Question

Now you want to combine the highest Sharpe ratio portfolio (the Optimal risky Portfolio O) you found out above with a risk-free asset to create a Portfolio C for your client to get an even more efficient portfolio. The risk-free asset, the 30-day U.S. Treasury Bills, provides a risk-free annual rate of return of 1%

a. Suppose your client says her risk tolerance of 5.5%, what is the expected return and risk of her combined portfolio C ?
b. How much weight (your client’s wealth distribution) should you put into Portfolio O (the risky asset) and in the risk-free asset in the above situation to create Portfolio C ?
c. How does the weight in each asset (Equity, Bond & the risk-free rate) in portfolio C look like? Give the interpretation on the portfolio’s weights for 100$ investment in portfolio C

Answer 1

The expected return and risk of Portfolio C depend on the risk-free rate, the returns of Portfolio O, and the investor's risk tolerance. Exact allocation cannot be provided without specific data on Portfolio O. Investments should be weighted to meet the client's desired risk level, and the distribution of a $100 investment in Portfolio C is determined by these weights.

Step-by-step explanation:

In order to determine the expected return and risk of a combined portfolio C, which includes a risk-free asset and the Optimal risky Portfolio O, one must consider the investor's risk tolerance and the expected return of the risky portfolio. However, without the provided returns, standard deviations, or correlations for Portfolio O, we cannot perform the exact calculations needed to answer the student's question. That said, we can discuss the general approach to this kind of problem.

When combining a risk-free asset with a risky asset, the expected return on the combined portfolio C can be calculated using the formula:

Expected Return on Portfolio C = (Weight of Portfolio O * Expected Return of Portfolio O) + (Weight of Risk-Free Asset * Risk-Free Rate)

Similarly, the risk for the combined portfolio will be proportional to the risk of the risky portfolio since the risk-free asset has no risk. The client's risk tolerance can be used to determine the weight of assets in the portfolio. Normally, the Capital Allocation Line (CAL) is used to combine risk-free and risky assets, where the slope of the line is the increase in the expected return per unit of risk. The weights should balance to the investor's desired risk level, which in this case is 5.5%.

As for the distribution of $100 investment in Portfolio C, it would depend on the proportion invested in each asset. Assuming the weight is calculated, one could simply multiple the weight by $100 to find the amount invested in each asset.