced to choose passive management when it would overall prefer active management.

StABle vAlue MANAgeMeNt fee StRuCtuReSSome stable value managers assess a fee on all the assets in the separate account or pool the manager manages. If such a manager manages some portion of the assets directly, and retains sub-advisors to manage other portions, the man-ager’s fee does not fall as a result of retaining sub-advisers, since the sub-advisers’ fees are paid from the sub-advised portfolios, which remain part of the stable value manager’s fee asset base. Such a manager actually has a cost incentive to place as high a percentage of assets with sub-advisors as possible, although, of course, that incentive could easily be outweighed by many other factors: desire to build a track record for various mandates, desire to grow assets under direct management, desire to sell stable value management based on performance managing underlying assets, etc.

Other managers might charge separate fees for their man-agement of underlying assets and their management of the stable value option as a whole. While ERISA would prohibit their use of discretion to double fee, if the plan sponsor exercised the discretion to direct a certain portion



somewhat the allocation of the surplus. What is not in doubt is that participants remain the overwhelming benefi-ciaries of the stable value surplus after the financial crisis, as before.

StABle vAlue POOled fuNdSAs far as I know, no issuers of stable value investment contracts lost money on a single contract as a result of the financial crisis of 2008. However, that is not the case for sponsors of stable value pooled funds.

Some stable value pooled funds offer plans a “put” right to investing plans. That right gives participating plans an option to exit at contract value after some stated period of time, most commonly 12 months. If a plan’s fiduciary knows that the market value of the pooled fund is less than the contract value, and is not likely to rise to contract value by the end of the put period, one could argue, assuming a reasonable subsequent placement is available, that the fidu-ciary has a duty to put the plan’s position to the pooled fund.

In the modern world where essentially all stable value investment contracts other than GICs mean that continuing participants absorb any losses on withdrawals where market value is less than contract value,14 the ability of prudent plan fiduciaries to exercise an economic put against the pooled fund could lead to a death spiral for the fund.

The prospect of such a spiral presents the pooled fund spon-sor with an array of unpalatable choices. The sponsor can do nothing, paying out exiting plans an ever greater premium over market value while the crediting rate for continuing plans falls, eventually to zero. At the point where the last plan exits, the wrap providers will be paying on the wrap contract. However, it is likely that following this course will expose the pooled fund sponsor to a claim of breach of its ERISA fiduciary duty. The plans that receive a zero rate will point out that the plan sponsor should have terminated the pooled fund when the threat began to materialize, so that all participants would have been treated equally. I judge

this a very powerful argument. In particular, if anything in the death spiral allows wrap providers to escape, the pooled fund sponsor could face very substantial financial liabilities.

Certainly if any provision of a wrap contract for the pooled fund would permit wrap coverage for one or more contracts to lapse during the death spiral, the dilemma faced by the pooled fund sponsor would intensify. However, to the extent that the sponsor of a pooled fund with a put feature used non-participating contracts, the danger of a death spi-ral would be reduced.

fixed RAte PROduCtS NON-PARtiCiPAtiNg With ReSPeCt tO WithdRAWAl exPeRieNCe: A gOOd ANSWeR tO MANy CuRReNt StABle vAlue PROBleMSThe potential problems for sponsors of pooled funds with put provisions discussed above do not exist to the extent that such funds are invested in non-participating with respect to withdrawal experience (NPWE14) contracts. For a fund invested entirely in NPWEs, a stampede out the door would have no effect at all on rates continuing participants would receive. A fund with a substantial volume of NPWEs and participating contracts that took projected cash flows into account in setting crediting rates would substantially mitigate the death spiral risk.

However, the value of NPWEs is not restricted to pooled funds with puts. The stability of the crediting rate of any stable value fund or option would be substantially enhanced when there was a substantial allocation to NPWEs. In par-ticular, plans that offer a competing money market option might be able to purchase NPWEs when traditional PWEs would not be available.

POOled fuNdS With Put feAtuReS diSAdvANtAge PARtiCiPANtSFrom an issuer perspective, the liability duration of a pooled


tection, funds without a plan put feature, other things equal, are clearly superior to those with a put feature.

CONCluSiONStable value continues to provide outstanding value to defined contribution plan participants, markedly greater than current or potential competitors for a DC plan safe option. The managers of stable value pooled funds and plan options may be forced to move outside their current com-fort zones to deliver the full potential of stable value to the participants whose money they are managing, but the need of stable value managers to adjust to new market realities should not be confused with any fundamental problems with one of the true triumphs of financial engineering, stable value.

fund with a put feature is much shorter than that of a pooled fund where the exit is at the lower of contract value or market value, one common alternative to the predominant pattern.

For that reason, an issuer of a participating product cannot prudently agree to an underlying asset duration in a product with a put feature as long as the issuer could permit it in a fund without a put provision. Given the normal yield curve, this means expected lower returns. It is difficult to see how a plan sponsor could prudently choose this option in the context of a retirement income program.

From the perspective of expected long-term returns to participants with no sacrifice of participant principal pro-

END NOTES

1 The author is a member of the Investment Section Council and works in the law department of Metlife supporting stable value and other retirement income products. He previously worked at INVESCO, a leading stable value manager, and has written extensively about stable value.

2 See Paul J. Donahue, Plan Sponsor Fiduciary Duty for the Selection of Options in Participant-Directed Defined Contribution Plans and the Choice Between Stable Value and Money Market, 39 aKRon l. ReV. 9 (2006), at 18-19, which describes the requirement for an “income-producing, low-risk, liquid fund.” My view that a short duration bond fund could meet this requirement is not universally shared, but I will illustrate returns for such a fund in my return comparisons.

a. The investment contract is effected directly between the fund and the issuer and prohibits the fund from assigning or selling the contract or its proceeds to another party without the consent of the issuer.

b. Either (1) the repayment of principal and interest credited to participants in the fund is a financial obligation of the issuer of the investment contract, or (2) prospective interest crediting rate adjustments are provided to participants in the fund on a designated pool of investments held by the fund or the contract issuer whereby a financially responsible third party, through a contract generally referred to as a wrapper, must provide assurance that the adjustments to the interest crediting rate will not result in a future interest crediting rate that is less than zero. If an event has occurred such that realization of full contract value for a particular investment contract is no longer probable (for example, a significant decline in creditworthiness of the contract issuer or wrapper provider), the investment contract shall no longer be considered fully benefit-responsive.3

c. The terms of the investment contract require all permitted participant-initiated transactions with the fund to occur at contract value with no conditions, limits, or restrictions. permitted participant-initiated transactions are those transactions allowed by the underlying defined-contribution plan, such as withdrawals for benefits, loans, or transfers to other funds within the plan.4

d. An event that limits the ability of the fund to transact at contract value with the issuer (for example, premature termination of the contracts by the fund, plant closings, layoffs, plan termination, bankruptcy, mergers, and early retirement incentives) and that also limits the ability of the fund to transact at contract value with the participants in the fund must be probable of not occurring.

3 The term probable is used in this FSp consistent with its use in FASB Statement No. 5, Accounting for Contingencies.




Paul J. Donahue, FSA, MAAA, is senior counsel for MetLife. He can be contacted at [email protected].

4 An investment company registered under the Investment Company Act of 1940 (the Act) would not meet this requirement because Rule 22c-1 under the Act requires transactions between the investment company and its shareholders to be exe-cuted at current net asset value. Under Rule 2a-4 of the Act, current net asset value is computed using the fair value of the investment company’s portfolio securities.

e. The fund itself must allow participants reasonable access to their funds.5

5 paragraph 11 of SOp 94-4 provides guidance for determining whether certain restrictions violate the provision that partici-pants in the investment company have reasonable access to their funds. Restrictions that do not violate this provision shall also not be considered to violate the provisions in paragraph 7(c)

4 This paragraph summarizes my treatment of the same topic in my article Stable Value Re-examined, 54 Risks and RewaRds 26 (Investment Section of the Society of Actuaries, August, 2009), pp. 26-27.

5 I will refer to these contracts in what follows as “stable value investment contracts.”6 Data through June, 2012. I am grateful to Besim Demiri of Metlife’s Corporate Benefit Funding Division, for his assistance

with the numerical analysis that underlies the tables below. 7 I have used three-month Treasury bill yields to approximate money market returns. These returns are generally slightly higher,

with slightly lower standard deviations, than the corresponding IBC taxable money fund statistics, but I chose to use them, assuming for the sake of conservatism in the comparison to stable value that plan money funds returns would be somewhat better than the taxable average. Other choices might have shown slightly higher results for money market funds, but not sufficient to affect materially the analysis and the conclusions.

8 I have chosen a simple approximation to an FDIC product based on the expected return described for one such product of money market plus 75 bps.

9 I have used the Barclay’s U.S. Government 1-3 Index returns less 20 bps to approximate the return of such a fund. It is worth noting that some ERISA counsel have suggested that a return as volatile as that of this return would arguably not qualify for the income producing, low risk, liquid option. I have nowhere seen any suggestion that any longer fund could possibly qualify.

10 I describe the origins of stable value in greater detail in my article “What AICpA SOp 94-4 Hath Wrought: The Demand Characteristics, Accounting Foundation and Management of Stable Value Funds,” 16:1 benefits QuaRteRly 44 (First quarter, 2000), pp. 55 ff.

