Modern Portfolio Theory and Practice


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My experience applying the ideas of modern portfolio theory.

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Modern Portfolio Theory and Practice

  1. 1. Modern Portfolio Theory and Practice -or- Get Rich Slow -or- Why the Real Mutual Fund Scandal is Legal David Roodman Summer 2007
  2. 2. Lesson 1: Do save/invest <ul><li>Have 3-6 months of expenses in cash </li></ul><ul><ul><li>Split between money market and short-term bond fund </li></ul></ul><ul><li>Save in tax-favored vehicles early and often </li></ul><ul><ul><li>For savings made early in life, the subsidy is large </li></ul></ul><ul><ul><li>A window of opportunity closes every 12/31. </li></ul></ul><ul><li>If you lack 401(k)/403(b) access, favor Roths. </li></ul>
  3. 4. Modern Portfolio Theory (Harry Markowitz, 1952) <ul><li>Universe of investible securities characterized by 3 sets of numbers: </li></ul><ul><ul><li>Expected return of each security (say, per month) </li></ul></ul><ul><ul><li>Standard deviation of future (monthly) returns </li></ul></ul><ul><ul><li>A correlation matrix for expected returns. </li></ul></ul><ul><li>Investor’s task: choose portfolio that maximizes expected total return for a given level of “risk” (standard deviation of overall portfolio return) </li></ul>
  4. 5. MPT, cont’d <ul><li>Diversification principle: </li></ul><ul><ul><li>Suppose Netzoot and Zipcom are tech stocks that have an expected return of 10%/year and an s.d. of return of 4%, and have an expected correlation of 0.5. Then a 50/50 portfolio of the two will have: </li></ul></ul><ul><ul><ul><li>expected return = 10% </li></ul></ul></ul><ul><ul><ul><li>s.d. of return =3.47% (    of portfolio=3/4 of   of either) </li></ul></ul></ul><ul><ul><ul><li>Same return, lower risk! </li></ul></ul></ul><ul><ul><li>90/10 bond/stock portfolio less risky than 100% bond </li></ul></ul><ul><li>Lesson 2: Diversify . Own some of everything. </li></ul>
  5. 6. Can diversification eliminate risk? <ul><li>No. There is an irreducible component of variation in returns that is shared by all stocks. No amount of diversification will eliminate it because all stocks have it: market risk. Stocks tend to rise and fall together. </li></ul><ul><li>Model: r IBM =  +  r market    constants </li></ul><ul><li>In theory,  embodies the only component of risk investors care about: systemic or market risk. Variation not explained by this model, idiosyncratic risk, does not matter because it washes out in a diversified portfolio. </li></ul>
  6. 7. MPT, cont’d <ul><li>Markowitz developed algorithm to pick optimal portfolio for given level of risk </li></ul><ul><li>We don’t know expected return, s.d. of return, future correlations. </li></ul><ul><li>Can try using past values as estimators. </li></ul><ul><li>Applied his algorithm to this information. </li></ul><ul><li>Didn’t work so well: weird portfolios or unremarkable returns. </li></ul>
  7. 8. Efficient market hypothesis (Eugene Fama, 1965, Chicago dissertation) <ul><li>Market is a “random walk”: “efficient” </li></ul><ul><li>“ Efficient” does not mean prices are correct. </li></ul><ul><li>Rather: all available information is already incorporated into stock prices </li></ul><ul><li>Changes in prices caused only by unpredictable arrivals of new information, or pure noise in trading </li></ul><ul><li>Beating the market is impossible except by chance </li></ul><ul><li>“ Research” by stock & bond analysts is a waste of time </li></ul><ul><li>Monkeys throwing darts at stock page do as well on average </li></ul>
  8. 9. EMH, cont’d <ul><li>Backed by lots of empirical evidence that investors/mutual funds rarely beat the market consistently—no more than should happen by chance </li></ul><ul><li>Think of it this way: ~90% of trading by large institutions with same information and methods. Can’t all be above average. </li></ul><ul><li>Lesson 3: Practice humility </li></ul>
