Some investors use the Sharpe ratio as a way of comparing the benefits of owning shares of stock in a company to the risks. The Sharpe ratio of a stock is defined as the ratio of the difference between the mean return on the stock and the mean return on government bonds (called the risk-free rate rf) to the SD of the returns on the stock.
Sharp ratio = y̅ – r_f / s

The mean return on government bonds is r_f = 0.0033 per month (that is, about 1>3 of 1% per month, or 4% annually).

(a) Find the Sharpe ratio of stock in these three companies. Which looks best from this investment point of view?

(b) Form a new column by subtracting rf from the return each month on Dell. Then divide this column of differences by the SD for Dell. What’s the mean value for this column?

(c) How does the Sharpe ratio differ from the type of standardizing used to form z-scores?