11 See my article, “The Stable Value Wrap: Insurance Contract or Derivative? Experience Rated or Not?” 37 Risks and RewaRds 18 (Investment Section of the Society of Actuaries, July, 2001).

12 See footnote 4 above.13 Indeed, I generalize from the position I took in Plan Sponsor Fiduciary Duty, see above footnote 2, to state that it is difficult

to see how a plan sponsor can choose any option other than stable value for the income-producing, low-risk, liquid option and discharge the sponsor’s fiduciary duty.

14 I am going to refer to stable value contracts where participant withdrawal activity affects the contract’s crediting rate as participating with respect to Withdrawal Experience or pWE. Contracts where the crediting rate does not affect the contract’s crediting rate I will refer to as NpWE contracts or simply NpWEs.



TAkING STOCk: REVISITING THE lOSER’S GAME

By Nino Boezio

achieved, they revert to a Loser’s Game strategy of merely surviving each round and hoping to win out through better endurance.

An extension of the above analysis is that one should avoid making mistakes when the competition is fierce and of equal ability, for it is also a Loser’s Game. Being able to win the Loser’s Game requires a substantial edge, which most people will not be able to accomplish or demonstrate under such a strongly competitive environment.

Mr. Ellis’ focus in the article was ultimately on the invest-ment business. He cites how the investment industry has changed in its character as it evolved over the decades from the 1920s to the 1970s. When the market environment was conservative (as it was in the 1930s and 1940s), members of the investment industry focused on such themes as preser-vation of capital and safety (which we can view as a Loser’s Game mindset of not taking chances and making mistakes), and this set the stage for the Winner’s Game and the bull market of the 1950s. The new possibility of making “big money” as highlighted in the 1950s bull market, attracted some of the best and brightest people (the winners) into the investment business of the 1960s. However, the environ-ment eventually self-destructed as many investment funds were established and even more talented people entered the investment industry, resulting in diminishing returns and the set-up of the Loser’s Game of the 1970s (i.e., these winners were eliminating many of the market inefficien-cies and any mispricing, resulting in fewer opportunities to benefit from the errors of others). One could be perceived as competing against amateurs (the losers) in the 1930s to 1940s creating a Winner’s Game environment, but in the 1960s and 1970s (when the article was written) one was competing against the professionals (the winners) setting up a Loser’s Game. To sum up Mr. Ellis’ analysis of the investment business as he saw it evolve, in a Winner’s Game, a professional can make great investment returns if the competition consists mostly of amateurs or less-skilled professionals. In a Loser’s Game however, where one is

S ome of you may have read the article “The Loser’s Game” written in the 1970s by Charles Ellis,1 which has occasionally been cited in various financial

media. Mr. Ellis brought together a number of important findings that helped us understand general strategies for performing well against our peers, which were dependent upon our skill set and the nature of the competition. His findings are still very relevant for us today.

One of Mr. Ellis’ examples included a study performed by Dr. Simon Ramo regarding the game of tennis. Professional players would win the game by scoring more points against their opponents, and this was termed a Winner’s Game. Amateur players, on the other hand, would not beat their opponents by scoring points, but would actually beat themselves by conceding points, and this scenario was referred to as a Loser’s Game. In other words, profession-als would win against other professional opponents by superior skill, while the amateurs would lose against their amateur opponents by making more mistakes. Moreover, amateurs would take more chances against other amateurs in an effort to win, which actually caused them to make even more errors (this was therefore a much less effec-tive strategy than a more conservative game plan). The main message was that approaches to the game are very different dependent upon the ability of the players—vic-tory in one circumstance is determined by the skill of the professional (a winner), while victory in the other is determined by the mistakes of the amateur (the loser).

Many other games and competitions also involve numerous variables and provide opportunities for potential mishaps, such that it is easy to hurt performance if one is not very adept or expert at it. Mr. Ellis extends his discussion to areas such as warfare, politics, card games, other sports (such as football and golf), and even to the investment busi-ness. Interestingly, the Winner’s and Loser’s Strategy can sometimes even change during the same competition. Mr. Ellis cites prize fighting as one example, where fighters often try for a knockout early in the fight (this employ-ing the Winner’s Game mentality) but if this goal is not


Game environment, we would primarily only need to focus on (b) to win. But due to the evolution of our various indus-tries to one of intense competition and involving many sophisticated players, (a) to (d) now have to be considered. A simplified view of some recent developments could include the following:

The Financial Crisis of 2007-2009—The drive to be a win-ner can be one of the reasons the financial crisis developed. The desire to achieve investment and financial performance that was better than the competition was a motivating fac-tor to apply new approaches. Those who introduced these ideas, strategies or products early in the business or product cycle benefitted greatly. But the assessment of whether one truly had a skill in that particular investment or product area was often not properly done. Risk management, compli-ance, product due diligence and other proper analysis and safeguards were not often in place, violating (a), (b) and (c) above. The ultimate winners in the financial crisis were those who more strongly focused on (b), but the tempta-tion was too strong to do what everybody else was doing as mentioned under (d), so many organizations and people suffered.

Hedge Funds—The initial successful performers in the hedge fund arena tended to be those who best understood the principles of (a) and (b) above. In a fund-of-hedge funds approach, the overlay hedge fund manager was also looking for those who were taking full advantage of their abilities to perform in (a) and (b). Unfortunately, the major mistakes occurred in the areas of (c). It was also becoming apparent as time went on, that many hedge funds were in the (d) cat-egory of not being truly able to succeed against other play-ers, but refused to admit it. Some may have then undertook more risk and leverage in order to keep the extra edge and to portray greater skill, but eventually it led to their demise. Career Progression—Going back 30 years or more, one could obtain a good paying job simply by having a univer-sity degree or a set of credentials. A resume only needed

competing not against amateurs, but against many other professionals (winners) of similar ability (this time not only amateurs of similar ability), the opportunity to make great investment returns through superior skill is limited. In a Loser’s Game, one may actually want to be defensive (and thus make less mistakes) in order to survive, since a slip-up can be very costly as other skilled professionals are there to take advantage of it.

Mr. Ellis did not conclude that in an investment industry dominated by very talented investment professionals we should therefore consider only passive strategies—rather the task of identifying whether an investment professional or manager had the necessary skill to beat the market was becoming much more difficult, and that investment man-agement firms should acknowledge this reality. And if such a skilled investment manager cannot be identified, then a passive strategy could be a consideration.

Mr. Ellis’ concluding comments on how to win the Loser’s Game in investment management were also very useful and insightful. His remarks were as follows:

(a) Play your own game and let the others make the mis-takes;

(b) Know what you are good at and keep it simple;(c) Concentrate on your defenses; and (d) Do not take it personally (i.e., it is just becoming harder

to succeed and it is not your fault).

Interestingly the themes cited in (a) to (d) still resonate today and help to explain why we have some of the current global financial and economic problems.

hOW the WiNNeR’S ANd lOSeR’S gAMe APPlieS iN OtheR AReASMr. Ellis’ concluding remarks do shed important light on where we are currently in the investment and financial industry, and how we arrived at some of our current global problems and emerging trends. If we were in a Winner’s


TAkING STOCk | FROM pAGE 17


the principles identified in (a) to (d). The corporate leader-ship may feel embarrassed to admit that the company can-not do everything well, especially if it has a lot of resources and staff. But outsourcing certain tasks can result in cost savings and better quality. It can also result in improved corporate performance.

the WiNNeR’S ANd lOSeR’S gAMe tOdAy iN iNveStMeNt MANAgeMeNtThere has been a regular debate between active and passive investing for several decades now. Some are adamantly opposed to active management, while others attack pas-sive management. We have had a proliferation of exchange traded funds (ETFs) which accommodate those who do not want to make asset manager or security selection decisions. On the other hand, it is important to realize that we can never expect investment performance to be above aver-age if we just stay passive. For certain sectors and themes, there are investment managers who do appear to have skill to outperform the market. Sometimes advantages or disad-vantages can be attributed to geography, motivations of the investment managers, their technology and skill sets, invest-ment research capabilities and techniques, the newness of a strategy, and even the size of the organization. The choice between active and passive strategies can lead to a discus-sion about the perceived investment performance and cost. This is where consultants and investment advisors can bring additional value to an investment relationship.

CONCludiNg ReMARKSMr. Ellis’ article is still of relevance since it cites vari-ous themes and observations which have not changed. Interestingly, his points also have major implications for the competitive climate we have in many industries today. Companies are pushed to achieve better results and they are not always able to deliver them. They feel a pressure to do something differently while not always being capable to deliver added performance, and they may not fully real-

to list the ability to perform basic day-to-day duties in order for a candidate to be seen as a good employment prospect by an employer. Today, with the intense competi-tion for positions and the greater proliferation of education and credentials among job candidates, job seekers often get coached about the need for differentiation, branding, performing a self-assessment of skills, building interview-ing skills (including not saying the wrong things), citing personal success stories in a resume, and looking for ways to stand out from the crowd. Interestingly these areas do follow (a) to (d) above. These attributes are also becoming important for those wanting to keep a job.

Business Diversification—We have seen companies which have done very well in their core businesses. But they then would want to expand into other business lines, only to find later that this was a bad idea and then would exit at a finan-cial loss. These companies were doing the opposite of that mentioned in (a) and (b). The survivors learned from their mistakes and moved back to a basic strategy.

