INVESTMENT for Master and PH.D students Fan Longzhen Course overview ? The focus of this course is on financial theory and empirical evidence that are useful for investment decisions. The topics include: ? Financial theory: This include portfolio theory, CAPM, APT, discount factor model, they are important for decision-making in investments; ? Empirical study approaches: GMM, Fama-Macbeth regression, time-series, cross-sections test of pricing model, ect. ? Empirical evidence in the equity market. This includes patterns in cross- section of stock returns, the time-series behavior of stock returns---time varying expected returns and stochastic volatility. ? Market efficiency and active investments: we start with the efficient market hypothesis, which is useful for modeling financial markets. Because efficient market theory is not a perfect description of the reality: some prices are almost certainly ‘wrong’, active investment can have effective results. Topics in active investment include security analysis, active portfolio management, hedge funds, and risk management issues. Introduction ? Assets: real assets and financial assets; ? Financial assets:divided by markets ? Money markets:currencies; ? commercial papers; T-bills; ? Capital markets: Government debt ; Corporate debt; ?stocks; ? Derivatives: options, forward, and futures; ? Investment: stock market investment. Role of financial asset 1. Allocating resources: transfer resources across time(money market); transfer resources across different states (derivatives); 2. Communication information:Market reflect relevant information; Example 1: Allocating resources across time ? Consider an individual who live for two dates: now (t=0) and later (t=1); ? She is endowed with 100 new and 25 later; ? Her happiness (utility) depends on her consumption now and later: C0 and C1 ; ? She prefer a smooth consumption path over time; ? There is a borrowing/lending market with zero interest rate; To be continued 1. Without the loan market, she consume her endowments: C0=100, C1=25. 2. With the loan market, she lend 37.5 now and receive 37.5 later, her consumption is C0=62.5 and C1=62.5, the same over time, she is now better off. 3. At the endowment, she prefer 1 later over 1 now; at the optimum, she is different between 1later and 1 now. Example 2 allocating resources across different states 1. Consider an individual, who lives for two dates: now (t=0) and later (t=1). At t=1, the economy can be in state a and state b; 2. She is endowed with 100 in state a and 25 in state b; 3. Her happiness (utility) depends on her consumption in the two possible state: Ca, and Cb, 4. She prefer similar consumption level in the two states; 5. There are a financial market where the price of a security that pays 1 only if state a occurs is the same as that of a security that pays 1 only if state b occurs; To be continued 1. Without the securities market, she consumes her endowments: Ca=100, Cb=25; 2. With the security market, she sell 37.5 unit of security a and buy 37.5 units of security b. Her consumption is Ca=62.5, and Cb=62.5, the same in the two states, she is better off; 3. At endowment, she prefer 1 in state b over 1 in state a; 4. At the optimal consumption, she is indifferent between 1 in state a and 1 in state b. First pricing principal: No free lunches— No arbitrage opportunities Definition: an arbitrage is an investment opportunity such that 1. It requires no positive investment today but yield positive payoff in the future; 2. It yield positive payoff today without requiring positive payments in the future; Absence of arbitrage establishes relations among securities prices; Example: IBM shares are traded on NYSE at 100, the current $/� exchange rate is 2.0, what is the price of IBM shares traded on London stock exchange. Key assumptions of arbitrage pricing: 1. More is better than less; 2. No frictions, such as trading costs; short sales constraint Second pricing principal: supply equals demand ---market in equilibrium Market equilibrium determines security prices in term of “fundamentals” ? Expectation of future cash flows; ? Risk in the future cash flows; ? Investor’s preference toward risk. Example: