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What is Jensen's alpha?

Jensen’s alpha:
It is developed by Michael Jensen in 1968. It helps to measure the risk adjusted return of a security in relation to market return. It uses Capital Asset Pricing Model. It tells about the extra return earned by security in market index. It is also known as abnormal return or alpha.  Alpha can be positive and negative. If it is negative then the portfolio return is less than the market return. If it is positive than the portfolio return is more than market return. The portfolio which has positive Jensen’s alpha is considers better for the investment.

Formula:
αp = Rp – [Rf + βp (Rm – Rf)]
Where,
αp = Alpha of portfolio
Rp = Return of a portfolio
βp = Beta of a portfolio
Rm = Market return
Rf = Risk free rate of return

Advantages of Jensen’s alpha:
·         It helps to select the portfolio which gives excess return in relation to market return.
·         It helps to measure the performance of hedge funds.

Disadvantages of Jensen’s alpha:
·         It uses single factor model that is CAPM which only considers the market risk.
·         It does not consider the unsystematic risk related to firm specific.

Difference between Jensen’s alpha and Treynor ratio: Both the treynor ratio and Jensen’s alpha is based on systematic risk. But the treynor ratio uses beta for calculation while Jensen’s alpha uses CAPM model.

Difference between Jensen’s alpha and Sharpe ratio: The Jensen’s alpha is based on systematic risk and uses CAPM model to calculate risk adjusted return in relation to market risk. While the Sharpe ratio considers the total risk which includes systematic risk and unsystematic risk. It uses standard deviation for total risk.

Example: Find out the Jensen’s alpha with the help of given information:
·         Stock A has expected return of 12% and risk free rate is 3.6%. The market return is 14.5% and beta coefficient is 1.23.

Solution: αp = Rp – [Rf + βp (Rm – Rf)]
= 12 – [3.6 + 1.23 (14.5 – 3.6)]
= 12 – [3.6 + 1.23*10.9]
= 12 – [3.6 + 13.41]
= 12 – 17.01
= -5.01%

Example: Find out which investment gives excess return from the given investment portfolio (with the help of Jensen’s alpha formula).

Investment Portfolio
Expected rate of return
Beta
Market return
A
9.6%
1.02
10.2
B
11.0%
2.15
10.3
C
8.6%
0.56
7.0
D
11.3%
-0.88
11.0
The risk free rate for all the investment is 5%.

Solution: αp = Rp – [Rf + βp (Rm – Rf)]
Investment portfolio A:
= 9.6 – [5 + 1.02 (10.2 -5)]
= 9.6 – 10.30
= -0.7%

Investment portfolio B:
= 11 – [5 + 2.15 (10.3 – 5)]
= 11 – 16.4
= -5.4%

 Investment portfolio C:
= 8.6 – [5 + 0.56 (7.0 – 5)]
= 8.6 – 6.12
= 2.48%

Investment portfolio D:
= 11.3 – [5 + -0.88 (11.0 – 5)]
= 11.3 – (-0.28)
= 11.58%

The investment portfolio C and D gives positive Jensen’s alpha that is 2.58% and 11.58% respectively. But the investment portfolio D gives higher Jensen’s alpha or return i.e. 11.58% over market return 11%. So, Investment portfolio D is best option than investment portfolio C.


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