  9. 10. Daily % change in AT&T stock vs. previous % change, ~1998-2003
  10. 11. 3 forms of EMH <ul><li>Weak: all past market prices and data are reflected in securities prices today. Technical analysis useless. </li></ul><ul><li>Semistrong: all publicly available information is reflected. Fundamental analysis useless. </li></ul><ul><li>Strong: all information is reflected. Even insider information useless. </li></ul><ul><li>I believe it is prudent in general to invest as if all are true (unless you have inside information!) </li></ul>
  11. 12. Implications <ul><li>The investment advice industry is a huge waste. To a first approximation, it adds no value. Indeed, it reduces value by sucking out $ billions. </li></ul><ul><li>High-priced stock-pickers who work for “actively managed” mutual funds are mostly rip-offs for investors </li></ul><ul><li>Expense rate on good index fund: ~0.25% </li></ul><ul><li>On typical “active” fund: 0.75-2.0% </li></ul>
  12. 14. Why should they tell you? <ul><li>Fund companies with actively managed funds benefit from myth </li></ul><ul><li>Brokers get trading commissions </li></ul><ul><li>Money magazines carry fund ads </li></ul><ul><li>TV channels and web sites must pretend to relevance </li></ul><ul><li>Market imperfection: people don’t notice 1-2%/year expense when earnings are volatile or high, and documentation is in fine print </li></ul>
  13. 15. Lesson 4: minimize turnover <ul><li>When you or your fund manager buy and sell it: </li></ul><ul><li>Creates taxable capital gains (if in taxable account) </li></ul><ul><li>Incurs trading commissions </li></ul><ul><li>Incurs losses because of bid-ask spread (not counted in expense ratios) </li></ul>
  14. 16. DALBAR survey of investors, 1984-2002 <ul><li>Average investor’s return on stocks: 2.57%/year. Turns $1000 into $1620 </li></ul><ul><li>S&P 500: 12.22%/year: $8940 </li></ul><ul><li>Inflation: 3.14%/year </li></ul><ul><li>I.e., average investor turned $1000 into $900 after inflation </li></ul><ul><li>S&P 500 turned $1000 into $5000 after infl. </li></ul><ul><li>Partly expenses; partly performance chasing </li></ul><ul><li>Big scandal in a country with a looming retirement crisis! </li></ul>
  15. 17. <ul><li>Expenses: </li></ul><ul><li>Vanguard S&P 500 index fund: 0.18%/year </li></ul><ul><li>Calvert “socially responsible” U.S. equity fund (class C shares): 2.10%/year </li></ul><ul><li>Is this socially responsible? </li></ul>An indignant question
  16. 18. Capital Asset Pricing Model (Sharpe and others, ~1964) <ul><li>If every investor has all of Markowitz’s information about future returns and applies his algorithm, then in the equilibrium, all investors will split their $ between risk-free asset and the same portfolio of all other assets. </li></ul><ul><li>i.e., outside of cash holdings, everyone will have 1% IBM, 2% AT&T, etc. </li></ul><ul><li>Ergo, the market will be 1% IBM, 2% AT&T,…. </li></ul><ul><li>Ergo, everyone will own an index of the market. </li></ul>
  17. 19. Index mutual funds <ul><li>Sharpe’s model unrealistic, but helped create idea of index mutual funds </li></ul><ul><li>Commonsense ideas of diversification, humility, low turnover, and low cost argue for index funds </li></ul><ul><li>First ones started ~1973. Vanguard and State Street(?). </li></ul><ul><li>They don’t call me the Index guy for nothing. </li></ul><ul><li>Or: more generally, passive asset class investing </li></ul>
