对外经济贸易大学投资学.ppt

Lecture 3 Risk and Return Key Concepts and Skills lKnow how to calculate the return on an investment lUnderstand the historical returns on various types of investments lUnderstand the historical risks on various types of investments Risk, Return and Financial Markets lWe can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets lLessons from capital market history There is a reward for bearing risk The greater the potential reward, the greater the risk This is called the risk-return trade-off Dollar Returns lTotal dollar return = income from investment + capital gain (loss) due to change in price lExample: You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return? lIncome = 30 + 30 = 60 lCapital gain = 975 950 = 25 lTotal dollar return = 60 + 25 = $85 Percentage Returns lIt is generally more intuitive to think in terms of percentages than in dollar returns lDividend yield = income / beginning price lCapital gains yield = (ending price beginning price) / beginning price lTotal percentage return = dividend yield + capital gains yield Example Calculating Returns lYou bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40. What is your dollar return? lDollar return = 1.25 + (40 35) = $6.25 What is your percentage return? lDividend yield = 1.25 / 35 = 3.57% lCapital gains yield = (40 35) / 35 = 14.29% lTotal percentage return = 3.57 + 14.29 = 17.86% Compound return Conventions for quoting rates of return : Usually we use APR, annual percentage rate APR=per-period rate*periods per year Sometimes we use EAR(effective annual rate) In continuous time, EAR=eAPR-1 St=S0ert, so rate of return equal Ln(St/S0) Rate of Return-example lSuppose you buy T-bill maturing in one month for $9,900. lHPR=(10000-9900)/9900=1.01% lAPR=1.01%*12=12.12% lEAR=(1+1.01%)12-1=12.82% Figure 12.4 Year-to-Year Total Returns Large-Company Stock Returns Long-Term Government Bond Returns U.S. Treasury Bill Returns Average Returns InvestmentAverage Return Large stocks12.4% Small Stocks17.5% Long-term Corporate Bonds6.2% Long-term Government Bonds5.8% U.S. Treasury Bills3.8% Inflation3.1% Risk Premiums lThe “extra” return earned for taking on risk lTreasury bills are considered to be risk-free lThe risk premium is the return over and above the risk-free rate Average Annual Returns and Risk Premiums InvestmentAverage ReturnRisk Premium Large stocks12.4%8.6% Small Stocks17.5%13.7% Long-term Corporate Bonds 6.2%2.4% Long-term Government Bonds 5.8%2.0% U.S. Treasury Bills3.8%0.0% Risk lRisk means the uncertainty of future outcome lRisk is unobservable lFinance literates have developed many measurements for risk, the simplest risk measurement is the standard deviation of asset return The population expected value and variance lThe expected rate of return is the weighted average rate of return, weighted by its possibility lThe variance is the deviation of the return from its expected value lThe square root of variance is the risk StateProb. of Stater in State .1 -.05 2.2.05 3.4.15 4.2.25 5.1.35 E(r) = (.1)(-.05) + (.2)(.05).+ (.1)(.35) E(r) = .15 Scenario or Subjective Returns: Example Standard deviation = variance1/2 Subjective or Scenario Var =(.1)(-.05-.15)2+(.2)(.05- .15)2.+ .1(.35-.15)2 Var= .01199 S.D.= .01199 1/2 = .1095 Using Our Example: Variance or Dispersion of Returns The sample mean and variance lThe actual population mean and variance are unknown, we have to estimate these values by sampling lThe sample mean and variance Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000 Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000 Normal distribution 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2. Characteristics of Probability Distributions Possibility of loss lSuppose asset return follows normal distribution, it is easy to compute the possibility of achieving a specified return level. Investors are particularly interested in the possibility that asset return is below zero lExample:suppose asset returns follow normal distribution with mean 10% and standard deviation of 20%, what is the possibility that asset return will below zero, what is the possibility that asset return will be above 20%? What is the possibility that asset return is between 5% and 15%? Z-value Possibility of loss lThe possibility that asset return is negative: lThe possibility that asset return is above 20% Figure 5.12 Wealth Indexes of Selected Outcomes of Large