Using only the stock and bond funds to achieve a portfolio expected return of 14%,we must find the appropriate proportion in the stock fund (wS) and the appropriateproportion in the bond fund (wB = 1 − wS) as follows:0.14 = 0.20 × wS + 0.12 × (1 − wS) = 0.12 + 0.08 × wS wS = 0.25
Question
Using only the stock and bond funds to achieve a portfolio expected return of 14%,we must find the appropriate proportion in the stock fund (wS) and the appropriateproportion in the bond fund (wB = 1 − wS) as follows:0.14 = 0.20 × wS + 0.12 × (1 − wS) = 0.12 + 0.08 × wS wS = 0.25
Solution
The text you provided is a mathematical calculation to determine the appropriate proportions of stock and bond funds in a portfolio to achieve an expected return of 14%. Here's the step-by-step solution:
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The equation given is 0.14 = 0.20 × wS + 0.12 × (1 − wS), which represents the expected return of the portfolio. The 0.14 is the desired return, 0.20 is the return of the stock fund, wS is the proportion of the portfolio in the stock fund, 0.12 is the return of the bond fund, and (1 - wS) is the proportion of the portfolio in the bond fund.
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The equation is then simplified to 0.14 = 0.12 + 0.08 × wS. This is done by distributing the 0.12 to the (1 - wS) and subtracting it from the 0.20 × wS.
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Finally, to solve for wS, you subtract 0.12 from both sides of the equation and then divide by 0.08. This gives you wS = 0.25.
So, to achieve a portfolio expected return of 14%, you should invest 25% of the portfolio in the stock fund and the remaining 75% in the bond fund.
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