📚 PASS Investment Adviser (Level 1) Difficulty: Intermediate ℹ️ Info   ~5 min read
📌 Chapter 14.4 — Calculation of expected rate of return for individual security

Imagine you are an analyst at a Mumbai-based brokerage firm, evaluating the risk profile of a mid-cap IT stock for a client’s portfolio. You have already calculated the expected return using probability-weighted scenarios, arriving at a respectable 12%. However, presenting this single figure to your investment committee often leads to a false sense of security, as it obscures the volatility lurking beneath the surface.

To truly assess the asset, you must shift your focus from the mean to the dispersion—the variance—which quantifies how far the actual outcomes are likely to stray from that 12% expectation.

Variance measures the squared deviations of possible outcomes from the expected return, weighted by their respective probabilities. By squaring these deviations, we penalize extreme outcomes, ensuring that large departures from the mean—both positive and negative—contribute significantly to our measure of risk. In the Indian equity market, where external factors like fluctuating oil prices or regulatory shifts in the IT sector can cause sudden price swings, variance serves as a vital signal of reliability.

A security with high variance suggests that your ’expected’ 12% is a fragile estimate, prone to being missed by a wide margin.

Consider two stocks: Stock A oscillates between 10% and 14%, while Stock B swings between -5% and 29%. Both might share the same 12% expected return, but their variance profiles tell fundamentally different stories. For a risk-averse client, Stock A is a predictable utility, whereas Stock B acts as a speculative instrument. Calculating variance allows you to differentiate between these assets quantitatively, moving beyond simple averages to provide a nuanced risk-adjusted recommendation that aligns with your client’s specific tolerance for uncertainty.

In practice, this calculation is the gateway to understanding the standard deviation, which brings our measure of risk back into the same units as our return percentage. When you build your valuation models, relying solely on expected returns leaves you blind to the ’tail risk’ that could derail a client’s long-term financial goals. Mastering variance enables you to translate abstract statistical dispersion into actionable professional judgment, ensuring your investment advice is rooted in a rigorous understanding of potential volatility.

Nuance

⚠️ Nuance
Candidates often conflate the probability of an outcome with the outcome itself when calculating variance. A common trap is forgetting to subtract the expected return from the outcome before squaring, or failing to multiply the squared result by the probability. Always remember that variance is a measure of ‘spread’; if all outcomes are identical, the variance must mathematically resolve to zero, a useful check to prevent calculation errors during high-pressure exams.

Check Your Understanding

Practice Question 1

An asset has two scenarios: a 25% return with 0.4 probability and a 5% return with 0.6 probability. What is the variance of this asset?

Practice Question 2

If an analyst calculates a variance of 0.0121 for a stock, what is the standard deviation?

This is a companion read for Section 14.4 — Calculation of expected rate of return for individual security from PASS Investment Adviser (Level 1) by Akhilesh Gururani, available on Amazon Kindle.

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