Tài chính doanh nghiệp - Lecture 5: Portfolio diversification and supporting financial institutions

Lecture 5: Portfolio Diversification and Supporting Financial InstitutionsPortfolio DiversificationAll that should matter to an investor is the performance of the entire portfolio.Mean and variance of portfolio matterLaw of large numbers means that spreading over many independent assets reduces risk, has no effect on expected return.Equally-Weighted Portfolio When Asset Returns are Independent & Same VarianceSame dollar value in each assetRebalancing each periodPortfolio expected return equals average of asset expected returnsPortfolio standard deviation equals asset standard deviation divided by Square root ruleInvestment Companies as Providers of DiversificationInvestment trusts (before 1940s)Mutual funds (especially index funds)Closed end investment companiesUnit investment trusts All these institutions can enable small investors to overcome transactions cost and lumpiness problems in achieving diversified portfoliosDoubts about DiversificationComplete diversification would imply holding much in fixed incomes, real estate, etc. But hasn’t stock market outperformed these?Equity Premium PuzzleGeometric average real stock market return 1871-1997: 7.0% (Siegel Table 1-1).Geometric average real fixed-income return 1871-1997: 1.7% (Siegel Table 1-2)Equity premium = 7.0%-1.7%=5.3%Puzzle: Why has equity premium been so high?Dominance of Stocks over Fixed Incomes?No thirty-year period since 1831-1861 when the return on either long-term or short-term bonds exceeded that on equities. (Siegel p. 15)Survey of Institutional Investors, Shiller, 1993“There is no thirty-year period since 1860 in which US government bonds have outperformed stocks.” Have you heard roughly this claim (even if details, such as the use of 30 years) are different? 1. Yes, often 52% 2. Yes, once or twice 22% 3. No 26%But is Equity Premium Robust?Geometric average US real stock market return 1802-1997: 7.0% (Siegel Table 1-1)Geometric average real fixed income return 1802-1870: 5.1% (Siegel, Table 1-2)Equity premium = 7.0% - 5.1% = 1.9%Equity premium was much smaller then.International EvidenceMedian real stock market appreciation rate for 39 countries 1926-96: 0.8% per year.Real stock market appreciation rate for US 1926-96: 4.3% per year. (Philippe Jorion and William Goetzmann, Journal of Finance 54:953-80, 1999.)So, US equity premium may reflect a selection bias.Optimal Portfolio Diversification in General CaseDrop assumption of equal weighting, independence and equal variancePut xi dollars in ith asset, I=1,..,n, where the xi sum to $1.Portfolio expected value = Portfolio variance (two assets) =Portfolio Variance, Three AssetsPortfolio variance = Efficient Portfolio Frontier with Two AssetsFrontier expresses portfolio standard deviation in terms of portfolio expected return r rather than in terms of x1. Efficient Portfolio FrontierRisk-Return Trade-Off and Holding PeriodsMutual Fund TheoremAll investors, regardless of risk preferences, will hold a combination of the riskless asset and the tangency portfolio of all risky assets.Therefore, only one asset need be made available to investors: a mutual fund that holds the tangency portfolio.Capital Asset Pricing Model (CAPM)CAPM Asserts that all investors hold their optimal portfolioConsequence of the mutual fund theorem: all investors hold the same portfolio of risky assets, the tangency portfolioTherefore the CAPM says that the tangency portfolio equals the market portfolioBetaThe CAPM implies that the expected return on the ith asset is determined from its beta.Beta (i) is the regression slope coefficient when the return on the ith asset is regressed on the return on the market.Fundamental equation of the CAPM:Do Mutual Funds Hold Optimal Portfolio?Completely diversified funds do not existMutual funds are classified into equity funds, fixed-income funds, etcMutual funds are further classified into styles: growth, income, blue-chip, etc.Index funds account invest in stock price indexes, such as S&P 500Index Funds$350 billion, or 8% of stock market invested in equity index funds in 2000.Much of this is in specialty index funds, such as Internet funds.Some other broadly diversified funds, however, may substitute for market index funds.Alfred Cowles 1891-1984Yale ’13Investment advisor, NYCFounded Econometric Society, Cowles FoundationEconometrica 1933 “Can Stock Market Forecasters Forecast?”Survey of Individual Investors 1999“Trying to time the market, to get out before it goes down and in before it goes up, is: 1. A smart thing to do; I can reasonably expect to be a success at it. 11% 2. Not a smart thing to do; I can’t reasonably expect to be a success at it. 83% 3. No opinion 5%Persistence of Mutual Fund PerformanceMutual funds that performed well last year tend to a little better than average this year. Effect is weak. William Goetzmann and Roger Ibbotson, Journal of Finance, 54:953-80, 1999.Survey of Individual Investors 1999“Trying to pick individual stocks, for example, if and when Ford Motor stock will go up, or IBM stock will go up, is: 1. A smart thing to do; I can reasonably expect to be a success at it. 40% 2. Not a smart thing to do; I can’t reasonably expect to be a success at it. 51% 3. No opinion 8%Survey of Individual Investors 1999“Trying to pick mutual funds, trying to figure out which funds have experts who can themselves pick which stock will go up, is: 1. A smart thing to do; I can reasonably expect to be a success at it. 50% 2. Not a smart thing to do; I can’t reasonably expect to be a success at it. 27% 3. No opinion 23%Growth of Mutual FundsIn 1982 there was one mutual fund account per ten US householdsIn 1998 there were almost two mutual fund accounts per US householdFlow of Funds Accounts published by Federal Reserve: Flow tables, level tables, and reconciliation tables.