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Paathshaala : Jensen's Alpha

Jensen’s Alpha

Jensen's model proposes another risk adjusted performance measure. This measure was developed by Michael Jensen and is sometimes referred to as the Differential Return Method. This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk (ßi). The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. Required return of a fund at a given level of risk (ßi) can be calculated as:

ri = rf + i (rM - rf)

Where, rM is average market return during the given period. After calculating it, alpha can be obtained by subtracting required return from the actual return of the fund.

Higher alpha represents superior performance of the fund and vice versa. Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive.

Alpha shows the fund’s performance relative to the benchmark and can demonstrate the value added by the fund manager. The higher the 'alpha' the better the manager.

Alpha is a risk-adjusted measure of the so-called "excess return" on an investment. It is a common measure of assessing an active manager's performance as it is the return in excess of a benchmark index or "risk-free" investment.

The alpha coefficient(αi) is a parameter in the capital asset pricing model. In fact it is the intercept of the Security Characteristic Line (SCL). One can prove that in an efficient market, the expected value of the alpha coefficient equals the return of the risk free asset:

E(αi) = rf.

Therefore the alpha coefficient can be used to determine whether an investment manager has created economic value:

  • αi< rf : the manager has destroyed value
  • αi= rf : the manager has neither created nor destroyed value
  • αi > rf : the manager has created value

The difference (αi- rf ) is called Jensen's alpha.

The concept and focus on Alpha comes from an observation increasingly made during the middle of the twentieth century, that around 75 percent of stock investment managers did not make as much money picking investments as someone who simply invested in every stock in proportion to the weight it occupied in the overall market in terms of market capitalization, or indexing. Many academics felt that this was due to the stock market being "efficient" which means that since so many people were paying attention to the stock market all the time, the prices of stocks rapidly moved to the correct price at any one moment, and that only luck made it possible for one manager to achieve better results than another, before fees or taxes were considered. A belief in efficient markets spawned the creation of market capitalization weighted index funds that seek to replicate the performance of investing in an entire market in the weights that each of the equity securities comprises in the overall market..

In fact, to many investors, this phenomenon created a new standard of performance that must be matched: an investment manager should not only avoid losing money for the client and should make a certain amount of money, but in fact should make more money than the passive strategy of investing in everything equally (since this strategy appeared to be statistically more likely to be successful than the strategy of any one investment manager).The name for the additional return above the expected return of the beta adjusted return of the market is called "Alpha".

A rational investor would not invest in an asset which does not improve the risk-return characteristics of his existing portfolio. Since a rational investor would hold the market portfolio, the asset in question will be added to the market portfolio.

Specific risk is the risk associated with individual assets - within a portfolio these risks can be reduced through diversification (specific risks "cancel out"). Systematic risk, or market risk, refers to the risk common to all securities - except for selling short as noted below, systematic risk cannot be diversified away (within one market). Within the market portfolio, asset specific risk will be diversified away to the extent possible. Systematic risk is therefore equated with the risk (standard deviation) of the market portfolio.

Since a security will be purchased only if it improves the risk / return characteristics of the market portfolio, the risk of a security will be the risk it adds to the market portfolio. In this context, the volatility of the asset, and its correlation with the market portfolio, is historically observed and is therefore a given (there are several approaches to asset pricing that attempt to price assets by modelling the stochastic properties of the moments of assets' returns - these are broadly referred to as conditional asset pricing models). The (maximum) price paid for any particular asset (and hence the return it will generate) should also be determined based on its relationship with the market portfolio.

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