Using Cross-Asset Class Information To Improve Portfolio Risk Estimation

Nick Wade Factset Risk Tour March 2012

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Northfield Risk for over 6 million traded securities globally, daily Over 300 client firms use our portfolio analytics to run anything from microcap

resources portfolios to enterprise risk The difficult stuff: unlisted assets; direct property and infrastructure, REITs, tax

sensitive rebalancing on over one million individual accounts We pioneered the adaptive hybrid model – learns as the market changes We launched the first production risk model to harness implied volatility – over 15

years ago From where we stand we are in a unique position to form a cohesive view of risk

and interactions across all marketable securities issued by a particular entity, and their interactions with other securities

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The Idea in Brief Any event or perception that has an effect on the size or uncertainty of the

future cashflows of an entity should affect the valuation and risk estimates of every marketable security issued by that entity, and every derivative security based upon them.

In stark contrast, a “traditional” risk model focuses in myopic fashion just on the

historical returns of a particular asset class. Our contention is that significant value can be added to the efficacy of risk

forecasts by exploiting the connections across asset classes, and harnessing a wide variety of “alternative” factors or conditioning information to arrive at expectations of risk that are mutually consistent across the entire capital structure of the firm, and related derivatives .

Harnessing Cross-Asset Class Information Makes Better Risk Forecasts

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Evidence of Linkage Market participants amplify connections across asset classes with “want to” and “have to”

trades. Diversification is weaker / absent in times of need. Khandani & Lo (2008) – quant meltdown of 2007 as asset class contagion vs. 1998 Russian

debt default Kritzman & Li (2010) – turbulence, contagion, skulls. During periods of market turmoil,

connections are much tighter. E.g. Normal -0.17, turbulent +0.76 Kritzman (again)… (2011) Systemic Risk: Absorption Ratio Connection for profit: -  Capital structure arbitrage -  Convertible bond arbitrage You need to have a good sense of the connections across asset classes in your risk model so that you can position your portfolio appropriately in any environment

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Really Obvious Cross-Asset Example “Traditional” Equity Risk Model Factors: Fundamental model: by construction looks to explore security risk just as a function of company

characteristics or attributes. A bit introspective… Macro models: in comparison look at other asset classes for signals:

Oil prices – commodity asset class affects equity asset class How? Energy cost to companies.

Interest Rates – fixed income asset class affects equity asset class How? Financing cost.

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Example: Harnessing New Signals 1997 Northfield Short Term Model (Nick Wade, Bob Kelley) Information from the option market conditions risk forecasts of the underlying

individual securities and their shared (factor) behavior; model balances historical behavior with market consensus forecast behavior over the term of the option contract.

2007 Northfield Near-Horizon Models (Anish Shah) A variety of signals can be used to condition risk forecasts… implied volatility, cross-

sectional dispersion, volume, open interest 2009 diBartolomeo, Mitra, Mitra – Using Quantified News Flows Non-traditional contemporaneous or forward-looking signals enhance model

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Bit More Complicated… Structural Models Merton (1974): an equity security can be considered a call option on the assets

of the firm. Alternatively, the lenders are short a put. Various nuances: -  Black and Cox (1976) “first passage” -  Bookstaber and Jacob (1986) “composite hedge” -  Leland (1994), Leland & Toft (1996) “tax issues”…and on and on… Simple way to think of it: A corporate bond can be represented as a government bond plus an

equity position. Corporate bond risk can be represented as government bond risk plus

equity risk (credit risk)

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Credit Risk We derive a solution of corporate bond’s credit factor exposures which are directly

related to the factor exposures of the associated company’s stock. The relation has the form: Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure Of the Stock

of the Bond Issuer Where; E is the market capitalization of the firm B is the market value of the firm’s debt …and the put and call are calculated with respect to the maturity of the particular

bond tranche With a model of 70,000 listed equities, we are in good shape to model credit

even for illiquid bonds!

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Why is this better? You could use ratings, but (in case you’ve been on Mars for the last three years) to

be honest they aren’t well regarded currently… You could use a history of actual defaults and several hundred fundamental analysts

and try and make better ratings… You could use spread changes (and we did) but estimating a decent spread requires

first of all having a decent price. And given the liquidity issues with corporate debt (and even government debt “off the run”) the prices are noisy.

