It is almost impossible to understand the actual performance of securities or investment portfolios when assessing investment returns without considering the risks taken. As specified by the Capital Asset Pricing Model (CAPM), every security has a required rate of return.

The Jensen index or alpha can help investors determine how far the realized return of the portfolio is from the return it should have received. This article will provide a deeper understanding of alpha and its practical applications.

Key points

- Alpha refers to the excess return of an investment that is higher than the benchmark return.
- Active portfolio managers seek to generate alpha in a diversified portfolio, diversification aims to eliminate unsystematic risks.
- Because alpha represents the performance of the portfolio relative to the benchmark, it is usually considered to represent the value that the portfolio manager increases or decreases the return of the fund.
- Jensen’s alpha considers the capital asset pricing model (CAPM) and includes a risk adjustment component in its calculations.

## Alpha definition

Alpha is calculated based on the capital asset pricing model. The CAPM equation is used to determine the return required for an investment; it is usually used to evaluate the realized performance of a diversified investment portfolio. Because it is assumed that the portfolio under evaluation is a diversified portfolio (meaning that non-systematic risks have been eliminated), and because the main source of risk in a diversified portfolio is market risk (or systemic risk), the beta is Appropriate indicators to measure this risk.

Alpha is used to determine the degree to which the realized return of the portfolio differs from the required return determined by CAPM. The formula for alpha is expressed as follows:

α = Rp – [Rf + (Rm – Rf) β]

Where:

Rp = Realized return of the portfolio Rm = Market return Rf = Risk-free interest rate

*β *= The beta of the asset

## What does Alpha measure?

Alpha measures the risk premium in beta (β); therefore, it is assumed that the portfolio being evaluated is very diverse. The Jensen index requires the use of a different risk-free interest rate for each time interval measured in a specified period. For example, if you use annual intervals to measure fund managers over a five-year period, you must check the fund’s annual return minus the return on risk-free assets (ie U.S. Treasury bills or one-year risk-free assets) for each year and compare it with The annual return of the market portfolio minus the same risk-free interest rate is correlated.

This calculation method contrasts with the Treynor and Sharpe metrics, because both examine the average return over the entire period of all variables (including portfolio, market, and risk-free assets).

Alpha is a good measure of performance that compares the realized return with the return that investors should receive for the amount of risk they take. Technically speaking, it is a factor that represents a different performance from the beta of a portfolio, and represents a measure of the manager’s performance. For example, it is not enough for investors to consider the success or failure of mutual funds by looking at their returns. A more relevant question is: Is the manager’s performance sufficient to justify the risk taken in order to obtain the above-mentioned return?

## Application result

A positive alpha indicates that the portfolio manager’s performance is better than expected based on the manager’s risk of the fund (measured by the fund’s beta). Negative alpha means that managers are actually doing worse than they should give the required return for the portfolio. The regression results usually cover a period between 36 and 60 months.

The Jensen Index allows the performance of portfolio managers to be compared relative to each other or relative to the market itself. When applying Alpha, it is important to compare funds in the same asset class. It doesn’t make sense to compare funds of one asset class (ie, large-cap stock growth) with funds of another asset class (ie, emerging markets), because you are essentially comparing apples and oranges.

The image below provides a good comparison example of alpha or “excess return.” Investors can use both alpha and beta to judge the performance of managers.

Table 1 | ||||||
---|---|---|---|---|---|---|

Fund name |
Asset Class |
Stock code |
Α 3 years |
Beta 3 years |
3 years tracking return |
5-year tracking return |

American Fund Growth Fund A | Big growth | AGTHX | 4.29 | 1.01 | 16.61 | 20.46 |

Fidelity large-cap stocks grow | Big growth | FSLGX | 7.19 | 1.04 | 22.91 | —— |

T. Rowe Price Growth Stocks | Big growth | Associated Press | 5.14 | 1.03 | 17.67 | 21.54 |

Vanguard Growth Index Fund Admiral Stock | Big growth | Wigax | 6.78 | 1.04 | 19.76 | 21.43 |

Table 1

The figures in Table 1 show that on the basis of risk adjustment, Fidelity’s large growth stocks have achieved the best results among listed funds. In the small sample provided above, the alpha for the four-year period exceeds that of its peers.

It is important to note that not only is it appropriate to compare between the same asset class, but the correct benchmark should also be considered. The most commonly used benchmark to measure the market is the Standard & Poor’s 500 Index, which is a representative of the “market”.

However, the characteristics of the asset classes contained in certain investment portfolios and mutual funds cannot be accurately compared with the Standard & Poor’s 500 Index, such as bond funds, industry funds, and real estate. Therefore, the S&P 500 index may not be a suitable benchmark case for the index. Therefore, the alpha calculation must include the relative benchmark of the asset class.

## Bottom line

Portfolio performance includes return and risk. The Jensen index or alpha provides us with a fair standard of manager performance. The results can help us determine whether the manager has added value or even extra value on the basis of risk adjustment. If so, it also helps us determine whether the manager’s expenses are reasonable when we review the results. Buying (or even keeping) an investment fund without this consideration is like buying a car that will take you from point A to point B without having to evaluate its fuel efficiency.

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