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Strategic Asset Allocation session 1

Strategic Asset Allocation session 1. Andrei Simonov. Agenda. Introduction, Course Outline, Requirements, Resources Reminder: SAA Definitions Historical Records of Returns on different securities Crisis in Investment Industry. Introduction. The field of Finance and Investments

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Strategic Asset Allocation session 1

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

  2. Agenda • Introduction, Course Outline, Requirements, Resources • Reminder: SAA • Definitions • Historical Records of Returns on different securities • Crisis in Investment Industry Strategic Asset Allocation

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

  4. 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

  5. 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 TA know by the end of the week) Strategic Asset Allocation

  6. 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

  7. My assumptions about you: • You know and understand basic regression analysis (what is R2, statistical significance, etc.) • You remember conditions of optimality from Econ 101 • You remember basics from Finance I • You are willing to learn... Strategic Asset Allocation

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

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

  16. Strategic Asset Allocation

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. Strategic Asset Allocation

  23. 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

  24. 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

  25. Random diversification: international vs. industrial Strategic Asset Allocation

  26. Eiling, Gerard, Hillion & de Roon (2009) • Adding currency deposits to industry portfolios is a winning recepie. Our conditional results show that international equity returns are primarily driven by industry and currency risk factors…The dominance of global industry factors over country factors is in line with the seven developed countries in our sample being among the most integrated equity markets in the world. Finally, we find that currency returns significantly improve the mean-variance efficiency of country, industry and world market portfolio returns. Strategic Asset Allocation

  27. How non-diversifiable risk changes with time (Campbell et al, 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 Strategic Asset Allocation

  28. Do you really have to go abroad to achieve international diversification? (based on Diermeier-Solnik 2001) No, It is enough to invest into companies that do business abroad. Ri=ai+biLocInd+SgijIndj+ SdijCurrencyj+ ei gij is “exposure” to foreign market risk, dij is “exposure” to foreign currency risk. Exposure is explained well by % of foreign sales, gij =li+mijForSalesj Strategic Asset Allocation

  29. 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) Strategic Asset Allocation

  30. Strategic Asset Allocation

  31. Non traded risks • 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 Strategic Asset Allocation

  32. Human 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 Strategic Asset Allocation

  33. Normative 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: Strategic Asset Allocation

  34. 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. Strategic Asset Allocation

  35. Constraints • 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 Strategic Asset Allocation

  36. Frontier with constraints Source:Ibbotson Assoc. Portfolios with s=20% No short sales B: 20% max Strategic Asset Allocation

  37. 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 Source: Ibbotson Assoc. R=15%, s=20% Strategic Asset Allocation

  38. Practicality: 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 returns. Strategic Asset Allocation

  39. Another example (GS 2003): • Here are forecasts given by “Wall Street Protagonist” (Columns 1 and 2) and set of portfolio weights that are generated by it. Asset Pricing Models

  40. Equilibrium and individual asset’ expected return • From previous section one can expect that ERP is between 4 and 6% and is fairly stable with time • One can make forecast for individual assets that are different from long term premium. • But by forecasting one asset class, we are implicitly making forecast for other asset classes as well. Asset Pricing Models

  41. Practicality: How to express views? • Method is due to Black & Litterman (Goldman Sachs). The core themes: equilibrium returns and views. • Investors normally have views/preferences. They are NOT incorporated into optimization process. • Views=mathematically expressed preferences of individual investors. Asset Pricing Models

  42. Equilibrium optimal portfolio • Imagine that the investor thin that US is still in recession. Thus, stocks will perform badly, and bonds will perform OK. • Mathematically, it is equivalent to assuming that bonds will go up 0.8%, and stocks will drop 2.5% • Result: see Table 8: Asset Pricing Models

  43. Updating of discrete probabilities 1. We have a probability estimate for event H: prior probability P(H) 2. New information D is gained 3. Update the estimate using Bayes’ theorem: posterior probability P(H|D) Asset Pricing Models

  44. The Bayes’ theorem The updating is done using the Bayes’ theorem: Asset Pricing Models

  45. Example: Using Bayes’ theorem 1,5 % of the population suffer from schizophrenia  P(S) = 0.015 (prior probability) Brain atrophy is found in • 30 % of the schizophrenic  P(A|S) = 0.3 • 2 % of normal people  P(A|S) = 0.02 If a person has brain atrophy, the probability that he is schizophrenic (posterior probability) is: Picture: Clemen s. 250 Figure: Posterior probability with different prior probabilities. Asset Pricing Models

  46. Updating of continuous distributions Choose a theoretical distribution, P(X=x|), for the physical process of interest. Assess uncertainty about parameter : prior distribution, f() Note: Uncertainty about X has two parts: 1. Due to the process itself, P(X=x|). 2. Uncertainty about , f(), later updated to f(|x1). Observe data x1 Update using Bayes’ theorem: posterior distribution of , f(|x1) Asset Pricing Models

  47. Updating of continuous distributions Bayes’ theorem for continuous  : • f(x1|) is called the likelihood function of  with a given observed data x1. • In most cases the posterior distribution can not be calculated analytically, but must be solved numerically. Asset Pricing Models

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