  18. 20. Interim conclusions <ul><li>Theoretical index fund covers all assets: foreign, domestic, stock, bond, housing </li></ul><ul><li>Real ones only cover subclasses </li></ul><ul><li>Lesson 5: Put your $ in a few very low-cost mutual funds, preferably index funds, covering all asset classes </li></ul><ul><li>Exact allocation that is best is a bit unclear because we do not believe Sharpe </li></ul><ul><li>Lesson 6: Obsess over expenses </li></ul><ul><li>Buy and hold. Minimize trading </li></ul><ul><li>Lesson 7: Exercise discipline. Never panic. </li></ul><ul><li>You will nearly match the market and beat most investors </li></ul>
  19. 21. Two things to ponder: 1. Risk vs. return <ul><li>Truism that the two go together </li></ul><ul><li>What is the evidence? </li></ul><ul><li>A generalization, not an iron law </li></ul><ul><li>There may be exceptions </li></ul><ul><li>No plausible theory says market will always accurately price risk since it is substantially unknowable and market itself creates price risk </li></ul>
  20. 22.   Geometric  From Malkiel, Random Walk Down Wall Street
  21. 23. Two things to ponder: 2. Herd behavior <ul><li>Bubbles and panics older than securities markets </li></ul><ul><ul><li>Dutch tulipmania in early 1600s </li></ul></ul><ul><li>Occur when people buy because the price has gone up, on the dangerous notion that past return predicts future return. </li></ul><ul><li>Buying causes appreciation, and vice versa… </li></ul><ul><li>Milder form: all actors unwittingly follow same strategy and reassured by results in short run—hedge funds today? </li></ul><ul><li>Don’t manias violate EMH? </li></ul>
  22. 24. Definitions <ul><li>Growth stocks: high-priced compared to current book value or earnings </li></ul><ul><li>Value stocks: opposite </li></ul><ul><li>Large-cap stocks: shares in big companies </li></ul><ul><li>Small-cap stocks: shares in small companies </li></ul><ul><li>Growth stocks called that because market evidently expects strong earnings growth </li></ul><ul><li>Value is a marketing euphemism? </li></ul>
  23. 25. Fama & French 1992 <ul><li>For each year in 1962-89, built simulated portfolios of U.S. stocks: growth, value, large, small, sorted by decile </li></ul><ul><li>3 deciles on value end beat 3 growth deciles 5%/yr </li></ul><ul><li>Good companies make bad investments and v.v. </li></ul><ul><li>Small beat large (not news) </li></ul><ul><li>Overall market return each year and small-large and value-growth return differences are factors </li></ul><ul><li>The 3 factors explain ~95% of the cross-sectional variation in mutual fund returns </li></ul>
  24. 26. From Robert Haugen, The New Finance: The Case against Efficient Markets, based on Fama & French 1992
  25. 27. Here’s where it gets weird <ul><li>Other research finds same value-growth pattern before 1960, and abroad. </li></ul><ul><li>Warren Buffet, Peter Lynch are value investors </li></ul><ul><li>But value stocks have had a lower standard deviation of returns than growth stocks: lower risk, higher returns! </li></ul><ul><li>According to EMH, Fama & French 1992 (new info.) should have sent $ pouring into value stocks, resulting in huge one-time gain, but lower returns to value stocks thereafter. Free lunches should not persist. </li></ul><ul><li>I read this in 1999, during “new economy” growth stock craze: exact opposite was happening. </li></ul><ul><li>(Maybe has happened now??) </li></ul>
  26. 28. From Robert Haugen, The New Finance: The Case against Efficient Markets, based on Fama & French 1992 Beta
  27. 29. 100 Most-Cited Researchers in Economics SOURCE: ISI Essential Science Indicators         Web based product from the September 1, 2002 update covering a ten year plus six month period, January 1992 - June 30, 2002.      RANK SCIENTIST PAPERS CITATIONS CITATIONS PER PAPER 1 SHLEIFER, A 50 1,717 34.34 2 FAMA , EF 20 1,242 62.10 3 LEVINE, R 22 1,205 54.77 4 KAHNEMAN, D 16 1,122 70.12 5 VISHNY, RW 23 1,043 45.35 6 MURPHY, KM 20 984 49.20 7 TVERSKY, A 13 901 69.31 8 SALAIMARTIN, X(*) 19 894 47.05 9 FRENCH , KR 14 881 62.93 10 ANDREWS, DWK 27 856 31.70
