Strategic Asset Allocation session 1 Andrei Simonov Strategic
- Slides: 76
Strategic Asset Allocation session 1 Andrei Simonov Strategic Asset Allocation 1 11/26/2020
Introduction l 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. l 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 2 11/26/2020
Overview of the course l l l l Strategic Asset Allocation Asset Pricing Models Tactical Asset Allocation Volatility & Skewness Information Processing by markets Market Neutral Investments Behavioral Finance Strategic Asset Allocation 3 11/26/2020
Resources and requirements: l l Courseweb page. I put some stuff on my page, but links are on courseweb Articles (package+web site) l l l 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 4 11/26/2020
Cases l 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. . . l Ideal case report is similar to consulting report: – – – l l 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 5 11/26/2020
My assumptions about you: You know and understand basic regression analysis (what is R 2, statistical significance, etc. ) l You remember conditions of optimality from Microecon. Course l You remember basics from prev. Finance courses l You are willing to learn. . . l Strategic Asset Allocation 6 11/26/2020
Agenda l l l Individual’s preferences, utility function Measurement of risk by variance Diversification – – l l A bit of math Industry diversification International diversification Latest evidence Shortcut to math: Excel! Risk accounting Strategic Asset Allocation 7 11/26/2020
Assets l l Real vs. Financial assets Role of financial assets – Consumption Timing – Allocation of Risk – Separation of Ownership l Various financial assets – – l Money market Fixed-income Equities Derivatives Trading the assets – types of market organizations – types of orders you can place Strategic Asset Allocation 8 11/26/2020
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 9 11/26/2020
Where to get data? l l Easiest: web search engine, financial sites (Yahoo, Infoseek, msn, etrade-SE, CNNfn, etc. ) Bulk suppliers – Bloomberg, Data. Stream, CRSP, Reuters, Trust, Commodity Systems, Inc. , Securities Data Corp. , etc. . . l l l Dividends Volume Splits Strategic Asset Allocation 10 11/26/2020
First Approximation Model of Investors’ Behavior: Assumptions: Single holding period l Investors are risk-averse l Investors are ”small” l The information about asset payoffs is common knowledge l Assets are in unlimited supply l Assets are perfectly divisible l No transaction cost l Wealth W is invested in assets l Strategic Asset Allocation 11 11/26/2020
Investors´ preferences l l Attitude to risk Time horizon (do not confuse with holding period) Non-traded risks (liabilities, labor income, human capital) Constraints Strategic Asset Allocation 12 11/26/2020
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 13 11/26/2020
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 14 11/26/2020
Investor’s preferences: Meanvariance framework l Representation by utility function of wealth W – u’(W)>0, u’’(W)<0 l Taylor Expansion: l Applying Expectations operator: l Simplest utility function is quadratic: u=W-0. 5 b. W 2 l Problem: satiation Arbitrary preferences: Asset returns are distributed as multivariate normal A dominates B if E(r. A) (>) E(r. B) and s. A <( ) s. B l l Strategic Asset Allocation 15 11/26/2020
Indifference curves l l l 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 16 11/26/2020
Measuring risk by variance l Variance – definition: probability weighted squared deviations from the expected value – based on probability distribution l Any drawbacks of this measure? – People do not behave that way (read Odean): l l l Overconfidence (“wrong” probability distribution) Regret (distinguish “gains” from “losses”) Should we use semi-variance? – Particularly in case of delegated portfolio management? Strategic Asset Allocation 17 11/26/2020
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 18 11/26/2020
The same story: Nasdaq vs. S&P 500 Strategic Asset Allocation 19 11/26/2020
Indices l Uses – Track average returns of Asset Class – Comparing performance of managers – Base of derivatives l Factors in constructing or using an Index – – Representative? Broad or narrow? How is it constructed? Subjectivity Factor (Bethleham Steel) Strategic Asset Allocation 20 11/26/2020
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 21 11/26/2020
The measurement of risk: Compare frequency distribution of bond rates of return and rates of returns of stocks Source: Ibbotson Assoc. Strategic Asset Allocation 22 11/26/2020