Technology—We have witnessed great change in the area of technology the last several decades. The fast pace of development, the proliferation of new products, the short time in which a company can stay on top, and the rapid speed at which a competitor can come up with a similar product (and better), can make one feel rather dizzy. The application of (a) and (b) are rather interest-ing, because what a company was good at yesterday may not be true today, and the environment can change dramatically in a matter of months. Playing defense as mentioned in (c) also becomes important, because the longer it takes for the competition to match with a similar product, the more successful the leading company will be (and these days that still usually spells significant profits). Outsourcing—Some companies unfortunately never do a proper internal analysis or never want to fully incorporate


ize their limitations. This generates a danger, in that risk becomes introduced because the persons and companies involved had not truly addressed their strengths and weak-nesses and had not established processes to deal with them; in other words they failed to adequately consider the points outlined in (a) to (d).

Similarly, at the individual level, persons may have not truly understood how to adapt to an employment marketplace that has been more competitive. They may adopt tactics that worked years ago but which are no longer effective today. As a result, their career positions in various organizations are in jeopardy, and they do not realize how they need to adapt in their chosen field and redefine their image, to find or retain positions in a new industry environment.

Winning in a Winner’s Game or Loser’s Game does involve a proper assessment of the competitive environment, a thor-ough and accurate self-assessment, and playing from your strengths while defending against your weaknesses. It is a very interesting way to view the world, but it is not truly complicated if one wants to maintain and advance in the various environments that exist in the global marketplace today, but rather it just involves more work.

END NOTES 1 Ellis, Charles D. “The loser’s Game”, Classics: An

Investor’s Anthology, Ed. Charles D. Ellis with James Vertin, Homewood: Business One Irwin, (1989) 524-535. Reprinted from The Financial Analysts Journal, Vol. 31, No. 4, July/August 1975, 19-26. New York: Financial Analysts Federation

Nino Boezio, FSA, FCIA, CFA, is with Segal Rogerscasey. He can be contacted at nboezio@ segalrc.com.


WHY U.S. INSURERS FARED BETTER THAN BANkS: DID kEY DIFFERENCES GIVE INSURERS AN EDGE DURING THE FINANCIAl CRISIS?By Max J. Rudolph and Rick Beard

many policyholders while keeping most assets in short- and intermediate-term (i.e., liquid) investments so claims can be paid quickly. Operating earnings provided regular cash flow even during the crisis. If incoming and outgoing cash flows are considered separately, premiums can be thought of as an asset that improves liquidity. Many products provide a savings element and cash values. Incentives encourage policy persistency, allowing insurers to invest in longer-term assets. The insurance industry did not experience a run-on-the-bank scenario during the crisis. iNSuReR RegulAtORy fRONtIn the United States, insurers are regulated by state govern-ments. Any state in which a company does business can provide oversight, but the primary regulator is the state of domicile or home state. A company’s regulatory capital requirement is reduced if its asset and liability cash flows are well matched, which generally means bonds domi-nate asset allocations. Capital requirements discourage, or minimize, volatile asset classes, such as equities and alternative investments. This makes insurance companies less susceptible to the ups and downs of the financial market. Reporting inconsistencies in many states (mainly minor) increase costs to the financial reporting process and frustrate managers, but the possibility of multiple states providing oversight in slightly different ways has advan-tages as well. Concentration risk comes in many forms.

Current international proposals seem intent on consistent standards. Regulations always deal better with past issues than future ones, and multiple sets of eyes looking at a company in slightly different ways are more likely to catch an emerging issue than a single regulator blinded by bureau-cratic consistency. Aig ANd RegulAtORy ARBitRAgeWhen an insurer is set up as a holding company (as AIG is), the states regulate its insurance subsidiaries but the

This article first appeared in CFA Magazine, May/June 2012, pp. 13 - 14. Reprinted with permission.

B anks created headlines. Insurers muddled through. Concerns about systemic risk focused on banks during the 2008 financial crisis, but the insur-

ance industry was relatively more stable. Some out-liers generated sensational coverage (primarily AIG through its financial products division). Other insur-ers used the federal government Troubled Asset Relief Program (TARP), and publicly held insurers writing variable annuities saw their market value erode. In gen-eral, however, mass insolvencies among life, health, and property/casualty insurers were never a major concern. Surprise, surprise—could proactive and conservative regu-latory and investment practices be good business practices?

To answer this question, the Society of Actuaries sponsored research intended to shed light on and learn from insurer practices. (The entire report can be found online at soa.org/research/research-projects/finance-investment/research-us-insurance.aspx) iNSuReR BuSiNeSS MOdelInsurers hold a majority of their assets in what are called general accounts. Separate accounts support liabilities such as defined-benefit plans or variable annuities, whereas the general account backs traditional insurance products, such as homeowner’s insurance and whole life insurance. This article will focus on general-account investing practices.

Insurance covers a wide range of ongoing customer rela-tionships, everything from a single payment to cover a spe-cific loss to recurring premiums for the rest of an insured’s life. Many of these payments are contractually required to continue the protection provided by the policy. Health and many property/casualty products operate as a revolving door driven by the law of large numbers, spreading risk over


domestic insurance industry. Other avenues provide easier access to funds for aggressive investors. leSSONS leARNedSo what lessons can be learned from this research to help insurers prepare for the next crisis? Some insurers struggled through the financial crisis, but those focused on gen-eral account products were in a better position to succeed. Through the survey and discussions with industry partici-pants, we reached a number of conclusions:

• Liquidity can go away very quickly, especially when everyone is counting on the same tools for risk mitiga-tion. This kind of systemic concentration risk is ongoing. Investors who proactively develop multiple sources of liquidity will be rewarded during a downturn.

• Insurers should actively manage liquidity, credit, and interest rate risks using specific stress scenarios and have the results reviewed with independent oversight.

• State guaranty funds should assess risk charges that are based on risk exposures. This practice aligns incentives and reduces moral hazard.

• Insurers have advantages related to cash flows during a crisis relative to other financial services firms—that is, they often have long-term contractual relationships with customers.

• Regulatory investment constraints are conservative rela-tive to other financial institutions, which tends to drive the most entrepreneurial investors elsewhere. This pro-vides a safety net that makes it harder for insurance company investment professionals to threaten company solvency through their investments.

• Insurer filings require transparent reporting of all securi-ties held. This requirement is more stringent than the disclosure demanded for other types of financial institu-tions and encourages insurers to stay with standard asset classes. It also seems to drive aggressive entrepreneurial personalities away from the industry.

company can select its overall regulator. As the Financial Crisis Inquiry Commission has explained, AIG chose a federal regulator (the Office of Thrift Supervision, or OTS) that was incapable of handling the complexity of the credit default swap products that AIG’s financial products division sold. In a clear case of models trumping common sense, gross exposures were ignored because default prob-abilities were assumed to be miniscule. Outside input, espe-cially when skeptical, was not welcomed. iNveStMeNt PRACtiCeSThe Society of Actuaries’ survey found that adherence to conservative investment policy statements (IPSs) was a principal contributor to the insurance industry’s portfolios surviving the downturn. Almost all had a formal, board approved IPS that they consulted and followed during the crisis. Implementing a proactive, living document enabled many insurers to hit the ground running when looking for bargains during the 2008–09 period. The IPS provided stability and much-needed guidance when working with board members who are not investment experts.

Internal (or outsourced) credit risk expertise helped mini-mize the insurance industry’s exposure to the worst effects of the housing bubble. Very few insurers had mate-rial subprime mortgage exposure by 2008, and many had sold the asset class completely before the crisis.

Insurance industry regulation is built around solvency protec-tion for policyholders. Transparency and conservative invest-ment policies are key components. Regulatory requirements force insurers to report each asset held at the end of a calendar year as well as purchases and sales. These reports are publicly available. Both capital requirements and regulatory concen-tration limits encourage conservative investment practices. This combination discourages the high flyers (those seeking to leverage capital and concentrate assets) from entering the


WHY U.S. INSURERS FARED BETTER THAN BANkS … | FROM pAGE 21


incorporates recurring premiums (along with regulatory conservatism and internal credit analysis) led to these results. Insurers are not known for their quick reactions to market changes, but the investment process they had in place provided conservative consistency. The IPS was the key to this success for insurers of all sizes and types. It provides a consistent process and plan that an invest-ment team can use to stay within conservative bounds in the event of future bubbles or during an actual crisis—because such possibilities have been considered proactively and contingency plans have been prepared in advance.

• Financial leverage (borrowing) limits flexibility during a crisis. The market can stay irrational longer than a com-pany relying on leverage can stay solvent. Insurers use low amounts of true borrowing, although their basic busi-ness model uses float (i.e., cash is collected today with promises to pay it back to policyholders at a later time).

• An IPS should evolve over time to reflect asset classes and liquidity tools available for use during both normal and crisis scenarios.

Overall, insurers did seem to perform better than banks during the recent crisis. A general business model that

“ “.… INSURERS ARE NOT kNOWN FOR THEIR qUICk REACTIONS TO MARkET

CHANGES, BUT THE INVESTMENT pROCESS THEY HAD IN plACE pROVIDED CONSERVATIVE CONSISTENCY.

