## Expected Return

__Expected Return__

The expected return on financial investment is the expected value of its return. It is a measure of the center of the distribution of the random variable that is the return.

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__Meaning:__

The expected return is the profit or loss that an investor anticipated on an investment that has a known historical rate of return (ROR). It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. Expected returns calculations are a key piece of both business operations and financial theory, including in the well-known models of modern portfolio theory (MPT) to the Black Scholes option pricing model.

__Calculation:__

__Investments:__

The formula for investment with various probable returns can be calculated as the weighted average of all possible returns which is represented as

- Expected return = (P1 x r1) + (P2 x r2) +…… + (Pa x ra)
- Pi = probability of each return
- Ri = Rate of return with different probability

__Portfolio:__

The expected return of a portfolio is a simple extension of a single investment to a portfolio which can be calculated as the weighted average of returns of each investment in the portfolio, and it is represented as

- Expected return = (w1 x r1) + (w2 X r2) + ….. + (wa x ra)
- Wi = weight of each investment in the portfolio
- Ri = rate of return of each investment in the portfolio

__Example:__

Let’s assume we have an investor interested in the tech sector. His portfolio contains the following stocks:

- Alphabet Inc. $500,000 invested and an expected return of 15%
- Apple Inc. $200,000 invested and an expected return of 6%
- Amazon.com Inc. $300,000 invested and an expected return of 9%

With a total portfolio value of $1 million the weights of Alphabet, Apple, and Amazon in the portfolio are 50%, 20%, and 30%, respectively.

Thus, the expected return of the total portfolio is 11.4%:

(50% x 15% = 7.5%) + (20% x 6% = 1.2%) + (30% x 9% = 2.7%)

7.5% + 1.2% + 2.7%

= 11.4%

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__Limitations:__

Note that it can be quite dangerous to make naïve investment decisions based entirely on expected return calculations. Before making any investment decisions, one should always review the risk characteristics of investment opportunities to determine if the investment aligns with their portfolio goals. In addition to this, wise investors should also consider the likelihood of a return to better access risk. After all, one can find instances where certain lotteries offer a positive expected return, despite the very low chances of realizing that return.

__Final Thoughts:__

The expected return is the amount of profit or loss an investor can anticipate on an investment. Essentially a long-term i=weighted average of historical results, expected returns are not guaranteed. It is calculated by multiplying potential outcomes by the odds of them occurring and then totaling these results.

**Author – Hariharan Krishnan**

**About the Author – **Hariharan Krishnan is currently in second year BAF and is also doing FRM part 1. He is passionate about financial markets and loves to play chess and outdoor games.

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