CAPM ? price securities based on fundamentals; ? price all securities; ? key to understanding economic forces behind security prices. Investment behavior under traditional finance ? Utility: level of satisfaction from a given wealth level; ? The higher the wealth level, the higher the utility. An individual tries to maximize the utility level. ? If the wealth is uncertain due to investment in risky assets whose future payoff are uncertain, the individual will maximize the expected utility of wealth. ? Investors exhibit risk-aversion behavior. Investment behavior under traditional finance ? Suppose that your original wealth is 100000, you have a bet of 50,000, with 50% probability winning and 50% probability losing. ? Expected utility ? Expected wealth ? If investor are risk averse ? )000,150(5.0)000,50(5.0))(( UUWUE ×+×= 100000]000,150000,50[5.0)( =+×=WE ))(())(( WEUWUE < Investor Behavior in Reality ? Preferences: choose A and B: ? A: sure gain of 240,000; ? ?B: ? Choose C or D ? C: sure loss of 750,000 ? ?D: ? ? ? 75.00 25.0000,1000 probabiltywith yprobabilitwith ? ? ? 75.01000000 25.00 probailitywith yprobabilitwith Investor Behavior in Reality ? Equivalent choices: ?A+D: ?B+C: ? ? ? ? 75.0760000 25.0240000 ? ? ? ? 75.0750000 25.0250000 Investor Behavior in Reality ? Which of the following sequences is more likely to occur when a coin is tossed: – A) HHHTTT or – B) HTHTTH Risk and uncertainty Consider Urn A with 100 red and blank balls: ? 50 read; 50 black; ? Consider drawing a ball; ? Bet on color, 10,000 payoff; ? Which color would you prefer; ? How much would you pay for such a game? Consider Urn. B with 100 red and black ball: ? Proportion unknown; Consider drawing a ball; ? Bet on color, 10,000 payoff; ? Which color would you prefer; ? How much would you pay for such a game? U.S. stock markets ? What about perfect market timing? ? Suppose Rt=max(S&P500,T-bills); ? What does 1 grow up to now statistic S&P 500 T- bills perfect mean(%) 1.01 0.31% 2.62 st.D(%) 5.67 0.26 3.7 Minimum(%) -29.73 -0.06 -0.06 median(%) 1.32 0.27 1.33 maximum(%) 42.56 1.35 42.56 sharp ratio 0.43 0 2.17 total raeturn $1,371 $14 ??? monthly returns 1926:1-1996:12 Risks in the long-run ? Consider 20-year horizon: ?R1(20): 1926:01 to 1945:12; ?R2(20): 1926:02 to 1946:01; ?… ?R613(20): 1977:01 to 1996: 12 ? (overlapping data) ? Does S&P500 dominates T-bills? statistic S&P500 T- bills S&P500- T- bills mean 10.81 3.69 7.12 st.D 3.31 2.7 4.16 Minimum 1.89 0.42 0.24 Median 11.46 3.2 6.62 Maximum 17.96 7.73 15.72 20-year retruns (1945:01-1996： 12） 1.53 3.81 5.54 154.95 508.17 1.0 1.0 1.0 1.0 1.0 T-bills Long-term T-bonds Long-term corporate bonds Large stocks Small stocks Total returnInitial Asset Real returns from 1926 to 1996 Returns on risky assets can be highly correlated to each other 1inflation 0.041S-stocks -0.020.811L-large stocks -0.150.110.251C-bonds -0.150.030.180.941T-bonds 0.41-0.09-0.040.220.241T-bills inflationS-stocksL-large stocks C-bondsT-bondsT-bills Cross correlations of annual nominal returns(1926-1996) 1 S-stocks 0.811 L-large stocks 0.140.311 C-bonds 0.070.250.961 T-bonds -0.060.110.590.581 T-bills S-stocksL-large stocks C-bondsT-bondsT-bills Cross correlations of annual real returns(1926-1996) Returns on risky assets can be highly correlated to each other Returns on risky assets are serially uncorrelated Serial correlations of annual asset returns T-bills 0.92 0.66 T-bonds -0.01 0.07 C-bonds 0.1 0.21 L-large stocks -0.01 -0.02 S-stocks 0.09 0.06 Nominal return Real return Serial correlation Investors ? Household sector ? preference for risk and return; ? live-cycle investing; ? market efficiency. ? No financial corporate sector ? Corporate preference for risk and return; ? Risk management. ? Financial intermediaries sector ? asset and liability management; ? stock selection; allocation. ? Capital market sector ? Market microstructure; ? trading technology Investment problem ? Begin at date 0 ?income yt, consumption ct; ? retire at date T; ? die at date T+L; ? How to invest your wealth w0 among various asset? ? How to define the problem? ? what is your objective? ? what information do you need? ? what choices do you have? 0 T T+L