# How to Calculate the Jensen’s Alpha

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.

## Required Data for Calculation of Jensen's Alpha

Portfolio/Stock Returns:

Obtain the historical returns of the stock you’re interested in. The real yield attained by the portfolio throughout the assessment period.

Benchmark Returns:

Get the historical returns of a benchmark index during the assessment span, often the NSE Nifty 50 for Indian stocks, SP500 for US stocks.

Risk-free Rate:

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.

Beta Indicator:

An evaluation of the portfolio’s inherent market risk in comparison to the broader market.

## How to Calculate Jensen's Alpha:

Now, Let’s extend each of those points in more details –

Calculate Stock Returns:

1. Obtain the historical prices of the stock from sources such as the NSE’s official website or other financial data providers.
2. Calculate daily returns using this formula: Return = (Current Price – Previous Price) / Previous Price

Calculate Benchmark Returns:

1. Acquire the historical values of the benchmark index, like NSE Nifty 50.
2. Calculate daily returns similarly to the stock 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.

1. Beta measures the stock’s volatility compared to the benchmark index.
2. This can be determined through regression analysis where stock returns are dependent and benchmark returns are independent.
3. Alternatively, many financial websites provide Beta values for stocks.

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)

## Determine Alpha:

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:

• A positive Alpha indicates that the stock has outperformed the benchmark index.
• A negative Alpha means the stock has underperformed compared to the benchmark.
• An Alpha of zero suggests the stock’s performance matched the benchmark.

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.

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