The Jensen's measure, or Jensen's alpha, is a risk-adjusted performance measure that represents the average return on a portfolio or investment, above or below that predicted by the capital asset pricing model (CAPM), given the portfolio's or investment's beta and the average market return. This metric is also commonly referred to as simply alpha.
Key Takeaways
The Jensen's measure is the difference in how much a person returns vs. the overall market.
Jensen's measure is commonly referred to as alpha. When a manager outperforms the market concurrent to risk, they have "delivered alpha" to their clients.
The measure accounts for the risk-free rate of return for the time period.
To accurately analyze the performance of an investment manager, an investor must look not only at the overall return of a portfolio but also at the risk of that portfolio to see if the investment's return compensates for the risk it takes. For example, if two mutual funds both have a 12% return, a rational investor should prefer the less risky fund. Jensen's measure is one of the ways to determine if a portfolio is earning the proper return for its level of risk.
If the value is positive, then the portfolio is earning excess returns. In other words, a positive value for Jensen's alpha means a fund manager has "beat the market" with their stock-picking skills.
Real World Example of Jensen's Measure
Assuming the CAPM is correct, Jensen's alpha is calculated using the following four variables:
Using these variables, the formula for Jensen's alpha is:
R(i) = the realized return of the portfolio or investment
R(m) = the realized return of the appropriate market index
R(f) = the risk-free rate of return for the time period
B = the beta of the portfolio of investment with respect to the chosen market index
For example, assume a mutual fund realized a return of 15% last year. The appropriate market index for this fund returned 12%. The beta of the fund versus that same index is 1.2, and the risk-free rate is 3%. The fund's alpha is calculated as:
Given a beta of 1.2, the mutual fund is expected to be riskier than the index, and thus earn more. A positive alpha in this example shows that the mutual fund manager earned more than enough return to be compensated for the risk they took over the course of the year. If the mutual fund only returned 13%, the calculated alpha would be -0.8%. With a negative alpha, the mutual fund manager would not have earned enough return given the amount of risk they were taking.
Special Consideration: EMH
Critics of Jensen's measure generally believe in the efficient market hypothesis (EMH), invented by Eugene Fama,and argue that any portfolio manager's excess returns derive from luck or random chance rather than skill. Because the market has already priced in all available information, it is said to be "efficient" and accurately priced, the theory says, precluding any active manager from bringing anything new to the table. Further supporting the theory is the fact thatmany active managers fail to beat the market any more than those that invest their clients' money in passive index funds.
The Jensen's alpha aims to do this and is calculated using a simple formula: Jensen's alpha = Portfolio return
Portfolio return
The rate of return on a portfolio is the ratio of the net gain or loss (which is the total of net income, foreign currency appreciation and capital gain, whether realized or not) which a portfolio generates, relative to the size of the portfolio. It is measured over a period of time, commonly a year.
https://en.wikipedia.org › wiki › Rate_of_return_on_a_portfolio
Jensen's Measure quantifies the excess returns obtained by a portfolio of investments above the returns implied by the capital asset pricing model (CAPM).
How do you calculate alpha? The formula that calculates alpha is: Alpha = R - Rf - beta (Rm - Rf). In this formula, R represents the portfolio's return, Rf represents the risk-free rate of return, beta represents the systematic risk of a portfolio, and Rm represents the market return, for each benchmark.
In finance, Jensen's alpha (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance instead of a market index.
A positive Jensen's Alpha indicates that the manager has outperformed the market, generating excess returns beyond what would be expected given the portfolio's risk exposure. This suggests that the manager has added value through skillful investment decisions or superior timing.
A positive Jensen's alpha suggests the fund manager's stock selection skill has delivered superior risk-adjusted returns. When comparing two funds with similar beta ratios, investors prefer the one with the higher alpha since this implies greater reward at the same level of risk.
Jensen's alpha=αp=Rp–[Rf+βp(Rm–Rf)] Jensen's alpha = α p = R p – [ R f + β p ( R m – R f ) ] If \alphap is positive, the portfolio has outperformed the market, while a negative value indicates underperformance.
Every security has a required rate of return, as specified by the capital asset pricing model (CAPM). The Jensen index, or alpha, is what helps investors determine how much a portfolio's realized return differs from the return it should have achieved.
Alpha measures the difference between expected and actual returns of a mutual fund, based on its beta. A positive alpha, no matter how small, is considered good. A negative alpha is considered bad or slightly below average, depending on how negative the number is.
In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis.
Alpha is also known as the level of significance. This represents the probability of obtaining your results due to chance. The smaller this value is, the more “unusual” the results, indicating that the sample is from a different population than it's being compared to, for example. Commonly, this value is set to .
It is also commonly used in mathematics in algebraic solutions representing quantities such as angles. Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level when proving null and alternative hypotheses.
Anything more than zero is a good alpha; higher the alpha ratio in mutual fund schemes on a consistent basis, higher is the potential of long term returns. Generally, beta of around 1 or less is recommended.
The alpha Mutual Funds formula is (End Price + DPS – Start Price)/Start Price. Here, DPS is Distribution per share. Alpha can be calculated alternatively by using CAPM. As CAPM is indicative of the expected returns from a specific fund, any figure deviating from the same is the alpha.
Introduction: My name is Velia Krajcik, I am a handsome, clean, lucky, gleaming, magnificent, proud, glorious person who loves writing and wants to share my knowledge and understanding with you.
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