What are the standard deviations of returns on stocks X and Y ?
Step 11 of 4
In order to find the standard deviation for both of these stocks we first need to find the variance. Because we completed the last problem we know that the expected return of stock X is 20% and the expected return of stock Y is 10%. These variables along with the other given inputs are all we need to determine the variance for each stock.
We can use the below equation in order to find the variance. In this equation we have each probability and to find the deviation from the mean we can subtract the overall expected return from each of the given returns in the various markets.
A portfolio’s expected return is , its standard deviation is , and the risk-free rate is . Which of the following would make for the greatest increase in the portfolio’s Sharpe ratio?
a. An increase of in expected return.
b. A decrease of in the risk-free rate.
c. A decrease of in its standard deviation.
Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.
a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?
b. What will be the par value of your holdings in the 20-year coupon bond?
Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of . Suppose an analyst studies 20 stocks and finds that one-half have an alpha of , and one-half have an alpha of . The analyst then buys million of an equally weighted portfolio of the positive-alpha stocks and sells short million of an equally weighted portfolio of the negative-alpha stocks.
a. What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profit?
b. How does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks?