Jensen’s Alpha proffers a precise method to evaluate the risk-adjusted performance by juxtaposing the actual portfolio returns against the expected returns derived from the Capital Asset Pricing Model (CAPM). Through the application of Python, the interplay between a portfolio’s actual return, its beta with respect to the market, and the market’s return itself is dissected, unraveling the intricacies of Jensen’s Alpha in quantifying the value added or subtracted by active portfolio management.
Obtain the historical returns of the stock you’re interested in. The real yield attained by the portfolio throughout the assessment period.
Get the historical returns of a benchmark index during the assessment span, often the NSE Nifty 50 for Indian stocks, SP500 for US stocks.
Usually denoted by government bond yields, representing the return on an investment deemed risk-free. In the context of Indian stocks, you might consider the yield on an Indian government bond.
An evaluation of the portfolio’s inherent market risk in comparison to the broader market.
Now, Let’s extend each of those points in more details –
Calculate Stock Returns:
Calculate Benchmark Returns:
Calculate Beta of the Stock:
Beta measures the stock’s volatility compared to the benchmark. It’s a crucial parameter in the Capital Asset Pricing Model (CAPM). We calculate the beta using regression analysis or by obtaining it from financial sources.
Calculate Expected Return with the Capital Asset Pricing Model (CAPM):
Using CAPM, we calculate the expected return of the stock. This calculation considers the risk-free rate, beta, and the difference between the benchmark return and the risk-free rate. It represents the return expected for the level of risk associated with the stock.
Expected Return = Risk-free Rate + Beta * (Benchmark Return – Risk-free Rate)
Finally, we compute Jensen’s Alpha by subtracting the expected return from the historical return. A positive alpha indicates that the stock has outperformed the benchmark, while a negative alpha suggests underperformance.
Alpha = Actual Stock Return – Expected Return
The value of Alpha offers insights:
It’s important to remember that while Alpha is valuable in assessing a stock’s performance against a benchmark, it should be used alongside other metrics for a complete evaluation of a stock’s potential.