The measurement of risk by variance (example: large-c. stocks from frequency table) Strategic Asset Allocation 23 11/26/2020
Optimal diversification: the ingredients Excess expected rate of return for each security i (organized into vector) l Variance of rate of return for each security i l Covariances of rate of return of security i with security j (organized into matrix) l Strategic Asset Allocation 24 11/26/2020
Optimal diversification (2) l What is covariance between x and y? Estimated as: l 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 l l Strategic Asset Allocation 25 11/26/2020
Example of calculation from table: stocks and bonds Strategic Asset Allocation 26 11/26/2020
Math of mean-variance optimization l Assume you have 1 SEK to invest into stock (m. S, s. S) and long-term bond (m. B, s. B). Strategic Asset Allocation 27 11/26/2020
Try to do the same with 10 assets… Strategic Asset Allocation 28 11/26/2020
Efficient Frontier Strategic Asset Allocation 29 11/26/2020
Using Excel to optimize l Lord gave us Microsoft. Use it! Use “Solver”. Can have many l Set up row or column of portfolio weights {xi} Variance: compute xi cov(Ri, Rj) xj l securities, add constraints. – Sum both ways to get portfolio variance l Expected return: xi E(Ri) – Or, if there is riskless asset, xi [E(Ri) – r] – Sum to get portfolio expected return l 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 , l under constraint that portfolio weights sum to 1 (in the absence of riskless asset) and possibly other constraints. Strategic Asset Allocation 30 11/26/2020
Example of spreadsheet Strategic Asset Allocation 31 11/26/2020
Random diversification: Sharpe diagram Portfolio risk approaches the average covariance between assets when the number of assets gets large. Strategic Asset Allocation 32 11/26/2020
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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 35 11/26/2020
History of Diversification l First Mutual Fund: Eendracht Maakt Magt (1774) l l l l l 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 36 11/26/2020
Diversification: 18 th Century Mutual Funds l In the portfolio construction the fund “will observe as much as possible an equal proportionality” l “Because nothing is completely certain, but subject to fluctuations, it is dangerous to allocate all capital to a single security” l “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 37 11/26/2020
Globalization and Financial Linkages l Common wisdom is that globalization and integration of markets accentuates financial linkages (correlations) – – – l 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 38 11/26/2020
Globalization and Financial Linkages l l Expansion of investment opportunities Lowering of transactions costs – Trade where costs are lowest – Competition among exchanges – Cross-listing / depository receipts / global shares l l Cost of capital / Expected returns Change in covariance structure of returns affecting portfolio risk / benefits of diversification Strategic Asset Allocation 39 11/26/2020
What is the overall effect? l l l 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 40 11/26/2020
International Diversification 2: Time-Varying Correlations 1. Correlations between countries are highly timevarying. 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 W 8612) Strategic Asset Allocation 42 11/26/2020
The Role of Emerging Markets l Expand the investment opportunity set l Are imperfectly correlated with existing markets l What is the relative contribution of changing correlations and evolution in the investment opportunity set for diversification benefits? Strategic Asset Allocation 43 11/26/2020
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Globalization: How do Correlations Change? l Does location of a firm matter? l Industry membership may become more important l What happens to residual risk? Strategic Asset Allocation 47 11/26/2020
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 48 11/26/2020
Industry vs. International Diversification APT-style estimation: S Ri=ai(t)+ dijbij. Natl. Market. Indexj+ Sd(1)ijgij. Global. Industry. Index+ ei where dij (d(1))=1 if firm i belongs to country (industry) j. This can be further simlified as S Ri=ai(t)+ dijbij(t)+ Sd(1)ikgik (t) + ei 2 -stage estimation as in Fama-Mc. Beth 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 49 11/26/2020
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 50 11/26/2020
Random diversification: international vs. industrial Strategic Asset Allocation 51 11/26/2020