Max Rudolph, FSA, CERA, CFA, MAAA, is founder of Rudolph Financial Consulting, LLC, in Omaha, Nebraska, and a member of CFA Nebraska. He can be contacted at max.rudolph@ rudolph-financial .com.

Rick Beard, CFA, CIPM, is managing director of Cardinal Investment Advisors and a member of the CFA Society of St. Louis. He can be contacted at [email protected].

SOA Investment Symposium

The Investment Section will host its premier conference, the Investment Symposium, March 14 and 15, 2013 in New York at the Marriott Marquis. The meeting is co-sponsored with the Professional Risk Manager’s International Association (PRMIA).

The 2013 themes will be the same as last year’s well-regarded conference. There will be four concurrent session tracks, focusing on Retirement, Portfolio Management, Quantitative Risk and ALM, and Economic/Accounting/Regulatory matters.

The Retirement track was new last year after having been dormant for a number of years. With the challenges facing our pension and individual retirement systems, it was time to bring this important topic back to the meeting. We are pleased the track was a success and that it can be brought back this year.

The general sessions are always a highlight of the meeting for the timeliness and high-caliber speakers. Last year’s general session topics were:

• A Retirement Debate, featuring Zvi Bodie of Boston University; Henry T.C. Hu of the University of Texas Law School; Ron Ryan of Ryan ALM; Michael Peskin of Hudson Pilot LLC; and Bud Haslett of the CFA institute. The panelists discussed their views on the retirement system’s challenges and opportunities.

• Europe: Hazard or Opportunity? Economists Paul Skinner of Wellington Management and Torsten Slok of Deutsche bank discussed the European sovereign debt crisis.

• Making Friends with Risk. Aaron Brown, noted author and risk manager at AQR Capital Management discussed how we can use risk management to improve decision making.

• A CIO roundtable, with senior investment managers Jay Vivian of IBM; Scott Sleyster of Prudential; Tiani Osborne of NativeOne Institutional Trading; and Laurence Siegel of the CFA Institute Research Foundation.

The Investment Symposium is a good opportunity to network with peers who work in investments while meeting the complex needs of insurance companies and retirement plans. We are looking forward to another great meeting in 2013.

For additional information including registration information and this year’s agenda, watch your email inbox and visit the Investment Symposium website, investmentsymposium.org.

SAVE THE DATE -



ANNOUNCING THE SOA INVESTMENT SECTION’S 2013 INVESTMENT CONTESTBy Thomas Anichini & Frank Grossman

entry. The message will include information about the list of eligible assets, portfolio constraints, the time period over which returns will be measured, and the submission dead-line too. If your SOA Directory email address is not current, now is a good time to update it.

Incidentally, the prize for attaining the top ranking in each category will be an iPad mini. We will announce the 2013 Investment Contest winners at the Investment Section Hot Breakfast at the 2013 SOA Annual Meeting to be held in San Diego in October—and very much look forward to seeing you there!

The fine print: the 2013 Investment Contest is open to SOA Investment Section members only (if you are not currently a member, please consider joining us); one submission per entrant; and only one prize per entrant; and Section Council members may participate in the contest but are not eligible to win a prize. See the forthcoming email message for addi-tional details regarding other contingencies.

“Once more unto the breach, dear friends, once more” – Henry V, III.i.1

T hankfully, the market turbulence that accompanied the 2008 Financial Crisis has subsided just a little. However, current conditions are such that one

might not wish to “cancel yellow alert” quite yet. The Federal Reserve’s various quantitative easing programs have set the price of short-term money to zero, effectively skewing the trade-off between risks and returns for many investors. Even though there are signs of recovery in some developing nations, the dismal prospect of continued low economic growth and stubborn unemployment closer to home continues to cloud the horizon. And best not to entirely discount the persistent threat of any unknown unknowns that may be lurking about.

Yet, given the steadfast and resolute nature of most invest-ment actuaries, undeterred by the present economic climate, what better time to dust-off an old idea with a new twist—an investment contest!

Section members are once again invited to submit their contest picks in the spirit of friendly competition. What’s new this time is the 2013 Investment Contest’s emphasis on taking market volatility into account when making asset allocation decisions. Hence, the challenge posed by the 2013 Investment Contest will be for members to assemble an asset portfolio which will prevail in one of the following three metrics:

• Highest cumulative total return;• Lowest weekly volatility (measured as standard devia-

tion of weekly total returns); or• Highest Sharpe Ratio, measured using the arithmetic

average of weekly total returns, and the standard devia-tion of weekly total returns.

So, prepare to gaze deeply (not too deeply!) into your crystal ball, and remain alert for the email message we will send to all section members in early March soliciting your

Thomas Anichini, ASA, is senior investment strategist for GuidedChoice. He can be contacted at [email protected].

Frank Grossman, FSA, FCIA, MAAA, is a senior actuary at Transamerica Life Insurance Company. He can be reached at frank.grossman@ transamerica.com.


WHY ARE CORpORATE pENSION plANS REDUCING RISk NOW?

By Evan Inglis

• Uncertain pension information results in a higher required return for a corporation’s equity. Because future earnings become less predictable, a higher return is demanded on equity investment. Equity investment in a pension plan adds no value for a corporation.

• Financial stakeholders in a corporation have access to all the equity exposure they want. Their individual efficient frontiers (presumably) guide their investment decisions and additional equity exposure through corporate pen-sion plans is less efficient and effective than an investor simply allocating more assets to equity directly in his/her portfolio.

• Because bonds are taxed at a higher rate than equities, equities provide less compensation for the risk taken when they are held in a non-taxable pension trust.

• When financial analysts look at a pension plan spon-sor’s financial information, they typically reverse out the smoothing in pension expense information. They may also expand the balance sheet by consolidating the pen-sion assets and liabilities similar to the way a subsidiary would be treated. With this view, key financial metrics such as the debt to equity ratio look very different and the risk posed by the pension assets and liability is apparent.

Even from an investment perspective—looking at the pen-sion plan on its own without the context of the sponsor’s business—the wisdom of making large equity investment in corporate pension plans is questionable:

• The equity risk premium is smaller, given that the lowest risk investment is long duration bonds, so the compen-sation for taking on equity risk is smaller than for other investors.

• Many pension plans have short time frames for equity risk to pay off. Frozen plans will be forced to be fully funded within seven years by PPA rules.

W hy are corporate pension plans reducing risk now, when conditions for de-risking seem so poor—interest rates are lower than low, and

equities seem to offer reasonable if not favorable opportu-nity? In a nutshell, the question of how to invest pension assets is becoming a corporate finance issue rather than an investment issue. The corporate finance view looks at the pension plan from the perspective of a shareholder in the plan sponsor’s business. Plans are bigger relative to the size of their plan sponsors than they used to be, and they cannot be ignored in thinking about the financial prospects of the plan sponsor’s business.

While pension accounting and funding rules still incorporate a lot of smoothing and averaging, they have moved close enough to pure market measurements that short-term vola-tility in the funded status is an issue. Despite the conven-tional wisdom that pension plans are long-term investors, most corporate pension plans can no longer take this view. Although the transition is slow for many, corporate pension assets are being allocated with a shorter term view in mind.

There are a number of reasons why the corporate finance view of pension investing leads to very different approaches than have been used in the past. These include:

• Business results are cyclical and equity investment makes pension costs cyclical as well. Another way to say this is corporations double up on beta (their own corporate beta, plus the beta in their pension investments) to the extent that they invest pension assets in equities.

• Unpredictable pension results causes lots of problems for a corporate plan sponsor. Some of the problems relate to the plan itself (such as additional notices and benefit restrictions). Other problems include difficulty in plan-ning capital expenditures, hits to balance sheet equity and investor concerns about uncertainty in earnings and cash flow.


actuaries and investment professionals, did not need to learn good risk management. However, as we move through time and enter the 2000s when equity markets took a turn for the worse, we also find rules that changed to recognize the financial situation of pension plans more immediately and directly. Plan liabilities had grown large as populations aged and interest rates dropped, so the pension plan had a bigger impact on the corporation.

In 2012, tough lessons have been learned and plan spon-sors are changing their approach, some slowly, some dra-matically. Not all of them are conscious of the shift from an investment perspective to a corporate finance perspective, but the actions (closing, freezing, lump sum settlements, group annuity purchases) tell the story. It may be useful to describe explicitly the corporate finance considerations—looking at the pension plan with a shareholder’s eyes—for DB plan sponsors who are struggling to deal with pension risk.

• Most corporate pension plans intend to reduce their equity exposure over the next several years, which may put downward pressure on equity prices and upward pressure on long bond prices. First movers may have an advantage.

It’s hard to get excited about investing in bonds with yields as low as they are in the middle of 2012, but for corporate pension plans, the problems with mismatching assets and liabilities have become all too apparent during the 2000s. It’s ironic that the de-risking of pension plans has acceler-ated as interest rates have dropped.

Why has it taken so long for these compelling consider-ations to become drivers of pension plan investment strate-gies (indeed, even today many plans have still not made this adjustment)?

