Strategic Asset Allocation session 1

1. Strategic Asset Allocation session 1 Andrei Simonov Strategic Asset Allocation

2. 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 June one should know what does that mean to be investment professional. Strategic Asset Allocation

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

4. 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. Strategic Asset Allocation

5. Cases • 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. Strategic Asset Allocation

6. 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 prev. Finance courses • You are willing to learn... Strategic Asset Allocation

7. Agenda • 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 Strategic Asset Allocation

8. Assets • 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 Strategic Asset Allocation

9. Equity • 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) Strategic Asset Allocation

10. 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... • Dividends • Volume • Splits Strategic Asset Allocation

11. First Approximation Model of Investors’ Behavior: Assumptions: • Single holding period • Investors are risk-averse • Investors are ”small” • The information about asset payoffs is common knowledge • Assets are in unlimited supply • Assets are perfectly divisible • No transaction cost • Wealth W is invested in assets Strategic Asset Allocation

12. Investors´ preferences • Attitude to risk • Time horizon (do not confuse with holding period) • Non-traded risks (liabilities, labor income, human capital) • Constraints Strategic Asset Allocation

13. Risk Aversion Risk aversion: Reluctance to accept risk Why are people risk averse? Diminishing marginal utility of wealth. Utility from wealth U(w) Wealth Strategic Asset Allocation

14. Risk Aversion • Utility function of a risk-averse person satisfies: • U`(w) > 0 (Higher wealthHigher utility) • U``(w) < 0 (Diminishing marginal utility) • What does this imply for risk? • Consider this bet: Suppose you make $30,000 a year. Flip a coin. If heads, I give you another $30,000. If tails, I take your entire year’s salary. Will you take the bet? • Why not? Strategic Asset Allocation

15. Investor’s preferences:Mean-variance 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 sA <() sB Strategic Asset Allocation

16. Indifference 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 Strategic Asset Allocation

17. Measuring 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? Strategic Asset Allocation

18. 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) Strategic Asset Allocation

19. The same story:Nasdaq vs. S&P 500 Strategic Asset Allocation

20. Indices • 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) Strategic Asset Allocation

21. Examples: Stock and Bond Indices • 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 Strategic Asset Allocation

22. The measurement of risk:Compare frequency distribution of bond rates of return and rates of returns of stocks Source: Ibbotson Assoc. Strategic Asset Allocation

23. The measurement of risk by variance (example: large-c. stocksfrom frequency table) Strategic Asset Allocation

24. Optimal diversification: the ingredients • Excess expected rate of return for each security i (organized into vector) • Variance of rate of return for each security i • Covariances of rate of return of security i with security j (organized into matrix) Strategic Asset Allocation

25. Optimal diversification (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 Strategic Asset Allocation

26. Example of calculation from table: stocks and bonds Strategic Asset Allocation

27. Math of mean-variance optimization • Assume you have 1 SEK to invest into stock (mS,sS) and long-term bond (mB,sB). Strategic Asset Allocation

28. Try to do the same with 10 assets… Strategic Asset Allocation

29. Efficient Frontier Strategic Asset Allocation

30. Using 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. Strategic Asset Allocation

31. Example of spreadsheet Strategic Asset Allocation

32. Random diversification: Sharpediagram Portfolio risk approaches the average covariance between assets when the number of assets gets large. Strategic Asset Allocation

34. Strategic Asset Allocation

35. Henry 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. Strategic Asset Allocation

36. History 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 Strategic Asset Allocation

37. Diversification: 18th 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” Strategic Asset Allocation

38. Globalization and Financial Linkages • 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 Strategic Asset Allocation

39. Globalization and Financial Linkages • 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 Strategic Asset Allocation

40. 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? Strategic Asset Allocation

42. International Diversification 2: Time-Varying Correlations • Correlations between countries are highly time-varying. • Result of Solnik can be due to segmentation period used. • There is striking similarities between end of XIX and XX centuries. • (Based on Goetzmann et. al. NBER W8612) Strategic Asset Allocation

43. The 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? Strategic Asset Allocation

45. Strategic Asset Allocation

47. Globalization: How do Correlations Change? • Does location of a firm matter? • Industry membership may become more important • What happens to residual risk? Strategic Asset Allocation

48. Bottom Line: International Diversification 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 adding • value by using a top-down strategy through European country • allocation.” (Freiman, 1998) New Holy Graal: Industry Diversification Strategic Asset Allocation

49. Industry vs. International Diversification APT-style estimation: Ri=ai(t)+SdijbijNatlMarketIndexj+ Sd(1)ijgijGlobalIndustryIndex+ ei where dij (d(1))=1 if firm i belongs to country (industry) j. This can be further simlified as Ri=ai(t)+Sdijbij(t)+ Sd(1)ikgik (t) + ei 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 ai(t)+bij (t) is return on geographically diversified industry portfolio. ai(t)+gij(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. Strategic Asset Allocation

50. Industry vs. International Diversification(2) We can use MAD (mean absolute deviation) statistics (due to Rouwenhorst): MAD(t)=Swi(t-1)|bij(t)| Strategic Asset Allocation