## Abnormal Return Definition

Abnormal Returns is defined as a variance between the actual return for a stock or a portfolio of securities and the return based on market expectations in a selected time period and this is a key performance measure on which a portfolio manager or an investment manager is gauged.

### Explanation

When we want to judge whether security or a group of securities have over or underperformed its peers, we need to figure out on what parameters can we judge such performance; therefore, the investment community has come up with such measures as the Abnormal return to articulate how much of such performance can be attributed to the skills of the portfolio manager and his scheme of asset allocation Asset AllocationAsset Allocation is the process of investing your money in various asset classes such as debt, equity, mutual funds, and real estate, depending on your return expectations and risk tolerance. This makes it easier to achieve your long-term financial goals.read more and stock selection.

When we compare the performance of a portfolio, we use a proportional market index as a benchmark over which we calculate the excess. For example, if we want to compare a portfolio of financial sector stock in India, we may use the Nifty Bank Index, while if we have a portfolio of large-cap stocks in the US, then we can have the S&P 500 as our benchmark.

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For eg:

Source: Abnormal Return (wallstreetmojo.com)

### Abnormal Return Formula

It is represented as below,

**Abnormal Return Formula = Actual Return – Expected Return**

### How to Calculate Abnormal Return?

To calculate the Expected returnCalculate The Expected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more, we can use the Capital Asset pricing modelCapital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more (CAPM). The following is the equation for the model:

**E _{r} = R_{f }+**

**β (R**

_{m }– R_{f})Here, E_{r }= Expected return in the security, R_{f }= risk-free rate, generally the rate of a government security or savings deposit rate, β= risk coefficient of the security or the portfolio in comparison to the market, R_{m}= Return on the market or an appropriate index for the given security such as S&P 500.

- Once we already have the expected return, we subtract the same from the actual return to calculate Abnormal return.
- When the portfolio or security has underperformed the expectations, the Abnormal return will be negative. Otherwise, it will be positive or equal to zero, as the case may be.

As per the prudent approach, it is better to take a look at the risk-adjusted return. This is in keeping with the concept of risk tolerance because otherwise, the portfolio manager may deviate from the IPS goals and take up highly risky investment to generate Abnormal return.

In the case of multiple periods, it may be helpful looking at the standardized returns to see if the portfolio is constantly beating the benchmark. If this is the case, then the standard deviation of the Abnormal return will be lower, and then we can say that the portfolio manager has genuinely made a better stock selection than the benchmark.

### Example of Abnormal Return

Suppose we are given the following information. Use this information to calculate abnormal return.

- Rf: 4%
- Rm: 12%
- Beta of the Portfolio: 1.8
- Beginning Value of Portfolio: $50,000
- Ending Value of Portfolio: $60,000

**Solution:**

**Step 1: **Calculation of Er of Portfolio

So we have calculated the expected return using the CAPM approach as follows:

E_{r} = R_{f} + β (R_{m }– R_{f})

E_{r} = 4+1.8*(12% – 4%)

E_{r}** = 18.40%**

The above calculation is done before the period under consideration starts, and it is only an estimation. When this period expires, we can calculate the actual return based on the market value at the beginning and the end of the period.

**Step 2:** Calculation of Actual Return can be done as follows,

Actual Return = Ending Value – Beginning Value/Beginning Value*100

=$60000 – $50000/$50000 * 100**=20.00%**

**Step 3:** Abnormal Return Calculation.

=20.00% – 18.40%**=1.60%**

### Importance

**Performance Attribution Metric:**It is directly affected by the stock selection of the portfolio managerPortfolio ManagerA Portfolio Manager is an executive responsible for making investment decisions & handle investment portfolios for fulfilling the client’s investment-related objectives. Also, he/she works towards maximizing the benefits & minimizing the potential risks for clients. read more. Therefore this measure is a key to judge her performance as compared to the appropriate benchmark and thereby it also helps in determining her performance-based compensation and skill-level**A check on Harmful Divergence:**As mentioned earlier, Abnormal return can be negative if the actual return is lower than the expected return. Therefore, if this is for multiple periods, then it acts as an alarm for reducing the divergence from the benchmark index because it points out to a poor stock selection**Thorough Quantitative Analysis:**As it can be calculated simply, it is a popular measure in the investment community, however, coming up with the correct estimates of the inputs of the CAPM model is not an easy task, as it involves the use of regression analysis to predict beta and a thorough observation of the past return numbers of the market index, therefore if done correctly, these estimates pass through a sieve of a thorough quantitative analysis and are therefore more likely to produce numbers with greater predictive power**Time Series Analysis:**Using a measure called the CAR or the cumulative abnormal return helps analyze the effect of corporate actions such as dividend payout or stock splitStock SplitStock split, also known as share split, is the process by which companies divide their existing outstanding shares into multiple shares, such as 3 shares for every 1 owned, 2 shares for every 1 held, and so on. The company's market capitalization remains unchanged during a stock split because, while the number of shares grows, the price per share decreases correspondingly.read more on the prices and return of the stock. It further helps analyze the effects of external events such as events on which certain corporate liabilities are contingent, for example, legal action or the settlement of a court case.

CAR is calculated by taking the sum of the abnormal returns over a specific period.

### Conclusion

To sum up, we can say that Abnormal return is most important, a measure which can help in gauging the performance of the portfolio manager and the correctness of his insights of market movement. This further gives asset management companiesAsset Management Companiesset Management Company is a company that takes the financial assets of a person, company or another asset management company (generally this will be high net worth individuals) and use the assets to invest in companies that use those as a operational investment, financial investment or any other investment in order to grow the investment.read more ground to base the performance-based bonuses or commissions of their portfolio managers and a justification of the same for client understanding.

Also, as it can be positive or negative, it can indicate when the divergence from the market index is not fruitful and should be narrowed, for the better performance of the portfolio.

### Recommended Articles

This has been a guide to Abnormal Return and its definition. Here we discuss the formula for calculation of abnormal return along with an example and downloadable excel template. You can learn more from the following articles –

- Asset Allocation Calculator
- Formula of Annualized Rate of Return
- Total Return Calculation
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