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05/13/22 Strategic Asset Allocation 1 4106 Advanced Investment 4106 Advanced Investment Management Management Strategic Asset Strategic Asset Allocation Allocation session session 1-2 1-2 Andrei Simonov

9/14/2015 Strategic Asset Allocation 1 4106 Advanced Investment Management Strategic Asset Allocation session 1-2 Andrei Simonov

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Page 1: 9/14/2015 Strategic Asset Allocation 1 4106 Advanced Investment Management Strategic Asset Allocation session 1-2 Andrei Simonov

04/21/23Strategic Asset Allocation1

4106 Advanced Investment4106 Advanced Investment Management Management Strategic Asset Allocation Strategic Asset Allocation sessionsession 1-2 1-2

Andrei Simonov

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AgendaAgenda

Introduction, Course Outline, Requirements, Resources

Taxonomy of Securities and MarketsDefinitionsHistorical Records of Returns on different

securitiesNew Economy and Investment Industry

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Introduction Introduction The field of Finance and Investments

– Individual agents making decisions to supply capital to the markets

– Firms getting capital from the financial markets (when, where, how?)

– Capital Markets acting as market clearing device. Goal of the course:

– To familiarize you with ”real world” of investments.

– To give broad overview of modern investment issues. By the end of teh course one should know what does that mean to be investment professional.

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Overview Overview of the courseof the course Strategic Asset Allocation Asset Pricing Models Tactical Asset Allocation Volatility & Skewness Information Processing by markets Market Neutral Investments Behavioral Finance

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Resources and requirements:Resources and requirements: Courseweb page. I put some stuff on my page, but

links are on courseweb Articles (package+web site)

Provide deeper insight, latest developments No econometrics, just general idea

Wall Street Journal or Financial Times Access to Internet, some Excel experience, basic

knowledge of econometrics It is assumed that basic courses are still

remembered by you. Groups of 2-3 (pls let secretary know by the end of

the week)

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Cases Cases (50% of the grade).(50% of the grade). What case report is NOT:

– Not copy of textbook or article.

– Not exercise in history of economics or finance. I do not care (at least, in that class) who got Nobel Prize for what...

Ideal case report is similar to consulting report:– Analysis of data that is in the case (preferrably statistical analysis)

– Covering all relevant issues (pros and cons)

– Take the position and defend it!

– Case report is not War and Peace. Be brief!

– Please understand what you are writing about.

– Cases are due before the discussion session. Do not spend more than 2 days on ANY case! Class discussion is part of the case work.

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Investment Project Investment Project (40% of the grade).(40% of the grade). Main Goal: to give you hands-on experience in basic

investment management. Developing the trading game plan by early Oct.

– Main goal: lock-in the group into chosen strategy

– Main document: short ”prospectus” (see web site for details).

Trade (October-December) Write final report (deadline around Dec. 10 )

– Assess your performance. What worked and what did not? Were your constraints binding?

– What did you learn?

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My assumptions about you:My assumptions about you:You know and understand basic regression

analysis (what is R2, statistical significance, etc.)

You remember conditions of optimality from Microecon. Course

You remember basics from Finance I and Investments

You are willing to learn...

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AgendaAgenda

Individual’s preferences, utility function Measurement of risk by variance Diversification

– A bit of math

– Industry diversification

– International diversification

– Latest evidence Shortcut to math: Excel! Risk accounting

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AssetsAssets Real vs. Financial assets Role of financial assets

– Consumption Timing– Allocation of Risk– Separation of Ownership

Various financial assets– Money market– Fixed-income– Equities– Derivatives

Trading the assets– types of market organizations– types of orders you can place

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EquityEquity Common stock Preferred stock Distinguish

dividend yield (Yt=dt-1/Pt) from

holding-period rate of return

Excess rate of return: Rt,t+1 – rt

(as when buying on margin)

t

ttttt P

dPPR 11

1,

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Where to get data?Where to get data? Easiest: web search engine, financial sites (Yahoo,

Infoseek, msn, etrade, etrade-SE, CNNfn, etc.) Bulk suppliers

– Bloomberg, DataStream, CRSP, Reuters, Trust, Commodity Systems, Inc., Securities Data Corp., etc...

