question archive a) The expected rate of return on the market portfolio is 12
a) The expected rate of return on the market portfolio is 12
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a) The expected rate of return on the market portfolio is 12.50% and the risk-free rate of return is 3.25%. The standard deviation of the market portfolio is 17.50%. What is the representative investor's average degree of risk aversion?
b) Stock A has a beta of 1.95 and a standard deviation of return of 41%. Stock B has a beta of 3.75 and a standard deviation of return of 65%. Assume that you form a portfolio that is 60% invested in Stock A and 40% invested in Stock B. Using the information in question 13, according to CAPM, what is the expected rate of return on your portfolio?
c) Using the information in questions a and b, what is your best estimate of the correlation between stocks A and B? Note that correlation is shown as a number rather than a percentage.
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Please refer the explanation part for detailed working.
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Step-by-step explanation
1)
| Market Return, Rm | = 12.50% |
| Risk Free Return, Rf | = 3.25% |
| Std. Dev. of Market, Sm | = 17.50% |
| Sharpe Ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk so it will show if a risk averse investor should take risk for excess return. | |
| Sharpe Ratio | = (Rm-Rf)/Sm |
| = (12.50 - 3.25)/17.50 | |
| = 0.53 | |
| So we will earn excess return of 0.48% per 1% risk in the market. | |
2)
| Market Return, Rm | = 12.50% |
| Risk Free Return, Rf | = 3.25% |
| Std. Dev. of Market, Sm | = 17.50% |
| Stock A: Beta, Ba | = 1.95 |
| Std. Dev, Sa | = 41% |
| Stock B: Beta, Bb | = 3.75 |
| Std. Dev, Sb | = 65% |
| Using CAPM, | |
| Return on Stock A, Ra | = Rf+Ba(Rm-Rf) |
| = 3.25 + 1.95(12.50 - 3.25) | |
| = 21.2875% | |
| Return on Stock B, Rb | = Rf+Ba(Rm-Rf) |
| = 3.25 + 3.75(12.50 - 3.25) | |
| = 37.9375% | |
| Portfolio Weights, | |
| Wa | = 60% |
| Wb | = 40% |
| So Return of Portfolio, Rp | = Wa*Ra +Wb*Rb |
| = 0.60*21.2875 + 0.40*37.9375 | |
| = 27.9475% |
3.
| Correlation between the two assets cannot be determined with this data. It could be positive or negative. |