If we wound the clock back 30 years, and looked at pension plans of the time, we would find much smaller, younger plans. Smaller plans did not have the same impact on the corporate financial situation and the corporate finance perspective could be ignored to a large extent. Plans grew dramatically during the 1980s and 1990s, but during that time, consistently high equity returns masked the potential financial problems that plans might pose and plan sponsors,

END NOTES 1 MAp-21 legislation may effectively extend this period

when the lower bound of the interest rate corridor applies

Evan Inglis, FSA, CFA, is principal and chief actuary at Vanguard, Investment Strategy Group. He can be contacted at [email protected].

WHY ARE CORpORATE pENSION plANS … | FROM pAGE 25


“IT’S IRONIC THAT THE DE-RISkING OF pENSION plANS HAS ACCElERATED

AS INTEREST RATES HAVE DROppED.


pRICING AND HEDGING FINANCIAl AND INSURANCE pRODUCTS pART 2: BlACk-SCHOlES’ MODEl AND BEYOND

By Mathieu Boudreault

have assumed that the stock could only take two possible values at the end of the period. The only risk in this market is related to the uncertainty regarding whether or not the stock will increase at the end of the period.

Of course, having only two possible values at the end of a period is unrealistic. Instead, the time horizon is split up into smaller time steps. To do so, we assume that at the end of each period, the stock can increase by a factor of u or decrease by a factor of d. A cell in the binomial tree is known as a node. For a given time period, the stock price at each node corresponds to all its possible realizations at that time. Figure 1 shows the possible outcomes of the price of the stock at each time period after three periods.

At time three, there are four nodes and hence four pos-sible stock prices. The price at the uppermost (lowermost) node corresponds to the case where the stock has increased (decreased) on three occasions out of three periods (trials). If a stock price increases (decreases) it is equivalent to a

T his paper is the second excerpt of the article, “Pricing and Hedging Financial and Insurance Products,” which will be available from the Society

of Actuaries’ website upon completion. Comments are welcome.

In 1973-1974, Fischer Black, Myron Scholes and Robert Merton provided the first tools to rationally value a finan-cial derivative.1 Those scientific contributions also helped launch the first U.S. options exchange in Chicago in 1973, known as the Chicago Board Options Exchange (CBOE). Since then, the market for derivatives has exploded to astronomic proportions. In 2008, 1.2 billion contracts were traded on the CBOE, and nearly $200 trillion of derivatives were traded just in the United States alone.

Over the years that followed their publication, the Black-Scholes’ model has quickly become the industry and aca-demic standard to price and hedge financial derivatives. Even though many academics and professionals (and Fischer Black himself!) acknowledged numerous holes in the approach and provided solutions to these, the Black-Scholes’ model still was widely used in 2012. It is an extremely useful and simple model that often acts as a start-ing point to understand the dynamics of simple and complex derivatives. Built upon the first excerpt, this paper discusses in length the Black-Scholes’ model, its weaknesses and its alternatives (such as the Heston model (see Boudreault 2012)) using concepts introduced in the first paper.

fROM the SiNgle-SteP BiNOMiAl tRee tO BlACK-SChOleS

Construction of Black-Scholes’ ModelLet us recall the single-step binomial tree presented in the first excerpt. The main purpose of the single-step binomial tree was to represent the outcomes of a very simple market in order to replicate the cash flows of a derivative. In this frictionless2

market where a stock and a Treasury bond are traded, we

Figure 1: Evolution of the stock price in a 3-step binomial tree



process known as geometric Brownian motion (GBM). The purpose of Black-Scholes’ model is to find the no-arbitrage price of derivatives under the assumption that the stock is traded at every instant. As in the single-step binomi-al tree model, the market is assumed to be frictionless where only a Treasury bond and a stock are traded. Unfortunately, the fact that the time step is infinitely small (or that the stock is continuously traded) complicates the mathematics and hides the intuition behind the most important results.

Replicating (Hedge) Portfolio The replicating (hedging) procedure in a general binomial tree works very similarly as in a single-step binomial tree, with the important exception that the replicating portfolio needs to be dynamically updated every time the stock price changes. It all boils down to solving a set of two equations with two unknowns at each node and each time period, valuing the portfolio from the maturity of the derivative to its inception. The next example and Figure 2 illustrate how this works in a two-step binomial tree.

“success” (“failure”) in the probability sense, and the price at this node corresponds to three successes (failures) out of three trials. To obtain the given price at node 1 (S0u

1d2), the stock price has increased only once in three periods, whereas there were two decreases. Hence, there was one success out of three trials. Consequently, the probabilities attributed to stock prices at a given time period are linked to a binomial distribution, which explains the name of the model.

Up to now, we have not attributed any unit of time to a peri-od. Hence, this tree could represent the evolution of the stock over three months, for example. One could also assume that a time period can be a week, a day, an hour, a second, etc. When the time period is infinitely small, the values of u and d are appropriate (a Cox-Ross-Rubinstein tree for example) and if the tree is valid over a finite time horizon, then the distribution of the stock price is lognormally distributed. In other words, the continuously compounded asset return is normally distributed. The set of all possible stock prices on any continuous time horizon is represented by a stochastic

Figure 2: Evolution of the stock price, Treasury bond and a derivative in a two-step binomial tree.

pRICING AND HEDGING FINANCIAl … | FROM pAGE 27


Example: Suppose that the evolution of the price of the stock is given by the two-step binomial tree of Figure 2. Assume as well that interest rates are flat at 2 percent and that the derivative pays off an amount given in the rightmost tree. Using replicating portfolios, what is the no-arbitrage price of this derivative, along with the strategies that should be followed at each time step and node?

Solution: In order to find the no-arbitrage price of this option, we have to find the replicating strategy at each time step and node. It is important to note that in a two-step bino-mial tree there are three one-step binomial trees to consider.

• When (or given that) the stock price is $120 after one year, there are two possible values at the end of the second year, that is, $125 or $99. In that particular tree, we want to replicate payoffs of $10 and $3 respectively in the upper and lower node. Since the Treasury bond is worth 1.0404 after two years, and solving for two equations and two unknowns, we find that we need 0.2692 units of stock and a loan of 22.74 units of the Treasury bond. At time 1, the option value is the cost of buying the latter portfolio, i.e., 0.2692 units of a stock worth $120 and a loan of 22.74 units times 1.02. Hence, the option is worth $9.12 when the stock is $120 at time 1.

• When (or given that) the stock price is $95 after one year, there are two possible values at the end of the second year, that is, $99 or $90. In that particular tree, we want to replicate payoffs of $3 and $1 respectively in the upper and lower node. Using a similar reasoning, we find that we need 0.2222 units of a stock and a loan of 18.26 units of a Treasury bond. The option is worth $2.48 at time 1 when the stock is $95.

• Finally, at time 0, we want to replicate an option that is worth $9.12 ($2.48) when the stock is worth $120 ($95) at time 1. Solving for the two equations and two unknowns, we find that 0.2654 units of a stock and a loan of $22.28 are necessary at time 0 to replicate the payoffs of the option at time 1. The cost of that

portfolio, i.e., the initial price of this option, is $4.26.

We see that the replicating strategy is dynamic: at time 0 we start by buying 0.2654 units of a stock. At time 1, depend-ing on the value of the stock, we either buy additional stock (from 0.2654 to 0.2692) when the stock goes up to $125, or sell some units of the stock (from 0.2654 to 0.2222) when the stock goes down to $95. Thus, applying the appropriate strategy in this context will ensure (within the scope of the example) that we can replicate the payoffs of the derivative, no matter what is ultimately observed at the end.

Applying the same logic of the previous example when the stock is traded continuously means that the risk manager has to continuously trade in the stock and the bond to make sure the replicating portfolio has the same value as the option. Once again, under no-arbitrage arguments, the initial cost of that replicating strategy will correspond to the price of the option. This price is given by the well-known Black-

Figure 3: Black-Scholes’ formula


IN ORDER TO FIND THE NO-ARBITRAGE pRICE OF THIS OpTION, WE HAVE TO FIND THE REplICATING STRATEGY AT EACH

TIME STEp AND NODE.““


strategy will exactly match the payoff of the derivative at its maturity, no matter what path is ultimately observed and no matter how likely each path really is (real-world prob-ability). As in the single-step binomial tree, the price of a derivative only reflects the cost of the positions necessary in the stock and the bond. This is exactly why the mean return on the stock (mu) is not a relevant input in the Black-Scholes’ formula; this formula only provides the cost of the replicating strategy given the latest price of the stock. The mean return mu is already a very relevant parameter when pricing the stock alone. However, no matter how likely the stock is to attain some level, the price of a derivative will always reflect the cost of its replication; there is no need to further account for mu.

Risk-Neutral PricingIn the single-step binomial tree, we were able to express the cost of the replicating portfolio as a discounted expec-tation of future cash flows. This expectation was taken with a different probability measure q and cash flows were discounted at the risk-free rate. This probability measure is known as a risk-neutral measure because only risk-neutral investors would expect a return equivalent to the risk-free rate on risky assets.

When we solve for the exact dynamics of the cost of the replicating portfolio in Black-Scholes’ model, it turns out that we arrive at a similar expression, that is, a discounted expectation of future cash flows, where the discount rate and the mean return on the stock are both the risk-free rate. This should have been expected because the Black-Scholes’ model is a limiting case of the binomial tree and in excerpt # 1, we found the cost of the replicating portfolio as a special type of expectation.

