CHAPTER 2 Risk and Rates of Return,Stand-alone risk Portfolio risk Risk & return: CAPM / SML,Investment returns,The rate of return on an investment can be calculated as follows:(Amount received Amount invested)Return = _Amount investedFor 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%.,What is investment risk?,Two types of investment risk Stand-alone risk Portfolio risk Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment.,Probability Distributions,It either will rain, or it will not only two possible outcomes,Probability Distributions,Martin Products and U. S. Electric,Probability distributions,A listing of all possible outcomes, and the probability of each occurrence. Can be shown graphically.,Investment alternatives,Return: Calculating the expected return for each alternative,How do the returns of HT and Coll. behave in relation to the market?,HT Moves with the economy, and has a positive correlation. This is typical.Coll. Is countercyclical with the economy, and has a negative correlation. This is unusual.,Expected Rate of Return,Summary of expected returns for all alternatives,Exp returnHT 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?,Discrete Probability Distributions,-60 -45 -30 -15 0 15 22 30 45 60 75 90 110,Rate of Return (%),Expected Rate of Return (15%),a. Martin Products,Probability of Occurrence,-10 -5 0 5 10 16 20 25,Rate of Return (%),Expected Rate of Return (15%),b. U. S. Electric,Probability of Occurrence,0.5 - 0.4 - 0.3 - 0.2 - 0.1 -,0.5 - 0.4 - 0.3 - 0.2 - 0.1 -,Continuous Probability Distributions,-60 0 15 110,Rate of Return (%),Expected Rate of Return,Martin Products,Probability Density,U. S. Electric,Measuring Risk: The Standard Deviation,Measuring Risk: The Standard Deviation,Calculating Martin Products Standard Deviation,Standard deviation calculation,Comparing standard deviations,Comparing risk and return,Measuring Risk: Coefficient of Variation,Standardized measure of risk per unit of returnCalculated as the standard deviation divided by the expected returnUseful where investments differ in risk and expected returns,Risk rankings, by coefficient of variation,CVT-bill 0.000HT 1.149Coll. 7.882USR 1.362Market 1.020,Collections has the highest degree of risk per unit of return. HT, despite having the highest standard deviation of returns, has a relatively average CV.,Investor attitude towards risk,Risk aversion assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.,Portfolio construction: Risk and return,Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections.,Expected return of a portfolio is a weighted average of each of the component assets of the portfolio. Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.,Calculating portfolio expected return,An alternative method for determining portfolio expected return,Calculating portfolio standard deviation and CV,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 than average risk. Why? Negative correlation between stocks.,Returns distribution for two perfectly negatively correlated stocks (r = -1.0),-10,15,15,25,25,Returns distribution for two perfectly positively correlated stocks (r = 1.0),Risk Reduction Combining stocks that are not perfectly correlated will reduce the portfolio risk by diversification The riskiness of a portfolio is reduced as the number of stocks in the portfolio increases The smaller the positive correlation, the lower the risk,Portfolio Risk,General comments about risk,Most stocks are positively correlated with the market (rk,m 0.65). 35% for an average stock. Combining stocks in a portfolio generally lowers risk.,Creating a portfolio: Beginning with one stock and adding randomly selected stocks to portfolio,p decreases as stocks added, because they would not be perfectly correlated with the existing portfolio.Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, p tends to converge to 20%.,