Business High School

the risk-free asset has an expected return of .03; the tangent portfolio has an expected return of .15 and a standard deviation of .25. if you are willing to invest in any portfolio, and you can accept a standard deviation of .2, what is the highest expected return that you can earn? group of answer choices .097 .148 .081 .126

Answers

Answer 1

The highest expected return you can earn with a standard deviation of 0.2 is .126 or 12.6%.

The highest expected return you can earn with a standard deviation of 0.2 can be calculated using the Capital Asset Pricing Model (CAPM). Here's a step-by-step explanation:
1. Identify the given information: The risk-free asset has an expected return of 0.03, the tangent portfolio has an expected return of 0.15 and a standard deviation of 0.25, and you can accept a standard deviation of 0.2.
2. Calculate the Sharpe ratio for the tangent portfolio: Sharpe ratio = (Expected return of tangent portfolio - Expected return of risk-free asset) / Standard deviation of tangent portfolio. In this case, Sharpe ratio = (0.15 - 0.03) / 0.25 = 0.48.


3. Determine the weight of the tangent portfolio in your desired portfolio: Weight = (Desired standard deviation - Standard deviation of risk-free asset) / (Standard deviation of tangent portfolio - Standard deviation of risk-free asset). Since the risk-free asset has a standard deviation of 0, Weight = (0.2 - 0) / (0.25 - 0) = 0.8.
4. Calculate the weight of the risk-free asset in your desired portfolio: This is simply 1 - Weight of tangent portfolio. In this case, it is 1 - 0.8 = 0.2.
5. Calculate the expected return of your desired portfolio: Expected return = (Weight of tangent portfolio * Expected return of tangent portfolio) + (Weight of risk-free asset * Expected return of risk-free asset). In this case, Expected return = (0.8 * 0.15) + (0.2 * 0.03) = 0.126.Therefore, the correct answer from the group of answer choices is .126.

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