Once again, the risk-neutral probability measure has noth-ing to do with the true probability associated with the stock price. When pricing a derivative, we do not assume that investors are risk-neutral. In fact, a short position in the derivative and an appropriate amount of stock

Scholes’ formula in the case of a plain vanilla call option. Figure 3 shows the famous Black-Scholes’ formula where t represents today, St is the current stock price, r is the risk-free rate, T is the maturity of the option, K is the strike price, σ is the volatility of log-returns and is the cumulative distribution function of a standard normal random variable.

We can rewrite the Black-Scholes’ formula in order to illustrate how many units of the stock and of the Treasury bond are necessary in every instant to exactly replicate the payoff of a call option, if the portfolio is continuously updated. Let Bt be the accumulated value of $1 invested for t years at the continuously-compounded risk-free rate, which is also the value of one unit of a risk-free Treasury bond. Figure 4 shows how the formula can be rewritten.3

The value at any time t of a call option is given by the value of its replicating portfolio, which has a portion invested in stocks and a portion invested in the risk-free Treasury bond . The latter, being

always negative, is in fact a loan at the risk-free rate. The number of units of stocks and bonds has to be dynamically updated because the stock price changes continuously (d1 and d2 are both functions of the current stock price).

Hence, as in the single-step binomial tree, if the risk man-ager can indeed trade at every instant the right number of stocks and Treasury bonds, the value of the replicating

Figure 4: Black-Scholes’ formula rewritten as the value of the replicating portfolio


“

“

WHEN pRICING A DERIVATIVE, WE DO NOT ASSUME THAT INVESTORS ARE RISk-NEUTRAl .


issuer. For risk management purposes, hedging errors, which is the difference between the value of the replicating portfolio and the derivative’s payoff at maturity (or any time period), are difficult to predict and can result in profits or losses ultimately. In both cases, it is extremely important to validate each assumption and the potential risk associated with a deviation to the true market dynamics.

Geometric Brownian MotionWhen applied to modeling stock (or asset) prices, the GBM requires that the continuously-compounded returns are independent and identically distributed as normal random variables. This is unfortunately not the case in practice for various reasons.

Behavior Of Observed ReturnsFinancial econometricians constantly study the behavior of asset returns (individual stocks and portfolios) at various time horizons (daily, monthly, etc.). One basic exercise they often do is compute various descriptive statistics of these returns as in Table 1. They have generally found that asset returns show negative asymmetry, which means that “the left tail is longer and the mass of the distribution is

yield a risk-free position. If the position is risk-free, then its cash flows should be discounted at the risk-free rate. Thus, risk-neutral valuation is only the consequence of the fact that we can trade in stocks and bonds to replicate the payoffs of a derivative. Under no-arbitrage pricing of derivatives, the level of risk premium included in the stock is useless.

ConclusionThe Black-Scholes’ model is the continuous-time equiva-lent of applying the one-step binomial tree at every instant. Under the absence of arbitrage, one can equivalently price a derivative using a replicating portfolio or by risk-neutral arguments. Although the mathematical tools are more complex (solving a partial differential equation or using the Girsanov theorem), the results are exactly the same, i.e., it is a type of expectation of discounted cash flows.

It should also be emphasized that the replicating strategy only tells us how to perfectly hedge the derivative given that the model’s assumptions are observed. In the more realistic case where the model’s assumptions do not hold, the hedge will not be perfect and may result in a random profit or loss. The next sections discuss the weaknesses of the Black-Scholes’ model and how practitioners and academics have dealt with these issues.

evideNCe AgAiNSt BlACK-SChOleS’ MOdelThe Black-Scholes’ model is extremely useful in various settings. However, one has to be careful because most of its underlying assumptions do not hold in practice. This has been largely documented, as for example in papers by Fischer Black titled, “The Holes In Black-Scholes” and “How To Use The Holes In Black-Scholes.”

Deviations between real market dynamics and the one given by a model can have very small or very large consequences on risk management. Indeed, serious mispricing of deriva-tives can lead to arbitrage opportunities and losses to its CONTINUED ON PAGE 32


concentrated on the right” (Wikipedia). This is contrary to a normal distribution as the latter is perfectly symmetric around the mean. Moreover, returns show fat tails, which is shown by a significant excess kurtosis. In a normal distribu-tion, the kurtosis is three, so that the excess kurtosis is zero. Although, the asymmetry is close to -1 at every observation frequency, the kurtosis is clearly much more significant at the daily level. Thus, asset returns clearly are not normally distributed and deviations from normality are greater at higher frequencies. We still have to investigate whether or not historical asset returns are independent and identically distributed as in a random walk.

A lot of academic and professional research has been devoted in the last several decades toward the predictability of asset returns and the efficient markets hypothesis (EMH). However, the EMH taken alone is very difficult to assess because an equilibrium pricing model has to be assumed, so that rejection of the EMH may as well be related to the fail-ure of the model to fit prices. Being central to the EMH, the random walk hypothesis is often investigated to determine the ability to “predict” asset returns.

Campbell, Lo and MacKinlay (1996) (Chapter 2) document three types of random walks. The simplest is one where increments are independent and identically distributed (i.i.d.). The second form of random walk is one where

Frequency # Data Mean Std. dev. Variance*100 Skewness(Excess) kurtosis

Daily 14063 0.02% 1.00% 0.0101 -1.0271 27.87

Weekly 2914 0.12% 1.80% 0.0325 -0.7027 6.28

Monthly 670 0.51% 3.60% 0.1293 -0.7320 4.15

quarterly 223 1.56% 6.29% 0.3956 -0.9974 3.85

Yearly 55 6.24% 12.94% 1.6754 -1.0943 3.91

Table 1: Descriptive statistics of the log-returns observed on the S&P500 from Jan. 1, 1957 to Nov. 9, 2012. Source: Federal Reserve of St. Louis’ Economic Data (FRED)

increments are independent, but not necessarily identi-cally distributed. The third type of random walk involves uncorrelated increments. There are various statistical tests to check for the validity of each type of random walk. However, it is not plausible that returns are identically dis-tributed (first type of random walk) because throughout the financial history, there have been changes in the economic and regulatory environments, in addition to technological advances. Moreover, it has been shown numerous times in the financial econometrics literature that squared asset returns are autocorrelated. Thus asset returns are not inde-pendent and this would lead to a rejection of the second type of random walk. Therefore, most empirical research testing the predictability of asset returns is focused toward the third type of random walk.

Empirical evidence (see for example Section 2.8 of Campbell, Lo and MacKinlay (1996)) shows that daily, weekly and monthly returns have positive and statistically significant autocorrelation (at the first lag), thus rejecting the random walk hypothesis. Another way to assess whether returns follow a random walk is to compare the variance of the process at different time horizons: this is known as the variance ratio test. In a random walk (even the third type), the variance of the process grows linearly over time as more increments are added to the total. Hence, the variance of annual returns should be about 12 times the variance



econometrics literature, we can find that asset returns show the following characteristics:• Non-constant and possibly stochastic volatility;• Jumps in asset prices (downward jumps more often

than not);• Jumps in the volatility as well.

While it is the role of behavioral finance and economics to explain why asset returns show these features, actuaries and other risk managers have to account for these characteristics of stock prices in pricing and hedging claims that are linked to the financial markets.

The insurance industry has shown particular interest in extending the Black-Scholes model to reserve their equity-linked insurance policies. For example, the regime-switch-ing log-normal model (RSLN) (Hardy (2001)) has been proposed for equity prices by the Task Force on Segregated Funds of the Canadian Institute of Actuaries whereas a discrete-time stochastic volatility model has been proposed by the American Academy of Actuaries (AAA) for vari-able annuities. It is important to note that the RSLN model features stochastic volatility (one possible value per regime) and by construction, the volatility jumps at each regime switch. The AAA’s model does feature a much greater spectrum of values for the volatility, but it lacks jumps in both the volatility and the price.

In the financial mathematics literature, more sophisti-cated continuous-time alternatives to the GBM also exist. The stochastic volatility model of Heston (1993) (dis-cussed below) remains very popular in the finance indus-try. For a thorough review of financial econometrics models applied to the context of reserving and hedg-ing variable annuities or segregated funds, the reader is invited to look at Augustyniak & Boudreault (2012).

Continuous Trading And RebalancingOne of the underlying assumptions of the Black-Scholes’

of monthly returns. It turns out that the variance ratio test rejects the random walk hypothesis (third type) at numer-ous horizons for equal-weighted portfolios. It was found that portfolios formed with the smallest firms have the most significant deviations from the random walk hypothesis. Finally, for individual securities the random walk hypoth-esis cannot be rejected and this should have been expected because individual stocks show company-specific noise that is mostly attenuated when aggregated into a portfolio.

Computing variance ratios in Table 1 also suggests that the random walk hypothesis is rejected with more recent data. We can see that daily returns are more variable (proportionally) than weekly, monthly or annual returns. This may be a sign of short-term mean reversion. In other words, an extreme daily return is often corrected in the next days, so that over a week, the weekly return has a more reasonable behavior. Short-term mean rever-sion is also backed by the decreasing kurtosis in Table 1.

Whether long-horizon returns (returns over periods longer than a year) also exhibit mean reversion is still an open debate among practitioners and academics. Proponents of long-term mean reversion often use widely accepted economic theories and models and pretend that mean rever-sion is supported in these theories. Others use statistical tests to measure their presence. In both cases, opponents of long-term mean reversion argue that the financial history is too short to obtain statistically significant results and that bubbles (NASDAQ or Japan for example) make it difficult to observe such reversion.

