Choose one stock and collect its monthly returns in the past 13 months (historical prices can be found under Historical Data on finance.yahoo). Compute the average monthly return and its standard deviation during this time period. Also, collect its beta information from any financial website.

Using the S&P 500 as a proxy, the market average monthly return is 2.21% and the standard deviation is 3.03%. The monthly risk-free rate is assumed to be 0.01%.

Based on the information, compute the Sharpe, Treynor and Jensen's measures for the stock you choose. Based on each criterion, did your stock beat the market?

An example from professor: TESLA

I collect Tesla (TSLA) historical monthly prices and compute its average monthly returns as 6.15%, with a standard deviation of 15.98% (see the attached file). Its beta is 2.01 on finance.yahoo.com.

Given the market return of 2.21%, market standard deviation of 3.03%, and the risk-free rate of 0.01%, we can compute the following.

TSLA's Sharpe = (R - Rf) / SD = (6.15% - 0.01%) / 15.98% = 0.38

Market's Sharpe = (Rm - Rf) / SDm = (2.21% - 0.01%) / 3.03% = 0.73

0.38 < 0.73, TSLA did not beat the market based on Sharpe.

TSLA's Treynor = (R - Rf) / Beta = (6.15% - 0.01%) / 2.01 = 3.05%

Market's Sharpe = (Rm - Rf) / 1 = (2.21% - 0.01%) / 1 = 2.20%

3.05% > 2.20%, TSLA beat the market based on Treynor.

TSLA's Jensen's Alpha = R - [Rf + beta * (Rm - Rf)]

= 6.15% - [0.01% + 2.01 * (2.21% - 0.01%)] = 1.72% > 0

TSLA beat the market based on Jensen's Alpha.

To summarize, TSLA under-performed the market based on Sharpe, but it outperformed the market based on Treynor and Jensen's Alpha during the past 12-month period.