Leveraging the connection with equities allows us to: Harness the most liquid market information (equities and options) Harness forward-looking signals e.g. implied volatility / implied correlation This allows us to adjust credit risk to reflect a change even if the bond didn’t

trade or the market is closed

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Implications Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure Of the

Stock of the Bond Issuer 1.  The closer the firm is to default (deeper into junk status) the higher the delta

of the put will be relative to the delta of the call. Given that option gamma is the same for puts as for calls the approach to junk status will tend to proportionately increase the ratio of two deltas more than it will decrease the ratio E/B per unit of decline in the firm asset value. That will make the bond’s factor exposures more similar to that of the stock and this reflects the empirical evidence that junk bonds w behave like equities.

The closer the firm is to default, the more similar the bond’s factor

exposures become to those of the stock - reflecting the empirical evidence that junk bonds behave like equities

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Implications 2 Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure Of the Stock of the

Bond Issuer Short term bonds of the same company are more volatile than the longer term bonds of

the same firm (just talking about credit risk here!) With shorter-dated options the put deltas are higher and the call deltas lower than those of

longer-dated options And this of course reflects the conventional logic that the longer term provides more room than

short term towards unbounded improvement than bounded decline. Despite that simple logic, the anecdotal bias in the industry has is that longer term bonds are

more credit risky than shorter term ones, partly due to bond duration vis-à-vis spread considerations, and confusion of higher periodic volatility with higher total premium charged for default risk (firm put option value).

Our finding sets the record straight and is one of the contributions of the model to a better

accord of mathematical rigor and conventional intuition in the area of finance.

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Market Implied Expected Life Using a structural model and our estimates of equity volatility estimate

the “market implied expected life” of firms •  For a 50% probability of default threshold, work the option math backwards to give us

the implied expiration of the option, which we term the “implied life” of the firm. •  See Yaksick (1998) for numerical methods for evaluating a perpetual

American option (include term-structure of interest rates) •  Makes different default probabilities for different bond issues very natural as

each maturity will lie at a different point in the survival time distribution

See diBartolomeo, Journal of Investing December 2010 A quantitative measure of the fundamental and “social” concept of sustainability The “sustainability” aspect of the credit risk stuff is also a way for

quants and fundamental investors to talk in a common language. To long-term fundamental investors, “risk” is the potential for a company to fall apart and go bankrupt. We now explicitly measure that.

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Previously Published Research Estimate market implied life monthly for all firms in Northfield US equity universe

December 31st 1991 to March 31st 2010. Mix of large and small firms, 4660 – 8309 names

Contrast two sub-samples: Financial Firms, Non-financial firms:

Risk taking is heavily concentrated in the largest financial firms Risk taking has been concentrated in the largest financial firms for at least 20 years

Implied  Life:   Median   Cap-­‐Weighted  

Revenue-­‐Weighted  

Financial   22.28   17.06   7.86  

Non-­‐Financial   14.74   18.42   17.60  

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Quantifying “Sustainability” MSCI KLD DSI 400 index of US large cap firms considered

socially responsible, 20 year history •  Typically about 200 firms in common with the S&P 500 •  Statistically significant difference in means

Testing on disjoint sets (i.e. DSI not S&P, S&P not DSI) Statistically significant difference in means for every time period

tested – socially responsible firms are expected to live longer!

Median  Implied  Life  

Average  Implied  Life  

Standard  Devia?on  

July  31st  1995   DSI  400   17   17.91   9.93  

S&P  500   14   15.40   9.28  

March  31st  2010  

DSI  400   30   26.39   11.45  

S&P  500   30   24.93   10.92  

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“Sustainability” Equity Investing vs. MinVar Mean   Annual  

Monthly   CumulaGve   Monthly   Compound  

Return   Return  Standard  DeviaGon   Return  

Q5  Equal   1.33   713.77   9.15   10.90  

Q1  Equal   1.03   790.86   3.64   11.50  

Q5  Cap   0.77   251.60   6.62   4.98  

Q1  Cap   0.79   414.32   3.78   7.77  

S&P  5002   0.75   347.74   4.32   6.78  

Q5  MV   1.77   2901.15   6.80   19.33  

Q1  MV   1.07   840.43   2.96   12.34  

(QuinGles  by  Implied  Life,  1992  through  March  2010,  maximum  of  200  posiGons)  MinVar  construc<on  benefits  only  apparent  in  “junk”  quin<le  

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The Value Premium When we invest in financially troubled “value” firms

•  These firms have obvious have bankruptcy potential •  We value these firms knowing they can go broke

When we invest in healthy “growth” firms

•  We assume they will exist in perpetuity •  In a DDM context most of the cash flows to be discounted tp

present value occur further in the future •  If growth firms have finite lives those far in the future cash flows

never happen and DDM will systematically overvalue these firms •  Anybody remember Digital Equipment?