Overall, the GBM assumption clearly does not hold. (Log-) Returns are not normally distributed: they generally show negative skewness and very fat tails. Moreover, returns do not follow a random walk: they have some form of autocor-relation,4 as shown by the Box-Pierce and variance ratio tests.

Realistic Alternatives To The GBMWhen we dig deeper into both the empirical finance and


WHETHER lONG-HORIZON RETURNS (RETURNS OVER pERIODS lONGER THAT AN YEAR) AlSO ExHIBIT MEAN REVERSION

IS STIll AN OpEN DEBATE AMONG pRACTITIONERS AND ACADEMICS.

““


tials between identical products and portfolios. Second, they can significantly increase the true cost of the replicating portfolio, forcing companies to hedge more intelligently or less frequently, which in the latter case is riskier. Different lending and borrowing rates, in addition to taxes, can be seen as an asymmetrical transaction cost structure, further reducing arbitrage opportunities.5 Finally, the fact that we can only buy an integer number of stocks (or a block of 100 stocks for example) is not a huge issue for investment banks since they trade millions of positions.

Overall, some of these simplifying assumptions on mar-ket frictions do have minor impacts, but transaction costs (including tax and interest differentials) can have signifi-cant effects for pricing and risk management purposes. The interested reader is referred to Black (1989) for a discussion of these frictions.

ConclusionWe have only listed a subset of the many problems encountered with the Black-Scholes’ model, i.e., the fact that observed asset returns do not follow a GBM, that con-tinuous rebalancing of the replicating portfolio is virtually impossible and that market frictions such as transaction costs and restrictions on short selling can reduce the quality of the hedge portfolio and lead to important losses. Two other holes in Black-Scholes also deserve more attention, especially for insurance companies that sell long maturity put options through their equity-linked policies.

Suppose for example that your company has issued an implicit five-year put option in equity-linked policies and you need to replicate its future cash flows with stocks and bonds. Stock markets crash worldwide and the option goes deeper into the money. By following the replicating strat-egy, you would need to sell more units of the stock, and in times of crises, finding a buyer at the other end can be difficult. To find a buyer, one would need to further reduce the price offered, which increases the hedging loss. That creates a type of liquidity risk. According to Hull (2008), this had further aggravated the October 1987 crash, and it is

model is that the stock is traded continuously, so that the replicating portfolio should also be updated con-tinuously. Physically this is virtually impossible that the stock be traded in continuous-time! Humans and com-puters have to take some time to analyze their positions and send orders to execute them. However, these delays between trades are melting down now with supercomput-ers that execute computations and trades in milliseconds, and massive investments by banks in communications infrastructures. Transaction costs also prevent an inves-tor to trade continuously in a stock to update its replicat-ing portfolio. Consequently, the fact that the replicat-ing portfolio cannot be updated continuously entails a potential for hedging errors. In fact, it is exposed to large moves from the stock between two portfolio updates. This hedging error can be reduced by systematically rebalancing more frequently, say daily or hourly, but this can be very costly.

To reduce transaction costs and potential hedging errors, there are two common solutions. First, practitioners usually update their portfolio only when it deviates significantly from delta-neutrality (or some other criteria). They can also combine this approach with other hedging schemes that involve making sure the portfolio is insensitive to other factors (hedging based upon Greeks are discussed later in the text).

Frictionless MarketIn many finance textbooks, either in the Black-Scholes’ model or others, it is assumed that markets are frictionless, i.e., there are no transaction costs, assets are perfectly liquid and divisible, lending and borrowing interest rates are the same, there are no taxes and no restrictions on long and short positions, etc. We will briefly discuss the impact of these elements on pricing and hedging derivatives.

Transaction costs such as bid-ask spreads, commissions and other fees are indubitably the most important market friction in the derivatives market. First they help prevent arbitrage that may come up with very small price differen-



Black-Scholes’ model for low-strike (high-strike) options: this is the so-called volatility skew (smile) for equity prices. Hence, the implied volatility is the sigma parameter in the Black-Scholes’ formula that replicates a given market price. The relationship between the implied volatility and the time to maturity is the volatility term structure. Finally, the rela-tionship between the implied volatility, the strike and the time to maturity is the volatility surface.

Practitioners have been using the implied volatility to deal with the asymmetry and fat tails of the return distribution for pricing and hedging purposes. The concept is widely known and used: the CBOE monitors an index known as the VIX, which is, loosely speaking, a compound measure of the implied volatility computed from a portfolio of traded options. Derivatives known as variance swaps are even issued on the VIX so that investors can protect against changes in volatility. However, as discussed by LeRoux (2006), the implied volatility is “the wrong number to plug into the wrong formula to get the right price,” describing how it is not necessarily the most adequate solution to deal with Black-Scholes’ imperfections.

Hedging With GreeksTo cope with the inability to trade continuously and the lack of normality of equity returns, practitioners have been using Greeks to improve the robustness of their hedge port-folio. For those familiar with the concepts of duration and convexity matching (immunization), hedging with Greeks is very similar. It comes from the Taylor expansion of the option price at the next time period (which is random) around the current stock price (which is known). Truncating the Taylor series to the first or second term, allows us to immunize first-order and second-order changes of the option price with respect to the stock. With fixed-income securities, matching the first-order derivative is known as duration matching but with options, this is known as delta-hedging. When both first- and second-order derivatives are matched, duration-convexity matching is equivalent to delta-gamma hedging. As with duration-convexity match-

reasonable to believe a similar issue may have contributed to the current recession.

It is postulated in the Black-Scholes’ model that the term structure of interest rates is flat and deterministic over time. This is, of course, unrealistic since the term structure is not constant and it moves randomly over time. In fact, changes in interest rates can be largely explained by random variations in the level, slope and convexity (curvature) of the term structure. Because the volatility of interest rates is much smaller than the volatility in stocks, pricing very short-term options can reasonably be done using deter-ministic interest rates. However, for long-term contracts, especially equity-linked insurance that matures after five to 20 years, interest rate risk can be important when pricing these contracts.

iMPACtS ON iNduStRy PRACtiCeSThe fact that equity prices do not follow a GBM and the inability to continuously rebalance the hedge portfolio are perhaps the two most important holes in Black-Scholes. They have had important and profound impacts on how the industry uses the Black-Scholes’ model. This section covers the implied volatility metric and hedging with Greeks.

Implied VolatilityWe have seen in Table 1 that equity returns clearly do not follow a normal distribution through the computation of very simple descriptive statistics. We found that asset returns are negatively skewed and they show fat tails. The lack of normality of asset returns also show in the histori-cal price structure of plain vanilla call and put options. We can see that low-strike put options are underpriced with Black-Scholes, meaning the left tail is underestimated with a normal distribution. Similarly, high-strike call options are overpriced with Black-Scholes, meaning the right tail is overestimated with a normal distribution. So instead of moving away from Black-Scholes, practitioners use a different volatility parameter to price options with differ-ent strikes. They increase (decrease) the volatility used in


derivative of the option’s price with respect to changes in the risk-free rate is known as rho.

In order to hedge an option with Greeks, one has to com-pute these sensitivities. First-order, second-order and partial derivatives have to be based upon a model and the industry standard is Black-Scholes. Although a Taylor series expan-sion shows that using more Greeks improve the quality of hedging, this is only guaranteed to be true when the market model is the same as the one used in computing sensitivi-ties. However, when the market dynamics (say Heston) are different than the one used to build the hedging strategy (Black-Scholes), it is not perfectly clear as to how using more Greeks is going to improve the quality of the hedge.

heStON MOdel ANd BeyONdFinancial econometric models are used in the insurance industry mainly to help represent the risk on securities such as stocks and bonds on both the asset and liability side of the company. For example, it can be used to generate mul-tiple scenarios to price equity-linked insurance, to assess the quality of a hedging strategy, etc. We now discuss how the wider use of complex financial models have an impact on the most basic risk management operations of an insurance company. To lighten the discussion, we will mainly discuss the Heston (1993) model, but most of the remarks also hold for models with stochastic volatility, jumps in prices and jumps in the volatility.

In Heston’s model, the variance of the continuously-com-pounded return is given by a Cox-Ingersoll-Ross process, i.e., the variance is mean-reverting and guaranteed to be posi-tive. There are two sources of risk: the volatility, and given the volatility, the stock price also has a stochastic element. Since only the stock is traded and one cannot buy one unit of volatility (yet), the underlying financial market is incomplete. Incomplete markets have been discussed in a trinomial tree in the first excerpt. Thus, Heston’s model has all the caveats of an incomplete market model, that is the price of most deriva-tives is not unique and the hedge cannot be perfect.

ing, delta-gamma hedging is exposed to the same caveats, i.e., it is only valid for a small time period.6 Otherwise, the terms that are ignored in the Taylor expansion can become more significant. Thus, the impacts of being unable to continuously update the replicating portfolio (or the lack of normality of asset returns) can be diminished by also hedging gamma.