– Look at departamental web site: http://www.hhs.se/secfi/Databases/Databases.htm

Dividends Volume Splits

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First Approximation Model of First Approximation Model of Investors’ Behavior: Assumptions:Investors’ Behavior: Assumptions:

Single holding periodInvestors are risk-averseInvestors are ”small”The information about asset payoffs is

common knowledgeAssets are in unlimited supplyAssets are perfectly divisibleNo transaction costWealth W is invested in assets

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Investors´ preferencesInvestors´ preferences

Attitude to risk Time horizon (do

not confuse with holding period)

Non-traded risks (liabilities, labor income, human capital)

Constraints

PortfolioAdvisor & Investor Type: Cash Bond Stock Bonds/StockFidelityConservative 50 30 20 1.500Moderate 20 40 40 1.000Aggressive 5 30 65 0.462Merrill LynchConservative 20 35 45 0.778Moderate 5 40 55 0.727Aggressive 5 20 75 0.267New York TimesConservative 20 40 40 1.000Moderate 10 30 60 0.500Aggressive 0 20 80 0.250

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Investor’s preferences:Mean-Investor’s preferences:Mean-variance frameworkvariance framework

Representation by utility function of wealth W– u’(W)>0, u’’(W)<0

Taylor Expansion:

Applying Expectations operator:

Simplest utility function is quadratic:u=W-0.5bW2

Problem: satiation Arbitrary preferences: Asset returns are distributed as

multivariate normal A dominates B if E(rA) (>) E(rB) and A <() B

2))~

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WEfWEb

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Indifference curvesIndifference curves All portfolios on a given

indifference curve are equally desirable

Any portfolio that is lying on indifference curve that is ”further North-west” is more desirable than any portfolio that is lying on indifference curve that is ”less Northwest”

Different investors (e.g., in risk aversion) have different indifference curves

Solid line, b=1, dashed line, b=2

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 1 2 3 4 5 6

Std. Dev.

Exp.

return

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Measuring risk by varianceMeasuring risk by variance Variance

– definition: probability weighted squared deviations from the expected value

– based on probability distribution Any drawbacks of this measure?

– People do not behave that way (read Odean): Overconfidence (“wrong” probability distribution) Regret (distinguish “gains” from “losses”) Should we use semi-variance?

– Particularly in case of delegated portfolio management?

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How to live with risk?How to live with risk? Know and classify risks into

asset classes. On what basis? Price risk (Country (incl.

Political risk), Industry,statistical categories)

Credit risk, counterparty risk Tail risk or risk of ruin

Most important classification concept: statistical correlation pitfalls of correlations quasi-arbitrage opportunities

(“convergence trades”): LTCM and limits of arbitrage (Shleifer &Visny)

Large vs. Small Cap: Total Return (01.1954=$1)

$1

$3

$5

$7

$9

$11

$13

$15

$17

1954 1959 1964 1969

Large CapSmall CapLarge CapSmall Cap

HIGH CORRELATIONr=0.99

LOW CORRELATION

r=0.5

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The same story:The same story: Nasdaq vs. S&P 500Nasdaq vs. S&P 500

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IndicesIndices

Uses– Track average returns of Asset Class

– Comparing performance of managers

– Base of derivatives Factors in constructing or using an Index

– Representative?

– Broad or narrow?

– How is it constructed?

– Subjectivity Factor (Bethleham Steel)

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Examples: Stock and Bond IndicesExamples: Stock and Bond Indices

1. Royal Dutch Petroleum nl e 9,02 2. Allianz Versicherung g i 5,52 3. Deutsche Telekom g t 4,06 4. ENI i e 3,63 5. France Telecom f t 3,53 6. ING Groep N.V. nl fi 3,16 7. Unilever N.V. nl fo 3,08 8. Daimler-Benz g ca 2,97 9. Telecom Italia Ord i t 2,86 10. Deutsche Bank g b 2,86

11. Siemens g m 2,77 12. Veba g m 2,69 13. Bayer g ch 2,50 14. Telefonica de Espane, S.A. i t 2,40 15. ABN-AMRO Hldg N.V. nl b 2,35 16. Societe Nationale Elf Aquitaine f e 2,33 17. Asicurazioni Generali S.p.A. (ENDESA) i i 2,32 18. AXA-UAP f i 2,30 19. Aegon N.V. nl i 2,24 20. L'Oreal (Ordinary) f co 2,23

21. Banco Bilbao Vizcaya s b 2,06 22. Philips Electronics N.V. nl tec1,82 23. Carrefour f r 1,73 24. Koninklijke PTT Nederland nl t 1,65 25. Mannesmann g ind1,65

