CHAPTER 2Risk and Rates of Return,Return and risk: concepts and measures Risk: Stand-alone risk VS. Portfolio risk Risk pricing: CAPM / SML,2.1 Return and risk:concepts and measures,Rate of return: (Amount received Amount invested) Return = _ Amount invested For example: if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.,Ch2 Risk and Return,The above is the so-called realized rate of return. For stocks you have not sold yet, it is more meaningful to talk about the Expected rate of return.,Ch2 Risk and Return,Return distribution (continuous),Investment return possibility distribution.,Ch2 Risk and Return,Return distribution (dispersed),“riskless”,cyclical,countercyclical,Ch2 Risk and Return,Return: Calculating the expected return for each alternative,Ch2 Risk and Return,Summary of expected returns for all alternatives,Exp return HT 17.4% Market 15.0% USR 13.8% T-bill 8.0% Coll. 1.7% HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?,Ch2 Risk and Return,Investment risk,Risk: 1.Uncertainty; 2.The chance that some unfavorable event will occur. Investment risk: Uncertainty of the securities rates of return/prices; the probability of earning a low or negative actual return.,Ch2 Risk and Return,Investment return possibility distribution.,Ch2 Risk and Return,How to describe risk? Standard deviation Coefficient of variance,Ch2 Risk and Return,Risk measure 1:standard deviation,Ch2 Risk and Return,Example:some investment alternatives returns,“riskless”,cyclical,countercyclical,Ch2 Risk and Return,Standard deviation calculation,Ch2 Risk and Return,Comparing standard deviations,Ch2 Risk and Return,Comments on standard deviation as a measure of risk,Standard deviation (i) measures total risk. The larger i is, the more likely that actual returns deviate from expected returns. For investment alternatives with the same expected return, i is a good measure to compare stand-alone risk; But for alternatives with different expected returns, no.,Ch2 Risk and Return,Comparing risk and return,* Seem out of place.,Ch2 Risk and Return,Risk measure 2: Coefficient of Variation (CV),A standardized measure of dispersion about the expected value, that shows the risk per unit of return.,Ch2 Risk and Return,Example: risk rankings by coefficient of variation,CV T-bill0.000 HT1.149 Coll.7.882 USR1.362 MP 1.020,Coll has the highest degree of risk per unit of return. HT, despite having the highest standard deviation of returns, has a relatively average CV.,Ch2 Risk and Return,Whether to choose the one with the lowest CV depends on our Risk attitude,Risk preference?,Risk neutral?,Risk aversion?,Ch2 Risk and Return,Investor attitude towards risk,Risk aversion assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. P.60 Required investment return K=KRF + RP,Ch2 Risk and Return,Risk premium (RP) the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities. P.61,Ch2 Risk and Return,2.2 Stand-alone risk and Portfolio risk,Ch2 Risk and Return,Stand-alone risk: the risk of holding just one asset. P.52 Portfolio risk: the risk of holding a group of assets p.62,Ch2 Risk and Return,Dont put your eggs in one basket! Is it so?,Ch2 Risk and Return,A mix of different securities is called A portfolio Is a portfolio good or bad? Decide its expected return and risk first!but, how?,Ch2 Risk and Return,Calculating portfolio expected return,Expected return of a portfolio,Ch2 Risk and Return,Example:,Assume a two-stock portfolio is created with $50,000 invested in both HT and Coll.,Expected return of HT,Expected return of COLL,Ch2 Risk and Return,An alternative method for determining portfolio expected return is:,Ch2 Risk and Return,But, the risk of a portfolio, p , is generally NOT the weighted average of the of the component assets.,Ch2 Risk and Return,Calculating portfolio standard deviation and CV,Expected return of portfolio,Ch2 Risk and Return,Comments on portfolio risk measures,p = 3.3% is much lower than the i of either stock (HT = 20.0%; Coll. = 13.4%). p = 3.3% is lower than the weighted average of HT and Coll.s (16.7%). Portfolio provides average return of component stocks, but lower risk than the average of the component stocks.,Ch2 Risk and Return,General comments about risk,Why? For a two-stock portfolio: Combining stocks not perfectly correlated in a portfolio generally lowers risk.,Ch2 Risk and Return,Most stocks are positively correlated with the market (k,m 0.65). 35% for an average stock.,Ch2 Risk and Return,Now, lets create a portfolio by adding stocks one by one. What will happen to the portfolios risk?,Ch2 Risk and Return,Creating a