The sustainability framework provides a potential explanation for the widely observed “value” return premium

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Forecasting rating changes and making money As part of our normal fixed income analysis we estimate “option-adjusted spreads”

for about 6 Million fixed income instruments on a monthly basis We combined rating levels from S&P, Moody’s and Fitch into a unified letter scheme

and then quantified them “AAA” at 10, “D” at 1, and scale intermediate levels inversely proportional to OAS

Predict rating change: the percentage change in the “simple” numerical value of the credit rating

…using implied life variables:

•  12 month percentage change in expected life as of prior month end •  12 month change in the cross-sectional Z-score of expected life

within the US equity universe

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A Modest But Encouraging Result Even with our simple model we could meaningfully predict

subsequent changes in bond ratings

•  Our model had a correlation of about 40%, R-squared of 0.16 •  A very high degree of statistical significance on coefficients (T > 4) •  R-squared was higher for subsets of lower grade bonds (i.e. NOT

“A”) •  These results are all conditional that a change in rating would

eventually take place since only such events existed in our data •  Non-events (no rating change) were excluded from the sample by

design

Perhaps our model would predict 14 of every 5 downgrades (Data: 8500 events from Barrons, 1992 – 2008)

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Comparison with Credit Rating Agencies Create a metric to compare our ratings to the published ratings: At each year end starting at 2005 we convert the expected life of issuer for each bond issue to

a Z score within rating category A negative Z score indicates that our metric suggests that the firm is less creditworthy than the

published rating Sort sample universe of 22000 bond issues into quintiles by Z score for 12/31/2006 (and nearly

identical result for 12/31/2007): Bottom quintile of 4400 bond issues: 2940 were from Wall Street firms that either went

bankrupt, were acquired or needed major government assistance The rogues gallery included:

•  Bear Stearns (534 issues), Merrill Lynch (868), Lehman Brothers (657), Morgan Stanley (257), CIT Financial (338), Countrywide (136) and Washington Mutual (24)

The model correctly identifies the biggest credit risks during GFC

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Z-score Within Rating (January 2006 Through June 2011)

-4

-2

0

2

4

6

8

10

12

14 Cumulative Q1/Q5 Return Spread

20  

Peak  Value  November  2008  

1200  bps  up!Doing  OK…  

Giving  it  all  back…  

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Default Correlations – our goal is joint probabilities

No model of credit risk is complete without the ability to estimate default correlations

Defaults are usually rare events so it’s impossible directly to observe default correlations over time

However, Equity return volatility and correlation are readily observable Zeng and Zhang (2002) shows asset correlations must arise from correlation of

both equity and debt components Qi, Xie, Liu and Wu (2008) provide complex analytical derivation of asset

correlations given just equity return correlation Interim result - we end up with asset correlations and asset volatilities

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Joint Default Probabilities

With asset volatility and correlations estimated we can use our preferred structural model to estimate default probability of a firm

Use method from Zhou (2001) to convert asset correlations to default correlations

We can now produce joint default probabilities across firms

However there are some pretty restrictive assumptions •  Firm must have debt today •  Firm must have positive book value today •  Balance sheet leverage must stay fixed in the future

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Another  Angle  on  Default  CorrelaGons  For example, if an event that causes a large change in the expected life of Bond X also causes a similarly large change in the expected life of Bond Y then their fates are likely intertwined. Formalize: Once the time series of expected lives have been calculated: we can estimate default correlation as the correlation of percentage changes in expected lives across firms Better than trying to correlate OAS spreads since bond prices are driven by liquidity effects

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Risk Models that exploit the connections across asset classes can greatly improve our ability to forecast risk and position portfolios safely in all environments

From our vantage point across all asset classes – whether listed or unlisted – we are in an excellent position

to create a holistic and mutually consistent representation of the risk of all marketable securities and derivatives issued by a particular firm; each individual part enhanced by its linkage to the rest.

Our model for credit risk harnesses our research and signals from equity risk, together with other non-

traditional signals. Our model for the expected life of firms effectively combines equity factor risk models and contingent claims

credit models in a unified framework Using expected life data as a metric for corporate credit risk allows for effective prediction of credit rating

changes, an explanation for the “value” premium, quantifies the fundamental qualitative concept of “sustainability”, and generates substantial alpha from corporate bond portfolios by using expected life related metrics as a better measure of credit risk

Minimum variance portfolio construction is helpful, but has more impact when used in conjunction with

sustainability

Conclusions