26. Alcatel Alshom (Electric&Electronic) f tec1,6427. Endesa s s 1,64 28. Eaux (Cie Generale des) f s 1,59 29. RWE d s 1,46 30. Nokia Ab Oy A fintec1,42

31. LVMH Moet-Hennesey Louis Vuitton f fo 1,27 32. Rhone-Poulenc SA f p 1,25 33. Paribas (Compagnie Financiere de) f b 1,23 34. Ahold Kon. nl co 1,13 35. Societe Generalee f b 1,09 36. Electrabel b s 1,07 37. Akzo Nobel N.V. nl ch 1,03 38. Repsol, S.A. s e 1,02 39. Fiat S.p.A. Ord i c 0,95 40. Elsevier N.V. nl m 0,94

41. Compagnie de St. Gobain f bu 0,92 42. Air Liquide (L') f ch 0,89 43. Credito Italiano S.p.A. Ord i b 0,84 44. Fortis b i 0,81 45. Portugal Telecom S.A. por t 0,78 46. Alliead Irish Banks ire b 0,75 47. Schneider f ind0,69 48. Metro g r 0,67 49. Petrofina S.A. b e 0,64 50. Dt. Lufthansa g tr 0,54

Dow Jones: price weighted arithmetic

Standard & Poors: value weighted arithmetic

Specialized indexes: Wilshire, Russell etc.

European indexes: Eurostoxx 50

Bond indexes: Lehman Brothers, Merrill Lynch, Salomon Brothers all value weighted

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The measurement of risk:The measurement of risk: Compare frequency distribution of bond rates of Compare frequency distribution of bond rates of

return and rates of returns of stocksreturn and rates of returns of stocks

0

2

4

6

8

10

12

14

16

18

20

-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% 60% 70%

Small stocks

Large stocks

Long-term T-Bonds

Source: Ibbotson Assoc.

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The The measurement measurement of risk by of risk by variancevariance (example: large-c. (example: large-c. stocksstocksfrom frequency table)from frequency table)

RoR/yearLarge Stock Frequency Rel.frequency Calc. Mean Calc. Var. Other way

-90% 0 0.00% 0.000% - 0-84% 0 0.00% 0.000% - 0-78% 0 0.00% 0.000% - 0-72% 0 0.00% 0.000% - 0-66% 0 0.00% 0.000% - 0-60% 0 0.00% 0.000% - 0-54% 0 0.00% 0.000% - 0-48% 0 0.00% 0.000% - 0-42% 1 1.41% -0.549% 0.00469 0.002142254-36% 1 1.41% -0.465% 0.00377 0.001533803-30% 0 0.00% 0.000% - 0-24% 2 2.82% -0.592% 0.00444 0.001242254-18% 0 0.00% 0.000% - 0-12% 1 1.41% -0.127% 0.00108 0.000114085-6% 10 14.08% -0.423% 0.00664 0.0001267610% 5 7.04% 0.211% 0.00174 6.33803E-056% 6 8.45% 0.761% 0.00080 0.000684507

12% 6 8.45% 1.268% 0.00012 0.00190140818% 6 8.45% 1.775% 0.00004 0.00372676124% 13 18.31% 4.944% 0.00126 0.01334788730% 4 5.63% 1.859% 0.00115 0.00613521136% 8 11.27% 4.394% 0.00463 0.01713802842% 4 5.63% 2.535% 0.00389 0.01140845148% 2 2.82% 1.437% 0.00294 0.00732676154% 1 1.41% 0.803% 0.00206 0.00457605660% 1 1.41% 0.887% 0.00276 0.00559014166% 0 0.00% 0.000% - 072% 0 0.00% 0.000% - 078% 0 0.00% 0.000% - 084% 0 0.00% 0.000% - 090% 0 0.00%

71 0.07706 Sum 18.718% 0.04202023 0.042020234

stdev 20.499% 20.499%

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Optimal diversification: the Optimal diversification: the ingredientsingredients

Excess expected rate of return for each security i (organized into vector)

Variance of rate of return for each security iCovariances of rate of return of security i

with security j (organized into matrix)

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Optimal diversificationOptimal diversification (2) (2) What is covariance between x and y? Estimated

as:

Why does covariance come in? By definition of correlation, covariance is also

correlation between x and y standard deviation of x standard deviation of y

Example of calculation from data table: stocks and bonds

yyxxT t

T

tt

111

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Example of Example of calculation calculation from table: from table: stocks and stocks and bondsbonds

