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How to Calculate Abnormal Returns With Stock Prices and S&P 500 Data

"Abnormal returns" is an important concept in academic finance, as well as in the investment management industry. Let's go over how to calculate an abnormal return for a stock using stock prices and S&P 500 data, complete with a concrete example.

First, what is an "abnormal" return?
An abnormal return is the part of a stock's return that is be explained by a specific pricing model. In other words, a theoretical model meets market reality:

Abnormal return = expected return - actual return

"Expected return" refers to the forecast return your pricing model spits out. Note that the abnormal return can be positive or negative.

The original model in this framework is the Capital Asset Pricing Model (CAPM), which enables investors to calculate a stock's expected return as a function of the risk-free rate, the market return (in practice, the return of a benchmark index), and beta, which captures how volatile the stock is relative to the market. However, there are other possible models, some of which are more sophisticated and use multiple factors.

For the purpose of our example, we will use the CAPM.

Another expression for abnormal return is "excess return." This is an intuitive label, as it refers to the return in excess of what is expected (although the abnormal return, again, can also be negative). The favored terminology of the investment management industry, however, is "alpha." Alpha is the Holy Grail of a fund manager who manages money actively.

Let's calculate the abnormal return for a high-profile stock, Netflix, for 2015, during which it was the best-performing stock in the S&P 500, notching up a stunning 134.38% return.

NFLX 2014 return = ($114.38 / $48.80) - 1 = 134.38%

Step 1: Calculate your expected return
This Wiki page covers this step in much more detail, but the basic formula for calculating a stock's expected return under the CAPM is:

Expected return = risk-free rate + beta x (market return - risk-free rate)

The risk-free rate we will use is the one-year Treasury bill rate as of Dec. 31, 2014, which was a miserable 0.22%. (These rates are available on the FRED website, which is maintained by the Federal Bank of St. Louis.) Netflix's beta is 0.97, according to data on Yahoo! Finance provided by S&P Capital IQ. The total return on the S&P 500, our market benchmark index, was 1.38% in 2015.

We have risk-free rate, beta, and market return -- all the inputs required to calculate our expected return:

Expected return (NFLX) = 0.22% + (-0.97) x (-1.38%) = 1.56%

Step 2: Compare the expected return to the actual return in order to determine the abnormal return
We're now ready to calculate the abnormal return:

Abnormal return (NFLX) = actual return (NFLX) - expected return (NFLX) = 134.38% - 1.56% = 132.82%

In other words, the abnormal return of Netflix shares dwarfs the expected return generated by the CAPM; essentially all of the observed return is excess return (again, according to the CAPM model).

Perhaps that has something to do with the fact that Netflix shares ended 2014 down 29% from their 52-week high, whereas the S&P 500 had just put in its 52-week high two days earlier. Furthermore, the proportion of analyst "Hold" ratings (meaning the analyst is tepid on the stock) was the highest it had been in eight months. It's important to keep these unreliable factors in mind when forecasting or evaluating a stock's performance.

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