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Portfolio Management - how to calculate the expected return for tangency portfolio?

• Hi, Need help on the following question. Logan is a fund manager preparing a performance report for his client. The risk free rate is 5% and the expected return on the investor's tangency portfolio is 13% with a standard deviation of 20%. a) calculate the portfolio's expected risk premium per unit of risk b) calculate the portfolio's expected return if the portfolio standard deviation is 20%. Thanks.

• Answer:

  1. Beta: To answer your question, one needs to have 'Beta'. On the basis of standard deviation of 20%, let us assume Beta to be 1.2. ...............(Beta is a measure of a stock's volatility in relation to the market. By definition, the market has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the market. A stock that swings more than the market over time has a beta above 1.0. If a stock moves less than the market, the stock's beta is less than 1.0. High-beta stocks are supposed to be riskier but provide a potential for higher returns; low-beta stocks pose less risk but also lower returns. 1.1 For details, please read: http://www.investopedia.com/articles/stocks/04/113004.asp#ixzz1vHj3s1kG) 2. As per CAPM*, the required formulae are: i. RequiredRateOfReturn = (RiskFreeReturn) + Beta(ExpectedRateOfReturn - RiskFreeReturn) ii. RiskPremium = Beta(ExpectedRateOfReturn - RiskFreeReturn) -*CAPM: http://www.investopedia.com/terms/c/capm.asp 3. Q1: Calculate the portfolio's expected risk premium per unit of risk: Ans: RiskPremium = Beta(ExpectedRateOfReturn - RiskFreeReturn) = 1.2(13-5) = 1.2*8 = 9.6% -Risk Premium with beta of 1.1: RiskPremium = 1.1(13 - 5) = 1.1*8 = 8.8% 4. Q2: Calculate the portfolio's expected return if the portfolio standard deviation is 20%. Ans: It is presumed that what you want to know is about the Required Rate of Return, since expected rate of return has already been given in the Question. RequiredRateOfReturn = (RiskFreeReturn) + Beta(ExpectedRateoOfReturn - RiskFreeReturn) RequiredRateOfReturn = 5 + 1.2(13 - 5) = 5+1.2*8 = 5+9.6 = 14.6% .