I’m a big fan of actually taking a look at a stock or portfolio of stocks and seeing how they’ve performed against a model that takes into account risk and expected return.  Jensen’s Alpha is a tool that will do that for us (one of many).  It will enable us to see if our portfolio has outperformed the market by specifically gauging the amount of risk we took on to get the return we’ve received.

To illustrate the practical application of Jensen’s Alpha, I’m going to look back at the first stock I recommended via this site.  In early July 2010 I wrote a post that first appeared on the Div-Net investment site arguing that Telefonica (TEF) was a buy.  (Note – Since the time of the post TEF has split, so the price quoted in the original post needs to be adjusted.)

For the sake of this example, let’s assume a year has passed and we’re doing an annual review of this investment.

The Jensen’s Alpha formual is as follows….

= Portfolio Return – [Risk-free return + (Market Return - Risk-free Return) * Beta]

= 34.47% – [1.0% + (32.15% - 1.0%) *.97]

= 34.47% – 31.22%

=3.25%

What the number above means if that holding TEF from 7/2/10 – 5/20/11 would have provided the investor with superior returns to the market (S&P 500).  Your investment would have outperformed the market in absolute terms with volatility factored into the measurement.

Here is how I received my inputs for the calculation above…

Risk Free Return = 1% (I’m using what I could expect to get from the best liquid savings account from a bank)

Market Return =1,333.27 (S&P on 5/20/11) – 1,022.58 (S&P on 7/2/10) = 310.69

• 310.69/1,022.58 = 30.38%
• (.602+.653+.553)/102.2 = 1.77% (I’m using the SPDR S&P 500 ETF as a proxy for the dividend yield calculation…3 dividend payments have been distributed since July 2nd)
• Total return = 30.38% + 1.77% = 32.15%

Beta =.97 (This beta figure compares TEF’s volatility against the S&P 500 over the past 5 years (obtained from Yahoo Finance)…The .97 measurement means that over 5 years the stock’s price, on average, has moved almost in sync with the S&P.)

• To properly do this calculation I should construct Beta on my own for the specific time period in question, but I’m too lazy.

Portfolio Return = 23.77 (Price on 5/20/11) – 19.15 (Price on 7/2/10) = +4.62

• 4.62/19.15 = 24.13% (Return from the stock’s price appreciation)
• (.8983 + 1.082)/19.15 = 10.34% (I’m adding the dividends paid on 11/3/10 and 5/3/10 to factor in Return on Investment based on dividend payments)
• Total return = 24.13% + 10.34% = 34.47%