How non-diversifiable risk changes with time (Campbell et al, 2000)? l l l 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 52 11/26/2020
European Equity Markets l Increased industry importance l Countries become less important – Why does it still matter? l Residual risk is increasing: cost of not being diversified is going up Strategic Asset Allocation 53 11/26/2020
Global Linkages of Other Markets l Bond markets – Interest rate correlations have increased in Europe before EMU – Reduction of Bond market diversification l Real estate markets – Non-tradable goods – But linked through l l l business cycle correlations Interest rate correlations exchange rate correlations Strategic Asset Allocation 54 11/26/2020
International Financial Linkages - Summary l There is reason to believe that international financial linkages are becoming stronger. – World is not yet a global place l Expansion of investment opportunity set should give some compensation for investors who seek diversification – Number of markets – Expansion of tradable assets: new markets / securities Strategic Asset Allocation 55 11/26/2020
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. S S Ri=ai+bi. Loc. Ind+ gij. Indj+ dij. Currencyj+ 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+mij. For. Salesj Strategic Asset Allocation 56 11/26/2020
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 57 11/26/2020
Optimal portfolio of riskless and risky assets: l What is ”riskless asset”? l l l What is expected value and std. dev. of returns of the portfolio with risky and riskless asset? Stock Exp. Return l No default risk No inflation risk No reinvestment risk rf 0 Strategic Asset Allocation ms Stock 50% 100% ss 58 11/26/2020
Capital Allocation Line l l 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 T Strategic Asset Allocation 59 11/26/2020
How to choose the ”right” portfolio? Strategic Asset Allocation 60 11/26/2020
Separation Property l 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. Strategic Asset Allocation 61 11/26/2020
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 62 11/26/2020
Human Capital l l l 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 63 11/26/2020
Normative multi-period AA: theory One risk-free asset (return r) and n risky assets with e=E[R] and var-covar matrix V. l Investor’s consumption-investment problem: l l Constant relative risk aversion (CRRA) utility: Strategic Asset Allocation 64 11/26/2020
Optimal dynamic portfolios: M is mean-variance portfolio l H is hedge portfolio against changes in variable x. l H does not matter for non-stochastic opportunity set or log –utility function. l Strategic Asset Allocation 65 11/26/2020
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 66 11/26/2020
Frontier with constraints Source: Ibbotson Assoc. Portfolios with s=20% No short sales B: 20% max Strategic Asset Allocation 67 11/26/2020
Time ”Diversification” l 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 68 11/26/2020
Risk accounting (simple “Value at Risk”) l Beta is just a re-scaled covariance: here i refers to return on security i p refers to return of portfolio Strategic Asset Allocation 69 11/26/2020
Risk accounting l Risk accounting: – share of standard deviation measured by means of beta of each security with respect to portfolio return: l 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 Strategic Asset Allocation 70 11/26/2020
Optimal diversification: condition of optimality (w/o constraint) How can you tell whether a portfolio p is well diversified or efficient? l For each security i, E(Ri) - r must be lined up with cov(Ri, Rp) or, equivalently, with: i = cov(Ri, Rp)/var(Rp) E(R ) - r l i Strategic Asset Allocation i or cov(Ri, Rp) 71 11/26/2020
Optimal diversification: condition of optimality l If that condition is not satisfied, the composition of portfolio p must be changed: i > 0, increase weight of security i l i < 0, decrease weight of security i l Strategic Asset Allocation 72 11/26/2020
Risk and return l l 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. Strategic Asset Allocation 73 11/26/2020
Attention: Default is not in the picture!!! Source: Moody’s Strategic Asset Allocation 74 11/26/2020
Practicality: Estimation Risk l 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… l All of those are coming from one common cause: difficulties in estimation of expected returns Strategic Asset Allocation 75 11/26/2020
Conclusion: l l 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. Strategic Asset Allocation 76 11/26/2020
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