Difficulties in adjusting average returns for risk present a host of issues, as the proper measure of risk may not be obvious, and risk levels may change along with portfolio composition. The following data is given for a particular sample period: Portfolio P               Market M           Average return                                      35 %                      28 %           Beta                                                     1.2                         1.0           Standard deviation                                42 %                      30 % Calculate the following performance measures for portfolio P and the market: Sharpe, Jensen (alpha) and Treynor. The Treasury bill rate during the period was 6 %. By which measures did portfolio P outperform the market? What do these measures mean or imply? Explain.

Assume that the short-term risk-free rate is 6%, the market index S&P500 is expected to pay returns of 30% with the standard deviation equal to 40%. Asset A pays on average 10%, has a standard deviation equal to 40% and is NOT correlated with the S&P500. Asset B pays on average 16%, also has a standard deviation equal to 40% and has a correlation of 1 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why.  (Beta of asset i (?i) = ?i ?iM / ?M, where ?i, ?M are standard deviations of asset i and market portfolio, ?iM is the correlation between asset i and the market portfolio)

a risk manager gathers the following sample data to analyze annual returns for an asset: 12%, 25% and -1%. he wants to compute the best unbiased estimator of the true population mean and standard deviation. the manager's estimate of the standard deviation for this asset should be closest to a. 0.0111 b. 0.0113 c. 0.1054 d. 0.1204.

2. Consider the following expected returns, volatilities, and correlations: Expected Standard Stock Return Deviation Correlation with Vital Correlation with Mital Correlation with Pital Vital 14% 6% 1.0 -1.0 0.0 Mital 44% 24% -1.0 1.0 0.7 Pital 23% 14% 0.0 0.7 1.0 a. Imagine a portfolio comprising solely of Vital and Mital. What portion of should be allocated to Vital stock to ensure a risk-free investment? your investment b. What is the portfolio's volatility when holding a $10,000 long position in Pital and a $2000 short position in Mital? wwwww c. In a market, there are two securities, Artis and Brotis. Currently, the price of Artis stands at £50. Looking ahead, the price of Artis next year will be £40 during a recession, £55 in normal economic times, and £60 in an expanding economy. The probabilities associated with recession, normal times, and expansion are 0.1, 0.8, and 0.1, respectively. Artis does not pay dividends and has a correlation of 0.8 with the market. On the other…