YearLarge stocks

Long-term T-Bonds

Cross product of deviations

1926 12.21% 4.54% 0.0000221927 35.99% 8.11% 0.0065671928 39.29% -0.93% -0.0167301929 -7.66% 4.41% 0.0018231930 -25.90% 6.22% -0.0034771931 -45.56% -5.31% 0.0616841932 -9.14% 11.89% -0.0142281933 54.56% 1.03% -0.0180221934 -2.32% 10.15% -0.0071651935 45.67% 4.98% -0.001110

1980 32.48% 13.17% 0.0156971981 -4.98% 3.61% 0.0029791982 22.09% 6.52% 0.0011561983 22.37% -0.53% -0.0057701984 6.46% 15.29% -0.0060231985 32.00% 32.68% 0.0533681986 18.40% 23.96% 0.0110051987 5.34% -2.65% 0.0057011988 16.86% 8.40% 0.0013461989 31.34% 19.49% 0.0267101990 -3.20% 7.13% -0.0028501991 30.66% 18.39% 0.0237481992 7.71% 7.79% -0.0011851993 9.87% 15.48% -0.0026711994 1.29% -7.18% 0.0140041995 37.71% 31.67% 0.0664481996 23.00% 0.10% -0.005476

mean 12.50% 5.31% 0.003057 Covvar 0.0415625 0.00633945 0.188344 Corrstdev 20.387% 7.962%

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Math of mean-variance optimizationMath of mean-variance optimizationAssume you have 1 SEK to invest into stock

(S,S) and long-term bond (B,B).

BSBSBBSSB

BSBSBBSSB

BSBSpBS

pBSp

BSBSBBSSp

BBSSBBSSp

w

wR

R

RrEwwts

wwww

wwrEwrEwrE

r

r

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r

2

)(22

2

)(,1..,min

problem theofsolution theis PortfolioFrontier Efficient

2

)()()(

22222

222

22222

2

22222

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Try to do the same with 10 assets…Try to do the same with 10 assets…

)()(

)(

:,on Multiply

01

0)(

0

1)(2

1min

..

......

..

),1,...,1,1,1(,...),,(

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2

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Efficient FrontierEfficient Frontier

0

5

10

15

20

25

15 17 19 21 23 25 27 29 31 33 35

Portfolio Risk (Std. Dev),%

Me

an

Po

rtfo

lio

Re

turn

s,

%

Global Minimum-Variance Portfolio

Efficient Frontier

BrAErECD

rVar ppT

p )(2)(1

)( 2Vww

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Using Excel to optimizeUsing Excel to optimize Lord gave us Microsoft. Use it! Use “Solver”. Can have many securities,

add constraints. Set up row or column of portfolio weights {xi} Variance: compute xi cov(Ri,Rj) xj

– Sum both ways to get portfolio variance Expected return: xi E(Ri)

– Or, if there is riskless asset, xi [E(Ri) – r]– Sum to get portfolio expected return

Maximize – portfolio exp. return - 1/2 portfolio variance for given . is risk aversion.– Or maximize portfolio exp. return for given portfolio variance (or standard

deviation), – Or minimize portfolio variance for given portfolio exp. return ,

under constraint that portfolio weights sum to 1 (in the absence of riskless asset) and possibly other constraints.

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Example of spreadsheetExample of spreadsheetCompositionER CompxERstd constraints correl

T-bills 0.00% 1.50% 0.0000 3.50% 0% 100% 1 0.5 0.4 0.1 0.4 0Mid-bonds 0.00% 3.50% 0.0000 9.00% 0% 100% 0.5 1 0.9 0.3 0.1 0.4Long-bonds 33.00% 4.00% 0.0132 11.50% 0% 100% 0.4 0.9 1 0.3 0 0.45International Bonds 0.00% 3.20% 0.0000 10.00% 0% 15% 0.1 0.3 0.3 1 0 0Real Estate 10.00% 5.00% 0.0050 9.00% 0% 10% 0.4 0.1 0 0 1 0.25North American Equities 42.00% 6.50% 0.0273 18.50% 20% 100% 0 0.4 0.45 0 0.25 1EAFE Equities 10.00% 7.50% 0.0075 21.00% 0% 20% 0 0 0 0.2 0.05 0.45Small Cap 5.00% 8.30% 0.0042 30.00% 0% 20% 0 0 0.3 0 0 0.65