The issuer of an option is also exposed to other risks than variations of the stock price. Other variables such as chang-es in interest rates and volatility can have a significant effect on the option price. It is possible to diminish the impacts of changes in these variables by using an approach similar to delta-gamma hedging. Indeed, using a multivariate Taylor series expansion of the option price with respect to many variables, one can develop a hedging strategy that consists in matching the sensitivity of liabilities and assets to many risks. The sensitivity of the options’ price with respect to each of many variables is given a name after a Greek letter (most of the time). For example, the first- and second-order derivatives of the option’s price with respect to changes in stock price are known as delta and gamma. The first order


“ “THERE IS NO CURE TO MODEl RISk: ONE CAN IMplEMENT MORE THAN ONE MODEl TO COME Up WITH MORE ROBUST

RISk MANAGEMENT STRATEGIES, AND OF COURSE, STRESS- AND BACk-TESTING ARE VERY IMpORTANT.


reality. To quote George Box, a famous statistician, “All models are wrong, but some are useful” and Black-Scholes’ model is widely used because it is indeed very useful. Actuaries and the insurance industry need to master the tools of mathematical finance, including the more complex models of stochastic volatility and jumps, to be more effec-tive at developing new products and hedge them appropri-ately in the financial markets.

Using a more sophisticated model does not necessarily guarantee success. No one can pretend to have a fool-proof understanding of a phenomenon. Hence, no one knows how the sophisticated model truly deviates from the true market dynamics. This relates to model risk, i.e., the unexpected consequences related to choosing a model over another, compared to the true dynamics of a phenomenon, which is unknown. There is no cure to model risk: one can imple-ment more than one model to come up with more robust risk management strategies, and of course, stress- and back-testing are very important.

A model can be useful, but it is crucial to understand its limitations. Many authors like Steven Shreve, Pablo Triana, Felix Salmon (in Salmon (2009)), Sam Jones (in Jones (2009)) among others blame users of financial models because they did not understand thoroughly enough the models they were using and their limits. The authors con-tend that the latter may have instigated (or worsened) the current financial crisis. It also highlights the difficulties a whole company can face when implementing a complex risk management strategy, especially if the modeling department (that can be highly technical) cannot efficiently communicate with the upper management and board (who have very limited technical knowledge).

In the third (and final?) excerpt, we will discuss specific issues tied with equity-linked insurance that have not been discussed yet, such as pricing and hedging lapses, resets, withdrawals and other guarantees.

To partly circumvent the non-uniqueness problem, Steven Heston has assumed some particular form of market price of risk, which only depends on one parameter. Contrarily to the Black-Scholes model where the passage from the real-world to the pricing measure is unique and straightfor-ward, the Heston model implies estimating the parameter related to the market price of risk to make the passage from the physical to the risk-neutral probability measures. This parameter should really be taken seriously, especially if one is interested in both risk management and pricing (under no-arbitrage) applications.

No matter how a financial model is going to be used ulti-mately, one has to determine its parameters based on some set of data. Although estimating a GBM is straightforward, it is generally not the case for the Heston model. Given a specific structure for the market price of risk, Heston obtains (quasi-) closed-form solutions for the price of plain vanilla options (calls and puts), which is very interesting since it can be used in the estimation/calibration process. Indeed, one can minimize the squared deviations between theoretical and observed options prices. The method is straightforward, but will only provide for parameters under the risk-neutral probability measure. For risk management purposes, those parameters will not be adequate, unless one appropriately estimates the parameter related to the market price of risk, or at least performs a sensitivity analysis of this parameter. One can also use the time series of volatil-ity indices such as the VIX to infer the dynamics of the variance part of Heston model. The approach has proven to have some value, and the interested reader is referred to Aït-Sahalia & Kimmel (2007). Finally, estimating the Heston model (or any stochastic volatility model with or without jumps) often relies on the use of particle filters. This is one of the only methods that is statistically efficient with these models.

CONCludiNg ReMARKSIt is undeniable that the Black-Scholes’ model has been the cornerstone of modern finance and financial mathematics. However, any model is by definition a simplification of



RefeReNCeSAït-Sahalia, Y. and R. kimmel (2007), “Maximum likelihood Estimation of Stochastic Volatility Models,” Journal of Financial Economics 83, 413-452.

Augustyniak, M. and M. Boudreault (2012), “An Out-Of-Sample Analysis of Investment Guarantees for Equity-linked products: lessons from the Financial Crisis of the late-2000s,” North American Actuarial Journal 16, 183-206.

Black, F. (1988), “The Holes in Black-Scholes,” Risk.

Black, F. (1989), “How To Use the Holes in Black-Scholes,” Journal of Applied Corporate Finance 4, 67-73.

Boudreault, M. (2012), “pricing and Hedging Financial and Insurance products, part 1: Complete and Incomplete Markets,” Risks & Rewards, August 2012, Society of Actuaries.

Campbell, J.Y, A. W. lo and A.C. Mackinlay (1996), The Econometrics of Financial Markets, princeton University press.

Hardy, M. R. (2001), “A Regime-Switching Model of long-Term Stock Returns,” North American Actuarial Journal 5 41-53.

Heston, S. (1993), “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bonds and Currency Options,” Review of Financial Studies 6, 327–343.

Hull, J.C. (2008), Options, Futures and Other Derivatives, 7th edition, prentice-Hall.

Jones, S. (2009) “The Formula That Felled Wall Street,” Financial Times, April 24th, 2009

leRoux, M. (2006), “A long-Term Model of the Dynamics of the S&p500 Implied Volatility Surface,” presentation to the Canadian Institute of Actuaries’ Stochastic Modeling Symposium, Toronto, April 3, 2006

Salmon, F. (2009), “Recipe for Disaster: The Formula That killed Wall Street”, Wired Magazine 17.03

Stone, S. (2007), “Understanding the Black-Scholes equa-tion”, Risk & Rewards, August 2007, Society of Actuaries.

END NOTES 1 The approach is often attributed to Black & Scholes’

seminal paper in 1973, but Merton applied similar prin-ciples to value the equity of the firm and its credit risk in 1974. Although some authors use the Black-Merton-Scholes terminology, we will use the more common Black-Scholes term to refer to their 1973 paper.

2 A frictionless market is one in which there are no transac-tion costs, no differences in lending and borrowing inter-est rates, no taxes, no constraints on buying and (short-) selling the assets, etc.

3 A call option pays the excess of the stock price over the strike price, only when the former is greater than the lat-ter. No matter what is the underlying stock price model, that preceding payoff can always be decomposed as a long position in a derivative that delivers one unit of the stock if its price is greater than the strike, and a short position in a derivative that pays an amount equivalent to the strike, only when the stock price is greater than the strike. Stone (2007) provides further insights into the Black-Scholes formula.

4 One may be tempted to exploit this finding to make money! However, even if autocorrelations are statistically different from zero, the implied R2s suggest that a very small percentage of the variance is explained by past returns.

5 Tax differentials between financial products (such as corporate and municipal bonds) are generally accounted for in prices because authorities work to prevent tax arbitrage.

6 Applying a delta-hedging strategy continuously is equiv-alent to applying the theoretical replicating portfolio of Black-Sholes.

ACKNOWledgMeNtSThe author would like to thank Nino Boezio, Dick Joss and Pierre-Laurence Marchand for their valuable comments.


Mathieu Boudreault, Ph.D., F.S.A. A.C.I.A. is Associate Professor of actuarial science in the Department of mathematics, at the Université du Québec à Montréal. He can be reached at [email protected].


SOA 2013 lIFE & ANNUITY SYMpOSIUM

By Frank Grossman

discussions, namely “Perspectives on Life Insurance and Annuities in the Middle Market” and “Discount Rates for Financial Reporting Purposes: Issues and Approaches.” Emile Elefteriadis will be moderating a point-counterpoint discussion session “Do Long-Term Guarantees in Insurance Products Make Sense?” And the Investment Section will once again be hosting a hot breakfast for early risers on Monday morning.

Aside from the usual sessions and presentations, the Investment Section has teamed up with Albert Moore and the Technology Section to deliver a new networking event Sunday afternoon prior to the meeting—the Thomas C. Barham III Speed Chess Tournament. This event is open to all chess-playing members of any actuarial organization, including actuaries not otherwise attending the symposium. Hope to see you there!

I t may not be quite “April in Paris” with chestnuts in blossom, but May in Toronto doubtless has some redeeming qualities. All the snow and ice will have

surely melted away by then. And there’s very little chance that NHL playoff entanglements will clog up the hotels and restaurants this year. But, best of all, the SOA Life & Annuity Symposium will be held at the Sheraton Centre Toronto from May 5–7, 2013.

The Investment Section will be sponsoring several ses-sions as this meeting, some in collaboration with other SOA sections. J. Scott Colesanti, who is an associate professor at Hofstra University Law School (and previ-ously spoke at our section hot breakfast at the 2011 L&AS in New Orleans), will be featured in a session titled “Responses to the Global Financial Crisis: A Transnational Perspective.” We are also sponsoring a couple of panel

Frank Grossman, FSA, FCIA, MAAA, is senior actuary, Corporate Actuarial, with Transamerica Life Insurance Co. He can be contacted at [email protected].

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WHEN YOU CANNOT MAkE IT TO AN SOA CONFERENCE: … · 2013. 3. 18. · CONTINUED ON PAGE 5 JApANESE EqUITIES AND BUll MARkET ECONOMICS By Steve Scoles Rewards s s& J apan’s financial