Below is a Key Rate Duration (KRD) analysis of a fictitious portfolio vs a benchmark index. In a scenario where the 5-year yield decreased while the 10-year yield increased today compared to yesterday, which would outperform the other (i.e. higher relative price gain)? The portfolio or the index? Assume the 2y and 20y rates remained the same day over day. Term 2y 5y 10y 20y Total Portfolio 1.8 2.4 4.5 8.1 16.8 Index 1.1 0.9 6.2 8.6 16.8 O The portfolio would outperform the index O The index would outperform the portfolio Each would perform the same since the overall portfolio duration is the same
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- An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor’s 500 Index), and U.S. Treasury bills (T-bills) during the past eight years. Rate Annual Averageof Return STANDARD DEVIATION OF RETURN BETA Portfolio X 10 13 0.40 S&P 500 12 10 1.00 T-bills 7 n/a n/a n/a = not applicable Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places. Treynor measure Sharpe measure Portfolio X 7.5 S&P 500 5An analyst wants to evaluate Portfolio X consisting entirely of US common stocks, using both the Treynor and Sharpe measures of the portfolio performance. The following table provides the average annual rate of return for the portfolio X the market portfolio (as measured by the Standard & Poor's 500 index) and US Treasury billds (Tbills) during the past eight years Average Return Standard deviation Beta Portfolio X 10% 18% 0.6 S & P 500 12% 13% 1 T bills 6% n/a n/a a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Briefly explain whether portfolio X underperformed, equalled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. b. Based on the performance of…You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.20 0.65 0.15 Return on P -20% 18% 32% The risk-free rate is currently 5%, and the market portfolio M has an expected return of 15% and standard deviation of 25%, and its correlation with P is .5. Is P an efficient portfolio relative to the market?
- Using CAPM to determine the expected rate of return for risky assets, consider the following example stocks, assuming that you have already compute the betas Stock Beta A 0.70 B 1.00 C 1.15 D 1.40 E -0.30 Assume that we expect the economy’s RFR to be 5 percent (0.05) and the expected return on the market portfolio (E(RM)) to be 9 percent (0.09), 1, what would this imply? With these inputs, what would the be the following required rate of returns for these five stocks, show the formula for each in your calculations.Assume the riskless rate of interest is 2% per year, and the expected rate of return on the market portfolio is 8% per year. According to the CAPM, what is the efficient way for an investor to achieve an expected rate of return of 5% per year? If the standard deviation of the rate of return on the market portfolio is 4%, what is the standard deviation of the portfolio producing the 5% expected return? • Plot the CML and locate the foregoing portfolios on the same graph. • Plot the SML and locate the foregoing portfolios on the same graph.A respected analyst forecasts that the return of the S&P 500 index portfolio over the coming year will be 10%. The one-year T-bill rate is 5%. Examination of recent returns of the S&P 500 Index suggest that the standard deviation of returns will be 18%. What does this information suggest about the degree of risk aversion of the average investor, assuming that the average portfolio resembles the S&P 500?
- Which one of the following indices would you use as the most appropriate proxy for the market portfolio and as part of the CAPM model: SP500, FTSE100, and the Dow Jones? Carefully justify your answer and provide all related reasons. Further, assuming a risk-free rate of 1%, an expected return of the market portfolio equal to 6% and a beta parameter of 1.5, with a current price of $100, what is the expected price of an underlying portfolio one year from now? More generally, explain the assumptions under the CAPM model, and mention what type of expected return does the model aim to capture.Assume that the risk-free rate, RF, is currently 8%, the market return, RM, is 12%, and asset A has a beta, of 1.10. (could be done on word document or excel). Draw the security market line (SML) Use the CAPM to calculate the required return, on asset A. Assume that as a result of recent economic events, inflationary expectations have declined by 3%, lowering RF and RM to 5% and 9%, respectively. Draw the new SML on the axes in part a, and calculate and show the new required return for asset A. Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 2%, to be14%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A. From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?…You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.20 0.65 0.15 Return on P -20% 18% 32% The risk-free rate is currently 5%, and the market portfolio M has an expected return of 15% and standard deviation of 25%, and its correlation with P is .5. What is the portfolio P’s beta?
- You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.20 0.65 0.15 Return on P -20% 18% 32% The risk-free rate is currently 5%, and the market portfolio M has an expected return of 15% and standard deviation of 25%, and its correlation with P is .5. What is the portfolio P’s beta? Does portfolio P have a positive or negative alpha relative to its required return given its level of risk? Would you characterize P as a buy or sell, and why?The analysts at FNB forecasted that the return on DJIA index portfolio over the coming year will be 14%. The one year T-Bill rate is 6%. While examining the recent returns of the DJIA index, the analysts estimated that the variance of these returns will be 12.4%. What is the degree of the risk aversion for the average investor, assuming the average portfolio resembles the DJIA indexAssume that the risk-free rate, RF, is currently 8%, the market return, RM, is 12%, and asset A has a beta, of 1.10. (could be done on word document or excel). a) Draw the security market line (SML) b) Use the CAPM to calculate the required return, on asset A. c) Assume that as a result of recent economic events, inflationary expectations have declined by 3%, lowering RF and RM to 5% and 9%, respectively. Draw the new SML on the axes in part a, and calculate and show the new required return for asset A. d) Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 2%, to be14%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A. e) From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?