Total 100.00%Foreign equity 10.00% 0% 20% covar

Mid + LT bonds 33.00% 0% 100% 0.001225 0.001575 0.00161 0.00035 0.00126 0Small Cap 5.00% 0% 8.40% 0.001575 0.0081 0.009315 0.0027 0.00081 0.00666

0.00161 0.009315 0.013225 0.00345 0 0.00957380.00035 0.0027 0.00345 0.01 0 00.00126 0.00081 0 0 0.0081 0.0041625

Portf var 0.014729616 0 0.00666 0.0095738 0 0.0041625 0.034225

Portf std 12.137% 0 0 0 0.0042 0.000945 0.0174825

ObjectivePortf ER 5.72% 0 0 0.01035 0 0 0.036075

CompxcovarxComp

0 0 0 0 0 00 0 0 0 0 00 0 0.0014402 0 0 0.00132690 0 0 0 0 00 0 0 0 0.000081 0.00017480 0 0.0013269 0 0.0001748 0.00603730 0 0 0 9.45E-06 0.00073430 0 0.0001708 0 0 0.0007576

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Random diversification: Random diversification: SharpeSharpediagramdiagram

jkPN

jkjkj

jkj

N

j

j

i

ijN

j

j

ijj

N

j

j

iij

N

jjP

NN

N

N

NNN

N

NN

Nw

www

2

22

1

1

11

2

1

1

1

2

1

22

lim

11

)1(

12

1

/1 Assuming

2

Portfolio risk approaches the average covariance between assets when the number of assets gets large.

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Henry Lowenfeld, 1909Henry Lowenfeld, 1909

“It is significant to see how entirely all the rest of the Geographically Distributed stocks differ in their price movements from the British stock. It is this individuality of movement on the part of each security, included in a well-distributed Investment List, which ensures the first great essential of successful investment, namely, Capital Stability.”

From: Investment and Exact Science, 1909.

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History of DiversificationHistory of Diversification

First Mutual Fund: Eendracht Maakt Magt (1774)

Danish and Viennese banks Danish Tolls and Holstein Russia and Sweden Brunswick and Mecklenburg Postal services of Saxony Spanish Canals of Taouste and Imperial British Colonies Essequebo Berbice Danish American Islands

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Diversification: Diversification: 1818thth Century Mutual Funds Century Mutual Funds In the portfolio construction the fund “will observe as

much as possible an equal proportionality”

“Because nothing is completely certain, but subject to fluctuations, it is dangerous to allocate all capital to a single security”

“Nobody will have reason to believe that all securities will stop paying off at the same time thereby losing the entire invested capital”

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Globalization and Financial Globalization and Financial LinkagesLinkages Common wisdom is that globalization and

integration of markets accentuates financial linkages (correlations)– Business cycle synchronization– Policy coordination– Coordination of institutions– Decrease in “home bias” of investors– Globalization of firms

Globalization and integration also allows country specialization

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Globalization and Financial Globalization and Financial LinkagesLinkages Expansion of investment opportunities Lowering of transactions costs

– Trade where costs are lowest

– Competition among exchanges

– Cross-listing / depository receipts / global shares Cost of capital / Expected returns Change in covariance structure of returns

affecting portfolio risk / benefits of diversification

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What is the overall effect?What is the overall effect?

Decrease in expected returns Higher correlation between asset markets More markets for investment Increase in the types of marketed securities Potential synchronization of business cycles Increased policy coordination

Net effect?

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International Diversification 2: International Diversification 2: Time-Varying CorrelationsTime-Varying Correlations

1872-2000 US France GermanyUK 0.265 0.351 0.143US 0.163 0.083France 0.189

Average correlation =0.199Integration, 1872-1914, 1972-2000 US France GermanyUK 0.345 0.467 0.369US 0.301 0.284France 0.520

Average correlation =0.381Segmentation, 1914-1971 US France GermanyUK 0.193 0.311 0.097US 0.101 0.041France 0.135

Average correlation =0.146

1. Correlations between countries are highly time-varying.

2. Result of Solnik can be due to segmentation period used.

3. There is striking similarities between end of XIX and XX centuries.

(Based on Goetzmann et. al. NBER W8612)

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The Role of Emerging MarketsThe Role of Emerging Markets

Expand the investment opportunity set

Are imperfectly correlated with existing markets

What is the relative contribution of changing correlations and evolution in the investment opportunity set for diversification benefits?