  28. 30. What’s going on? <ul><li>Fama says: some unobserved risk factor looms over these “distressed” value companies. Their true but unmeasured high risk is compensated by high returns. </li></ul><ul><li>I don’t buy it. They actually were riskier for 30 years but racked up much higher returns and lower volatility? </li></ul><ul><li>Fama is stuck. Maybe no Nobel </li></ul><ul><li>More plausible explanations come out of new field of behavioral finance, which he attacks rather vituperatively </li></ul><ul><li>“ Value premium” may be a permanent artifact of investor irrationality, i.e., human nature </li></ul>
  29. 31. My conclusion <ul><li>EMH is probably mostly true </li></ul><ul><li>Lesson 8: But the evidence on value stock outperformance (and maybe small stock outperformance) seems strong enough that I favor “tilting” </li></ul><ul><ul><li>E.g., instead of 50/50 value-growth, do 75/25. </li></ul></ul><ul><li>No one is saying value does systematically worse, so risk of long-term under-performance seems low </li></ul>
  30. 32. Lesson 9 :Vanguard is the best <ul><li>Essentially a cooperative </li></ul><ul><li>No incentive to take $ from customers and give it to own shareholders </li></ul><ul><li>Extremely low expenses </li></ul><ul><li>Wide selection of index and other funds </li></ul><ul><li>500 index fund now the world’s largest mutual fund. </li></ul><ul><li>From 0 in early 1970s, Vanguard has become largest mutual fund company in the world. </li></ul><ul><li>Also good: </li></ul><ul><ul><li>DFA (founded by Fama and others)—but for-profit and for millionaires </li></ul></ul><ul><ul><li>TIAA-CREF—non-profit, low-expenses, but few options WITH TIAA-CREF CANNOT DO WHAT I DID </li></ul></ul>
  31. 33. What I did <ul><li>Chose % allocations to different asset classes, covering as many as possible. </li></ul><ul><li>Put more abroad (33%) than is standard </li></ul><ul><li>“ Tilted” toward small and value (and small value) </li></ul><ul><li>70% stock, 30% bond (conventional for my age) </li></ul><ul><li>Just funds, no individual stocks </li></ul><ul><li>Rebalance once/year </li></ul><ul><li>Manage my IRA and wife’s, Vanguard, TIAA-CREF, etc., as a unit </li></ul>
  32. 34. Allocations
  33. 35. Data collection <ul><li>Database with daily price data and full transaction history. All distributions and fees counted </li></ul><ul><li>Maintain benchmark based on some Vanguard single-fund solutions that implement standard investment book pie charts via index funds (LifeStrategy, Target funds) </li></ul>
  34. 36. Real returns, 8/19/99–10/24/07
  35. 42. Bottom line <ul><li>My returns should continue to be less volatile. </li></ul><ul><li>Mostly likely: continuing gains relative to benchmark or parity </li></ul><ul><li>My wife and I can afford to die a half a year later </li></ul>
  36. 43. Total return on some funds in the portfolio Note: Not all funds held all 8 years.
  37. 44. “ Having spent nearly a decade writing about investment management for the little guy, I have come to the conclusion that I no longer believe in the basic premise of my public persona—a surreal cross between Harry Markowitz and Johnny Appleseed, as a friend put it. “ A decade ago, I really did believe that the average investor could do it himself. After all, the flesh was willing, the vehicles were available, and the math wasn’t that hard. “ I was wrong. Having emailed and spoken to thousands of investors over the years, I’ve come to the sad conclusion that only a tiny minority, at most one percent, are capable of pulling it off.” -- William J. Bernstein, Efficient Frontier, Winter 2003
  38. 45. For more <ul><li> and </li></ul><ul><li> </li></ul><ul><li>Haugen, The New Finance </li></ul><ul><li>Malkiel, Random Walk Down Wall Street </li></ul><ul><li>Bogle, Common Sense on Mutual Funds </li></ul><ul><li>Ellis, Winning the Loser’s Game </li></ul><ul><li>Bernstein, The Intelligent Asset Allocator </li></ul>