# Expected Return

## Meaning of Expected return

The expected return of an investment is the expected return an investor will get from an investment or a portfolio of investments. This assumed return is based on the concept of probability and hence, is not a certainty or an assured outcome. Returns from an investment under different scenarios are worked out. Then they are multiplied by the probability of occurrence of that situation. A sum of all these possible returns leads to the expected return of the investment or the portfolio.

A point worth mentioning is the fact that the potential returns from an investment are calculated based on prior or historical data. The future returns can vary significantly from the historic returns due to the uncertainty of the future. Therefore, there is no guarantee of the expected returns calculated. It is just a measure of the positivity of the returns from a particular investment. Based on previous similar instances, how much should one expect to get back on the investment.

An investor can compare the expected return from different available options and choose the best alternative.

## Calculation of expected return

Let us start with a simple example of a single investment. There is a 50% probability of the investment giving returns of 10%, a 60% probability of the investment giving 8% return, and a 20% probability of the investment giving a loss of 5%.

Thus, the expected return from the investment will be:

(0.5*10)+(0.6*8)+(0.2*-5)

=5 +4.8-1

=8.8% returns

Now let us see an example of a portfolio with investments in three different companies. An individual has invested US\$5000 in company A, US\$ 10000 in company B, and US\$35000 in company C. His expected returns are 20%, 30%, and 18%, respectively.

First, we will calculate the weights of each investment in the total portfolio of US\$ 50000. The weights for Company A, B, and C investment are first 10%, 20%, and 18%, respectively. Now the expected return from these three different investments will be calculated as:

(0.1*20)+ (0.2*30) + (0.7*18)

=2+6+12.6

=20.6%

Thus the total portfolio of US\$50000 should fetch a return of 20.6%. The simple average of the three expected returns is (20+30+18)/3= 22.67%. But our expected return from the portfolio is a little lesser at 20.6%. It is because a major portion of the investment (70%) is in the company with the least expected return of 18%.

## Importance of Expected Return

The concept of expected returns is fundamental from an investor’s point of view.

### Proper Alignment of Investments

It helps an investor to properly align his investments according to his risk-taking ability and investment goals. Also, it is a well-established principle that investments with higher expected returns will come with higher risk and vice-versa.

### Portfolio Management

The concept of portfolio management is particularly important in the case of multiple investments or portfolio investments. Expected returns are a guiding factor to decide how much to invest in which security or option. An investor can rank the various assets according to their expected returns. And thus could decide on their weights in the portfolio.

## Limitations

The concept has its limitations as well.

### Ignorance of Risk Factor

Let us take an example of two separate portfolios, A and B consisting of five equal investments in different assets. Also, based on historical data, the return from each of the investments have been as follows:

Portfolio A: 10%, 15%, 2%, -8%, 6%

Portfolio B: 3%,7%,5%,2%,8%

The expected returns of portfolio A- (10+15+2-8+6)/5= 5%

The expected returns of portfolio B- (3+7+5+2+8)/5= 5%

We see that the expected returns from both portfolios are the same. But if we calculate the standard deviation, Portfolio A has a standard deviation of 6, whereas portfolio B has a standard deviation of 2.55. Thus, we see that the concept of expected returns ignores the risk factor and deviations from the mean returns achieved over the years.

### Based on historical data

The calculated expected returns are based on historical data of returns achieved from assets over the last few years. Hence, there is no guarantee that the investment will yield the same returns as in the past. Also, an investor may miss out on an excellent investment opportunity solely based on the past performance index. Factors like market conditions or the management might have changed, resulting in the company substantially outperforming its past. But based on expected returns calculation, investors may not opt for the option. Therefore, they may lose the opportunity to earn handsome profits.

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