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Decomposing the Benefits of International Diversificationequally-weighted portfolio variance / average market variance

0.0

0.2

0.4

0.6

0.8

1.0

1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Rat

io p

ortf

olio

vol

atili

ty /

aver

age

mar

ket

vola

tilit

y

Core Countries (limited diversification)

Average four countries

All Countries (unlimited diversification)

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Eiling-Gerard 07:Eiling-Gerard 07:

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Globalization: Globalization: How do Correlations Change?How do Correlations Change?

Does location of a firm matter?

Industry membership may become more important

What happens to residual risk?

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Bottom Line: International Diversification Bottom Line: International Diversification Does Not Work as it Used to...Does Not Work as it Used to...

•Trade barriers disappear (NAFTA, EU, ASEAN, etc.)•Globalization of Business Enterprises,•Wave of intra-industry M&A (incl. cross-border M&A)

“…active portfolio managers will have increasing difficulty addingvalue by using a top-down strategy through European countryallocation.” (Freiman, 1998)

New Holy Graal: Industry Diversification

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Industry vs. International DiversificationIndustry vs. International DiversificationAPT-style estimation:

Ri=i(t)+ijijNatlMarketIndexj+ ijijGlobalIndustryIndex+ i

where ij ()=1 if firm i belongs to country (industry) j. This can be further simlified as

Ri=i(t)+ijij(t)+ ikik (t) + i

2-stage estimation as in Fama-McBeth procedure (time-series + cross-section)gives us time-series of prices of national and industry risk. One can interpret i(t)+ij (t) is return on geographically diversified industry portfolio. i(t)+ij(t) is return on industry-diversified national portfolio.

Small Print: (a) We miss all “other” firm characteristics-size, b/m, dividend payout ratio, leverage, etc. (b)We also assume that securities in country i have same exposure to domestic and foreign factors. (c) We do not address Ericsson problem. (d) Cavaglia et. al. (2001) consider 35 industries in 21 countries.

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Industry vs. International Diversification(2)Industry vs. International Diversification(2)We can use MAD (mean absolute deviation) statistics (due to Rouwenhorst):

MAD(t)=i(t-1)|ij(t)|

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Random diversification: Random diversification: international vs. industrialinternational vs. industrial

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How non-diversifiable risk changes How non-diversifiable risk changes with time (with time (CampbellCampbell et al et al, , 2000)2000)?? It increases... When before you

were OK with 10 stocks, now you have to use 50.

Why?– Younger

companies are on the market

– Internal capital markets are gone

– Competition– Institutions

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What about Sweden?What about Sweden?Sternbrink-Tengvall thesis: Swedish data

1988-2001.Firm-level volatility remains roughly the

same.Outside very large firms, market volatility

remains the same. With ERICSSON-likes it actually increases a bit.

Industry-level volatility increases for all industries. Market Industry Firm

1988-2001 0.233 0.156 0.6111988-1993 0.196 0.089 0.7151997-2001 0.285 0.220 0.494

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European Equity MarketsEuropean Equity Markets

Increased industry importance

Countries become less important

– Why does it still matter?

Residual risk is increasing: cost of not being diversified is going up

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Global Linkages of Other MarketsGlobal Linkages of Other Markets

Bond markets– Interest rate correlations have increased in Europe

before EMU– Reduction of Bond market diversification

Real estate markets– Non-tradable goods– But linked through

business cycle correlations Interest rate correlations exchange rate correlations

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International Financial LinkagesInternational Financial Linkages- Summary -- Summary -

There is reason to believe that international financial linkages are becoming stronger.– World is not yet a global place

Expansion of investment opportunity set should give some compensation for investors who seek diversification– Number of markets– Expansion of tradable assets: new markets /

securities

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Do you really have to go abroad to achieve Do you really have to go abroad to achieve international diversification? (based on international diversification? (based on Diermeier-Solnik 2001)Diermeier-Solnik 2001)

No, It is enough to invest into companies that do business abroad.

Ri=i+iLocInd+ijIndj+ ijCurrencyj+ i

ij is “exposure” to foreign market risk, ij is “exposure” to foreign currency risk.

