Abnormal Return

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.

Abnormal-Return

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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:

Er = R+ β (Rm – Rf)

Here, Er = Expected return in the security, Rf = risk-free rateRisk-free RateA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more, 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, Rm= 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 returnRisk-adjusted ReturnRisk-adjusted return is a strategy for measuring and analyzing investment returns in which financial, market, credit, and operational risks are evaluated and adjusted so that an individual may decide whether the investment is worthwhile given all of the risks to the capital invested.read more. 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

You can download this Abnormal Return Excel Template here – Abnormal Return Excel Template

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

Abnormal Return Example 1.1

So we have calculated the expected return using the CAPM approach as follows:
Er = Rf + β (Rm – Rf)
Er = 4+1.8*(12% – 4%)
Er = 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,

Abnormal Return Example 1.2

Actual Return = Ending Value – Beginning Value/Beginning Value*100
=$60000 – $50000/$50000 * 100
=20.00%

Step 3: Abnormal Return Calculation.

Abnormal Return Example 1.3

=20.00% – 18.40%
=1.60%

Importance

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 CompaniesAsset 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.

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