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. Assume your salary will be $40,000 per year. If you contribute $3,000 to the 401(k) plan, you will pay taxes only on $37,000 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 percent of your salary to the plan. As is common, there is a 5 percent match program. This means that the company will match your contribution dollar-for-dollar up to 5 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 funds 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. The company 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:

1. 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 funds 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 0.2 percent of assets per year.

2. Arias Small-Cap Fund. This fund primarily invests in small-capitalization stocks. As such, the returns of the fund are more volatile. The fund also can invest 10 percent of its assets in companies based outside the United States. This fund charges 1.7 percent of assets in expenses per year.

Question:

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 compared to the Arias S&P 500 Index Fund?

The standard deviations and return for the funds over the past 10 years are listed here. Assuming a risk-free rate of 3.1 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 11.80% 19.35%

Arias Small-Cap Fund 15.12 27.95