
Explanation:
Expected return of the portfolio = (Weight of Asset A * Return of Asset A) + (Weight of Asset B * Return of Asset B) = (1.3 * 14%) + (-0.3 * 9%) = 15.5%
Detailed explanation:
Recall that the capital market line represents the portfolios that optimally combine risk and return by combining the risk-free asset with the risky asset (market portfolio). An investor can move up or down this line by varying the weights that they invest in the risk-free asset and the risky asset. Rather than just split their money between the two assets, an investor who is willing to take more risk can borrow more money at the risk-free rate and invest it in the risky asset. Borrowing puts a negative weight on the risk-free asset. Let’s see how this comes about: Let the return on the risk-free rate be X, and the return on the risky asset be Y. Let’s say you have $100 in your pocket and here’s your initial plan: To invest $50 in the risk-free asset. To invest $50 in risky asset. But then you decide to take more risk; you will borrow $80 at the risk-free rate X and invest it in the risky asset. What’s your total investment? Risk-free asset: = $50 - $80 = -$30 (essentially a “give and take” scenario) Risky asset: $50 + $80 = $130. Thus, Expected Return = -$30/(-$30 + $130)X + $130/(-$30 + $130)Y = -0.3X + 1.3Y. In our case, X = 9%, Y = 14%. Expected return = -0.3 * 0.09 + 1.3 * 0.14 = 0.155
Things to Remember
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Q.3469 A portfolio manager is constructing a portfolio composed of two assets. Asset A is a risky asset with an expected return of 14% and a standard deviation of 22%, and asset B is a risk-free asset with an expected return of 9%. If the portfolio manager increases the weight of the risky asset to 130%, then the expected return of the portfolio is closest to:
A
0.182
B
0.155
C
0.167
D
0.1123
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