1. Using Probability Distributions. Suppose the returns on long-term corporate bonds and T-bills are normally distributed. Based on the historical record, use the NORMDIST function in Excel° to answer the following questions:
a. What is the probability that in any given year, the return on long-term corporate bonds will be greater than 10 percent? Less than 0 percent?
b. What is the probability that in any given year, the return on T-bills will be greater than 10 percent? Less than 0 percent?
c. In 1979, the return on long-term corporate bonds was —4.18 percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return of 10.56 percent in this same year. How likely is it that such a high return on T-bills will recur at some point in the future?
2. You recently graduated from college, and your job search led you to S&S Air. Since you felt the company’s business was headed skyward, you accepted the job offer. As you are finishing your employment paperwork, Chris Guthrie, who works in the finance department, stops by to inform you about the company’s new 401(k) plan. A 401(k) is a type of retirement plan offered by many companies. A 401(k) is tax deferred, which means that any deposits you make into the plan are deducted from your current income, so no current taxes are paid on the money. For example, assume your salary will be $30,000 per year. If you contribute $1,500 to the 401(k) plan, you will pay taxes only on $28,500 in income. No taxes will be due on any capital gains or plan income while you are invested in the plan, but you will pay taxes when you withdraw the money at retirement. You can contribute up to 15 per-cent of your salary to the plan. As is common, S&S Air also has a five percent match program. This means that the company will match your contribution dollar-for-dollar up to five percent of your salary, but you must contribute to get the match. The 401(k) plan has several options for investments, most of which are mutual funds. As you know, a mutual fund is a portfolio of assets. When you purchase shares in a mutual fund, you are actually purchasing partial ownership of the fund’s assets, similar to purchasing shares of stock in a company. The return of the fund is the weighted average of the return of the assets owned by the fund, minus any expenses. The largest expense is typically the management fee paid to the fund manager, who makes all of the investment decisions for the fund. S&S Air uses Arias Financial Services as its 401(k) plan administrator. Chris Guthrie then explains that the retirement investment options offered for employees are as follows:
a. Company Stock. One option is stock in S&S Air. The company is currently privately held. The price you would pay for the stock is based on an annual appraisal, less a 20 percent discount. When you interviewed with the owners, Mark Sexton and Todd Story, they informed you that the company stock was expected to be publicly sold in three to five years. If you needed to sell the stock before it became publicly traded, the company would buy it back at the then-current appraised value.
b. Arias S&P 500 Index Fund. This mutual fund tracks the S&P 500. Stocks in the fund are weighted exactly the same as they are in the S&P 500. This means that the fund’s return is approximately the return of the S&P 500, minus expenses. With an index fund, the manager is not required to research stocks and make investment decisions, so fund expenses are usually low. The Arias S&P 500 Index Fund charges expenses of 0.20 percent of assets per year.
c. Arias Small-Cap Fund. This fund primarily in-vests in small capitalization stocks. As such, the returns of the fund are more volatile. The fund can also invest 10 percent of its assets in companies based outside the United States. This fund charges 1.70 percent of assets in expenses per year.
d. Arias Large-Company Stock Fund. This fund invests primarily in large capitalization stocks of companies based in the United States. The fund is managed by Melissa Arias and has outperformed the market in six of the last eight years. The fund charges 1.50 percent in expenses.
e. Arias Bond Fund. This fund invests in long-term corporate bonds issued by U.S. domiciled companies. The fund is restricted to investments in bonds with an investment grade credit rating. This fund charges 1.40 percent in expenses.
f. Arias Money Market Fund. This fund invests in short-term, high credit quality debt instruments, which include Treasury bills. As such, the return on money market funds is only slightly higher than the return on Treasury bills. Because of the credit quality and short-term nature of the investments, there is only a very slight risk of negative return. The fund charges 0.60 percent in expenses.
QUESTIONS
a. What advantages/disadvantages do the mutual funds offer compared to company stock for your retirement investing?
b. Notice that, for every dollar you invest, S&S Air also invests a dollar. What return on your investment does this represent? What does your answer suggest about matching programs?
c. Assume you decide you should invest at least part of your money in large capitalization stocks of companies based in the United States. What are the advantages and disadvantages of choosing the Arias Large-Company Stock Fund com-pared to the Arias S&P 500 Index Fund?
d. The returns of the Arias Small-Cap Fund are the most volatile of all the mutual funds offered in the 401 (k) plan. Why would you ever want to invest in this fund? When you examine the expenses of the mutual funds, you will notice that this fund also has the highest expenses. Will this affect your decision to invest in this fund?
e. A measure of risk-adjusted performance that is often used in practice is the Sharpe ratio. The Sharpe ratio is calculated as the risk premium of an asset divided by its standard deviation. The standard deviations and returns for the funds over the past 10 years are listed below. Assuming a risk-free rate of 4 percent, calculate the Sharpe ratio for each of these. In broad terms, what do you suppose the Sharpe ratio is intended to measure?
|
|
10-Year Annual Return
|
Standard Deviation
|
|
Arias S&P 500 Index Fund |
9.15% |
19.35% |
|
Arias Small-Cap Fund |
14.05% |
26.82% |
|
Arias Large-Company Stock Fund |
9.53% |
23.82% |
|
Arias Bond Fund |
8.73% |
11.45% |
3. Work out this exercise on risk and return. Suppose you observe the following situation as depicted in the table below. If the risk-free rate is 8%, are these securities correctly priced? What would the risk-free rate have to be if they are correctly priced?
|
SECURITY |
BETA |
EXPECTED RETURN |
|
Cooley, Inc. |
1.6 |
19% |
|
Moyer Co. |
1.2 |
16% |
4. You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 11 percent. If your goal is to create a portfolio with an expected return of 12.4 percent, how much money will you invest in Stock X? In Stock Y?
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