Calculation of Expected Rate of Return for Individual Security

Expected return is the mean return an investor anticipates from a security over a specified horizon, based on all possible outcomes and their likelihoods. It is a forward‑looking measure, unlike historic realised returns which are backward‑looking.

In the NISM syllabus, expected return is used to compare securities, to estimate portfolio performance, and as an input to the Capital Asset Pricing Model (CAPM). The concept also appears in questions that ask you to choose the security with the higher expected return given different scenarios.

Exam candidates often confuse expected return with the simple arithmetic average of past returns. Remember: expected return incorporates probabilities of each outcome, while the average treats every past observation as equally likely.

• Probability‑weighted approach – used when future scenarios are explicitly given.
• Historical average – used when only past return data is available.

When a security can generate several distinct returns, each with a known probability, the expected return is the weighted average of those returns. The weight for each return is its probability of occurrence.

This method aligns with the definition of expected value in probability theory and is the preferred approach in the NISM exam when a question provides a scenario table.

Understanding why the formula works helps you avoid calculation errors. Each probability (p_i) represents the share of the total outcome space, so multiplying it by the associated return (R_i) gives the contribution of that scenario to the overall average.

If only past returns are available and no probabilities are given, candidates often use the simple arithmetic average as a proxy for expected return. This method assumes each observed return is equally likely in the future.

While the syllabus emphasises the probability‑weighted approach, the average return formula still appears in exam items that present a list of historical yearly returns.

Be cautious: the average does not account for volatility or skewness, so it may differ significantly from a probability‑weighted estimate when outcomes are unevenly distributed.

Expected return for an equity is the sum of expected capital‑gain return and expected dividend yield. SEBI defines total return as the combination of price appreciation and dividend income.

When probabilities are given for price change, you must also incorporate the known dividend yield (usually a fixed percentage). The formula becomes E(R) = Σ p_i × (Capital‑gain_i + Dividend_yield).

Exam questions may provide a dividend yield separately; forgetting to add it is a frequent mistake that reduces the calculated expected return.

Advisors use the expected return of each security to compute the portfolio’s overall expected return, which is the weighted average of individual expected returns based on allocation percentages.

In the NISM exam, you may be asked to calculate the portfolio expected return given the weights of two or three securities. The same probability‑weighted principle applies to each security before aggregation.

Understanding the concept also helps you explain to clients why a security with a higher historical average may still be less attractive if its future probability‑weighted return is lower.

Probability‑Weighted Expected Return: E(R) = \sum_{i=1}^{n} p_{i} \times R_{i}. Use when scenarios and probabilities are provided.

Historical Average Return: \bar{R} = \frac{1}{n} \sum_{i=1}^{n} R_{i}. Use when only past returns are available.

Total Expected Return with Dividend: E(R) = \sum_{i=1}^{n} p_{i} \times (R_{i}^{price} + Dividend_{yield}). Include dividend yield if given.