Adjusted R2

Country

International Market

Exposure

Foreign Currency Exposure

France 0.13 0.06Germany 0.31 0.09Italy 0.40 0.00Japan 0.22 0.24Netherlands 0.49 0.19Switzerland 0.32 0UK 0.22 0.17US 0.02 0.02

Exposure is explained well by % of foreign sales,

ij =i+ijForSalesj

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Word of caution:Word of caution:

“Trust companies…have reckoned that by a wide spreading of their investment risk, a stable revenue position could be maintained, as it was not to be expected that all the world would go wrong at the same time. But the unexpected has happened, and every part of the civilized world is in trouble…”

Chairman of Alliance Trust Company (1929)

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Word of caution II:What is teh Word of caution II:What is teh meaning of asset class?meaning of asset class?

Campbell,Sunderam,Viceira 2007:

Nominal t-bonds: Risk premia changes over time. In 80-es high correlation with S&P, in other periods corr is negative...

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Optimal portfolio of riskless and risky Optimal portfolio of riskless and risky assets:assets:

What is ”riskless asset”? No default risk No inflation risk No reinvestment risk

What is expected value and std. dev. of returns of the portfolio with risky and riskless asset?

)()(

)(

)1()(

PS

fSfP

SSP

fSSf

SSfSP

rr

rrE

wr

rwr

wrwrE

rf

Exp

. Ret

urn

0

s

s

Stock100%Stock

50%

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Capital Allocation LineCapital Allocation Line Meaning of CAL’ slope: Revard to variability Combining portfolio of risky assets and rf:

– Tangency portfolio (T) is the optimal risky portfolio to mix with T-bills

– Portfolios on (rf,T): positive fractions of risky portfolio and T-bills

– Portfolios on (T,) : go short in T-bills

0

5

10

15

20

25

15 17 19 21 23 25 27 29 31 33 35

Portfolio Risk (Std. Dev),%

Mea

n P

ortf

olio

Ret

urns

, %

rf

CAL=Capital Allocation Line

CAL1

CAL2

Portfolio A (100% stock, 0% risk free asset):Mean Return=18%, Std Dev=26%rf=5%Slope of CAL=(18-5)/26=0.5

T

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How to choose the ”right” portfolio?How to choose the ”right” portfolio?

0

2

4

6

8

10

12

14

16

18

15 16 17 18 19 20 21 22 23 24

Optimal portfolio for Risk-Averse investor

Optimal portfolio for Risk-Tolerant investor

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Separation PropertySeparation Property

One can see portfolio selection problem as a two-step routine:– Finding optimal risky portfolio (meat)– Adding enough risk-free asset to make the

dish eatable.

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Non traded riskNon traded riskss Human capital and death insurance Investment in residence Other consumption needs: saving for

retirement and life insurance Liabilities: B/S optimization You must consider that these are part and

parcel of your portfolio, but with immutable weights

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Human CapitalHuman Capital Most of the ”normal” individual wealth is in the form

of HUMAN CAPITAL. Assume that human capital supply (willingness to

work) is flexible and tradeable. Value of future cash flow decreases with time.

Share of stocks will go down with time The higher is the riskiness of human capital, the less is

the willingness to invest in stock Strong effect on portfolio decisions. Real estate can amplify riskiness of human capital

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Normative multi-period AA: theoryNormative multi-period AA: theory

One risk-free asset (return r) and n risky assets with e=E[R] and var-covar matrix V.

Investor’s consumption-investment problem:

Constant relative risk aversion (CRRA) utility:

1'

1

,1

,

~1

~ ..

,...,, maxmax

tttttt

T

t

t

wCTtt

wC

rCWWts

CUECCCUEtttt

Rw1w

1 ,ln

1,0 ,1)(

1

C

CCU

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Optimal dynamic portfolios:Optimal dynamic portfolios:

M is mean-variance portfolio H is hedge portfolio against changes in

variable x. H does not matter for non-stochastic

opportunity set or log –utility function.

