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Answer: 18.35%.
## Explanation Since the investor is investing 115% of their savings in the portfolio, this means they are borrowing 15% of funds at the risk-free rate and investing the entire amount (115%) in the market portfolio. ### Calculation: - Investment in portfolio: 115% - Borrowing (negative investment in risk-free asset): -15% - Risk-free rate: 8% - Portfolio expected return: 17% **Expected return formula:** \[ E[r] = (w_{rf} \times r_{rf}) + (w_p \times r_p) \] \[ E[r] = (-15\% \times 8\%) + (115\% \times 17\%) \] \[ E[r] = (-0.15 \times 0.08) + (1.15 \times 0.17) \] \[ E[r] = (-0.012) + (0.1955) \] \[ E[r] = 0.1835 = 18.35\% \] ### Key Points: - The investor is using leverage by borrowing at the risk-free rate - The beta (1.2) and standard deviation (5.5%) are not needed for this calculation - The expected return increases due to the leverage effect - This demonstrates the concept of the Capital Market Line (CML) where investors can achieve higher returns by borrowing at the risk-free rate to invest more in the market portfolio
Author: Tanishq Prabhu
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The expected return of a portfolio is 17% and the return on risk-free assets in the portfolio is 8%. The beta of the portfolio is 1.2, and the standard deviation of the portfolio is 5.5%. Assuming that an investor invests 115% of his savings in this portfolio, what is his expected return?
A
18.35%.
B
19.55%.
C
12.5%.
D
0.1345