FIN4504 Exam 2 Study Guide Chapters 5 and 6 Expected return and standard deviation of a portfolio The average holding period return you would earn if you were to repeat an investment in the asset many times It is also the mean of the distribution of HPRs and may be referred to as the mean return The expected return can be calculated by taking the sum of all the probabilities P s of a scenario multiplied by the HPR for that scenario r s The standard deviation of a security measures the risk in the same dimension as the expected return The standard deviation is the square root of the variance 2 equation shown below Combining two risky assets into a risky portfolio The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio with the portfolio proportions as weights rp w1r1 w2r2 w1 Proportion of funds in Security 1 w2 Proportion of funds in Security 2 r1 Expected return on Security 1 r2 Expected return on Security 2 When two risky assets with variances 1 2 and 2 2 respectively are combined into a 2 1 portfolio with portfolio weights w1 and w2 respectively the portfolio variance is given by p w1 2 You invest positive amounts in two stocks return on the portfolio is definitely between the return on the two stocks The standard deviation is not always between the standard deviation of the two stocks If the correlation is 1 it is definitely between 2 2w1w2 Cov r1 r2 2 w2 2 2 Sharpe ratio Measures the reward to variability ratio of any combined portfolio of a risky and risk free asset It is the risk premium of the risky asset reward divided by the standard deviation of the risky asset variability Also represents the slope that plots all possible risk return tradeoffs for a complete portfolio consisting of a given risky portfolio and a risk free portfolio It is the slope of the CAL As investors we want to maximize the Sharpe ratio Covariance Measures how much the returns of two risky assets move together We can get an idea of the covariance by looking at expected values of asset returns across scenarios and seeing how well they are in tandem with each other Depending on the information given there are two equations to find the covariance Cov r1 r2 r1 r2 s1s2 Note the covariance of a risk free asset and a risky portfolio is 0 because the risk free asset provides a constant return and will not fluctuate with the risky asset Correlation The correlation can range from 1 0 to 1 0 If the correlation is 1 0 Cov r1 r2 1 2 1 2 the securities would be perfectly positively correlated meaning they move exactly together If the correlation is 1 0 the securities would be perfectly negatively correlated meaning they move exactly opposite each other by equal amounts The effect of correlation on portfolio return and portfolio variance The relationship between portfolio risk and return depends on the correlation coefficient The smaller the correlation the greater the risk reduction potential If the correlation is 1 0 no risk reduction is possible Also when the correlation is 1 the standard deviation of the portfolio is the weighted average of each security s standard deviation When correlation is less than 1 portfolio risk is reduced because the standard deviation of the portfolio will be less than the weighted return of the portfolio When correlation is 1 the standard deviation of the portfolio can be reduced to zero if the weights of each security in the portfolio are chosen correctly To solve for these weights set the weighted standard deviation of the portfolio equal to zero p w1 1 w2 2 and w2 1 w1 You can then solve for w1 to find the correct proportions to eliminate risk Just because the correlation is 1 does not mean that the standard deviation is 0 The weights must be in the correct proportions for this equation to work Note the standard deviation of expected return on a portfolio is the weighted average of each security s standard deviation ONLY when the correlation coefficient is 1 Otherwise the standard deviation is lower than the weighted average Portfolios of less than perfectly correlated assets offer better risk return opportunities than the individual component securities on their own Minimum variance portfolio The minimum variance of a portfolio is where the combination of the risky assets results in the lowest possible standard deviation To solve for the MVP use the equation below The standard deviation of the MVP will be less than each asset alone and w2 1 w1 Optimal risky portfolio The best combination of risky assets to be mixed with safe asset to form the complete portfolio This could also be referred to as the risky portfolio resulting in the highest possible CAL The weights for this portfolio can be found by using the following equation w1 E r1 rf 2 E r 1 rf 2 2 E r2 r f 1 2 E r2 rf Cov r1 r2 2 E r1 rf E r2 rf Cov r1 r 2 Systematic non diversifiable market risk The risk that remains after diversification and is attributable to market wide risk sources Regardless of how well we diversify a portfolio there will always be market risk that cannot be reduced Firm specific diversifiable idiosyncratic unique risk The risk that can be eliminated by diversification Minimum variance frontier Includes portfolios that fall below the efficient frontier or the minimum variance portfolio Investors will never choose any point on this frontier because it is inefficient If you have two stocks with E r given given and correlation is 1 What is the expected return and deviation on the portfolio if no short selling is allowed at the Minimum Variance Return o Answer The return would be the return and of the lower risk stock Efficient frontier The graph representing a set of portfolios that maximizes expected return at each level of portfolio risk The portfolios on this frontier can be viewed as efficiently diversified The efficient frontier includes all points on the curve above the global minimum variance portfolio Global minimum variance portfolio This is the Minimum Variance Portfolio of the market generally found using an index because it is impossible to include every asset in the market Optimal risky portfolio when we use all assets to derive it The optimal risky portfolio of the market curve is the market portfolio If you held the market portfolio you can only be compensated for systematic risk This is where the Beta measurement comes from because unsystematic risk does not exist at this point CAL Capital Allocation Line The line connecting