,...)(', , 111

x

CC

C

rE

WCW

xC

WCWU

UBA

ννVH1RVM

HMHMw

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ConstraintsConstraints Liquidity Regulations: public or self imposed

SEC Pension funds: Employee Retirement Income Security Act

(ERISA); European directives no more than 5% in any publicly traded company Mostly domestic assets

Mutual funds: No borrowing. Association for Investment Management and Research (AIMR)

Taxes Unique needs: internal restrictions

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Standard Deviation (Risk)

Expected Return

0.0 42.03.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0 33.0 36.0 39.02.0

19.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

15.0

16.0

17.0

18.0

S&P500

IA Small Stocks

Russell 2000

MSCI Europe

MSCI Pacific TR

IA Corporate

IA 20Yr GvtIA 5YR Gvt

IA 1 Year GvtNon-US LT Gvt

30 Day TBILL

Gold

CRSP MidCap

Real Estate

S&P500 (20.0%)

IA Small Stocks (7.5%)MSCI Europe (19.7%)

MSCI Pacific TR (7.5%)

IA 5YR Gvt (4.5%)

IA 1 Year Gvt (20.0%)

Real Estate (20.0%)

S&P500 (51.8%)

IA Small Stocks (2.6%)

MSCI Europe (11.9%)

MSCI Pacific TR (10.2%)Real Estate (23.5%)

Frontier with constraintsFrontier with constraints

Source:Ibbotson Assoc.Portfolios with =20%No short salesB: 20% max

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Time ”Diversification”Time ”Diversification” Can you reduce risk by

holding assets longer?– Uncertainty in annual

rate of return goes down

– BUT!!! Uncertainty of total returns goes up

Position 56

S&P500 (37.6%)

IA Small Stocks (23.2%)

MSCI Europe (18.7%)MSCI Pacific TR (12.5%)

Real Estate (8.1%)

Time

Compound Annual ReturnPosition 56

Return Percentiles

Nov2001

Nov2020

Dec2005

Dec2010

Dec2015

-20.0%

60.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

95th Percentile Expected Value 5th Percentile

Time

Wealth (USD)Position 56

Wealth Percentiles

Nov2000

Nov2020

Dec2005

Dec2010

Dec2015

1

50

1

10

95th Percentile Expected Value 5th Percentile

Source: Ibbotson Assoc.R=15%, =20%

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Optimal diversification: condition Optimal diversification: condition of optimality (w/o constraint)of optimality (w/o constraint)

How can you tell whether a portfolio p is well diversified or efficient?

For each security i, E(Ri) - r must be lined up with cov(Ri,Rp) or, equivalently, with:

i = cov(Ri,Rp)/var(Rp)

i or

cov(Ri,Rp)

E(Ri) - r

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Risk accountingRisk accounting(simple “Value at Risk”)(simple “Value at Risk”)

Beta is just a re-scaled covariance:

here i refers to return on security i p refers to return of portfolio

p

pipi R

RRRR

var

,cov;

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Risk accountingRisk accounting Risk accounting:

– share of standard deviation measured by means of beta of each security with respect to portfolio return:

Interpretation of beta relative to investor’s portfolio :– If an investment item has a beta equal to 2 and if 1% of the total

portfolio value is invested there, then that investment accounts for 2% of the total risk (standard deviation) of the portfolio. (This the basis of “Value at Risk” scheme)

– It is not variance or stdev of investment item that counts– Only “systematic” risk matters

..332211 xxxRR pp

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Optimal diversification: condition Optimal diversification: condition of optimalityof optimality

If that condition is not satisfied, the composition of portfolio p must be changed:

i > 0, increase weight of security ii < 0, decrease weight of security i

piii RRrRE ,cov

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Risk and returnRisk and return

Recall: if an investment item has a beta equal to 2 with respect to portfolio and if 1% of the total portfolio value is invested there, then that investment accounts for 2% of the total risk (standard deviation) of the portfolio

In a portfolio that is properly constructed, all the investment items should plot along a (positively sloped) line, so that each bit of risk receives its proportionate reward.

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Attention: Default is not in the picture!!!Attention: Default is not in the picture!!!

Source: Moody’s

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Practicality: Estimation RiskPracticality: Estimation Risk Óptimization results are usually

suffering from:– Huge short positions in many assets in

no-constraint case.

– “Corner” solutions with zero positions in may assets if constraints are imposed.

– Huge positions in obscure markets with small cap

– Large shifts in positions when exp. returns or covariances changes just a bit…

All of those are coming from one common cause: difficulties in estimation of expected returnsexpected returns.

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Conclusion:Conclusion: SAA is first-order approximation when you determine

the structure of investment portfolio. Diversification over different asset classes, industries,

countries should be considered. It is based on sound statistical ideas, but practical

implementation may be plagued by instability of underlying economic processes and difficulties in estimation expected returns.

SAA does not utilize effectively wealth of economic information. Tactical asset allocation make an attempt to fix that.