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.

The mean return on government bonds is rf = 0.03% per day.

The table below describes the daily return of three stocks.

Date APPLE TESLA GM

01/10/2020 0.85% 4.46% 2.67%

02/10/2020 -3.23% -7.38% 0.26%

05/10/2020 3.08% 2.55% 1.64%

06/10/2020 -2.87% -2.75% -1.81%

07/10/2020 1.70% 2.73% 4.01%

08/10/2020 -0.10% 0.15% 1.87%

09/10/2020 1.74% 1.90% -0.16%

12/10/2020 6.35% 1.91% 0.16%

13/10/2020 -2.65% 0.98% -1.06%

14/10/2020 0.07% 3.28% -0.63%

15/10/2020 -0.40% -2.69% 2.90%

16/10/2020 -1.40% -2.05% 2.64%

19/10/2020 -2.55% -2.01% -0.30%

20/10/2020 1.32% -2.06% 6.75%

21/10/2020 -0.54% 0.17% 0.48%

22/10/2020 -0.96% 0.75% 4.58%

23/10/2020 -0.61% -1.21% -1.55%

26/10/2020 0.01% -0.08% -2.74%

27/10/2020 1.35% 1.05% -2.60%

28/10/2020 -4.63% -4.39% -2.29%

29/10/2020 3.71% 1.18% 2.35%

30/10/2020 -5.60% -5.55% -1.03%

02/11/2020 -0.08% 3.21% 0.06%

03/11/2020 1.54% 5.84% 2.32%

04/11/2020 4.08% -0.69% -0.31%

05/11/2020 3.55% 4.06% 5.39%

06/11/2020 -0.29% -1.86% 0.89%

09/11/2020 -2.00% -2.02% 3.98%

10/11/2020 -0.30% -2.59% 5.44%

11/11/2020 3.04% 1.65% -1.27%

12/11/2020 -0.23% -1.29% -3.06%

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

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