Question

You are discussing your 401(k) with Dan Ervin when he mentions that Sarah Brown, a representative from Bledsoe Financial Services, is visiting East Coast Yachts today. You decide that you should meet with Sarah, so Dan sets up an appointment for you later in the day.

When you sit down with Sarah, she discusses the various investment options available in the company’s 401(k) account. You mention to Sarah that you researched East Coast Yachts before you accepted your new job. You are confident in management’s ability to lead the company. Analysis of the company has led to your belief that the company is growing and will achieve a greater market share in the future. You also feel you should support your employer. Given these considerations, along with the fact that you are a conservative investor, you are leaning toward investing 100 percent of your 401(k) account in East Coast Yachts.

Assume the risk-free rate is the historical average risk-free rate (in Chapter 10). The correlation between the bond fund and the large-cap stock fund is .16. (Note: The spreadsheet graphing and “Solver” functions may assist you in answering the following questions.)

1. Considering the effects of diversification, how should Sarah respond to the suggestion that you invest 100 percent of your 401(k) account in East Coast Yachts stock?

2. After hearing Sarah’s response to investing your 401(k) account entirely in East Coast Yachts stock, she has convinced you that this may not be the best alternative. Since you are a conservative investor, you tell Sarah that a 100 percent investment in the bond fund may be the best alternative. Is it?

3. Using the returns for the Bledsoe Large-Cap Stock Fund and the Bledsoe Bond Fund, graph the opportunity set of feasible portfolios.

4. After examining the opportunity set, you notice that you can invest in a portfolio consisting of the bond fund and the large-cap stock fund that will have exactly the same standard deviation as the bond fund. This portfolio will also have a greater expected return. What are the portfolio weights and expected return of this portfolio?

5. Examining the opportunity set, notice there is a portfolio that has the lowest standard deviation. This is the minimum variance portfolio. What are the portfolio weights, expected return, and standard deviation of this portfolio? Why is the minimum variance portfolio important?

6. A measure of risk-adjusted performance that is often used is the Sharpe ratio. The Sharpe ratio is calculated as the risk premium of an asset divided by its standard deviation. The portfolio with the highest possible Sharpe ratio on the opportunity set is called the Sharpe optimal portfolio. What are the portfolio weights, expected return, and standard deviation of the Sharpe optimal portfolio? How does the Sharpe ratio of this portfolio compare to the Sharpe ratio of the bond fund and the large-cap stock fund? Do you see a connection between the Sharpe optimal portfolio and the CAPM? What is the connection?

Answer 1

1. Considering that the company is in the growth stage and aiming to achieve higher market share, though the investor believes in the company but being of conservative nature, Sarah would advise to go for diverse investing in funds rather than just investing the whole amount in just one stock fund. Higher the chances of returns, higher the risks associated with it.

2. Conservative investors look for a regular supply of money with time. They want their monthly returns to be sufficient for their living expenses adjusted with the inflation. But the high inflation rates and rising interest rates makes it difficult for them to earn their living expenses in risk-free bonds. Sarah will advise to invest in a mix of bond funds and stock funds to have a stable growth with minimum deviation.

3.

Bledsoe Large Company Stock Fund

10 year annual return = 11.85%

standard deviation = 15.41%

Bledsoe bond fund:

10 year annual return = 9.67%

standard deviation = 10.83%

Opportunity set of feasible portfolios can be plotted using the returns.

4. For the mixed portfolio, the standard deviation is calculated as:

and standard deviation of portfolio and bond are equal.

So,

On solving, we get

Expected return = 0.7*9.67 + 0.3*11.85 = 10.324%