Corporate Accounting and Financial Management · Security Analysis

Risk and Return of Securities in Security Analysis

Updated 11 October 2026 · Fact-checked

Return is the gain you earn from a security. Risk is the chance that the actual return differs from what you expected. Expected return is the probability-weighted average of possible returns. Variance is the probability-weighted squared deviation from it, and standard deviation is its square root. Higher standard deviation means higher risk.

Understand Risk and Return of Securities

When you buy a security, you expect a gain. That gain is the return. It comes from income (interest or dividend) and from the change in price (capital gain or loss).

But the future is uncertain. A share may give 20% in one year and a loss in the next. Risk is this uncertainty: the possibility that the actual return will differ from the expected return. In finance, we measure risk by how widely the possible returns are spread around the average.

Total risk has two parts. Systematic risk comes from factors that affect the whole market: inflation, interest rate changes, recession, policy changes, political events. You cannot remove it by diversification, so it is also called market risk or non-diversifiable risk. It is measured by beta. Unsystematic risk is specific to one company or industry: a strike, a management failure, a product failure, a regulatory action on one firm. Holding many different securities reduces it, so it is called diversifiable or specific risk.

Systematic risk includes market risk, interest rate risk and purchasing power (inflation) risk. Unsystematic risk includes business risk and financial risk. Business risk arises from the nature of operations. Financial risk arises from the use of debt.

To measure return and risk, you list the possible returns with their probabilities. Expected return is the weighted average. Variance and standard deviation show how far returns are likely to move from that average. Of two securities with the same expected return, the one with the lower standard deviation is less risky.

Key rules to remember

Holding period return: Return = (D + (P1 − P0)) ÷ P0; D is dividend or interest received, P0 is the purchase price, P1 is the end price. Multiply by 100 for a percentage.
Expected return (with probabilities): E(R) = Σ (pi × Ri); Multiply each possible return by its probability and add. Probabilities must total 1.
Expected return (historical data, equal weight): Average return = ΣR ÷ n; Use when past returns are given without probabilities.
Variance (with probabilities): σ² = Σ pi × (Ri − E(R))²; Take the deviation from expected return, square it, weight it by probability, then add.
Standard deviation: σ = √σ²; Same unit as return, so it is easier to interpret. Higher σ means higher risk.
Variance (historical, sample): σ² = Σ (R − average)² ÷ (n − 1); Use n instead of (n − 1) if the question treats the data as the whole population. Follow the question or state your assumption.
Coefficient of variation: CV = σ ÷ E(R); Risk per unit of return. Use it to compare securities with different expected returns. Lower is better.

How to solve Risk and Return of Securities questions

Use this method for any question that gives possible returns and asks for expected return, variance, standard deviation or a comparison.

1Read what is asked: expected return, variance, standard deviation, CV, or a choice between securities.
2List each outcome with its return and its probability. Check that probabilities add up to 1 (or 100%).
3Compute expected return: multiply each return by its probability and add.
4Find each deviation: Ri − E(R). Square it.
5Multiply each squared deviation by its probability and add to get variance.
6Take the square root to get standard deviation.
7If two securities are compared, also compute CV when their expected returns differ.
8Write a one-line conclusion naming the security with the lower risk or better risk-adjusted return.

Quickest way: Table method with short-cut variance

When to use it: Use when the question has three to five outcomes with probabilities and you have limited time.

Draw a table with columns: p, R, p×R, (R − E(R))², p×(R − E(R))².
Fill p×R and total it to get E(R).
Fill the deviation columns using that E(R).
Total the last column for variance, then take the root.
Alternative: variance = Σ p×R² − [E(R)]². This saves effort when E(R) is a whole number, but check the arithmetic carefully.

Common mistakes in Risk and Return of Securities

Taking the simple average of returns when probabilities are given
Students see a list of returns and add and divide out of habit.
Fix: If probabilities are given, always use the weighted sum Σ p×R.
Forgetting to take the square root, so variance is reported as standard deviation
The last step is easy to skip when the table is long.
Fix: Write σ² and σ on separate lines. Variance is in squared percent; standard deviation is in percent.
Squaring the deviation after multiplying by probability
Order of operations gets confused.
Fix: Square the deviation first, then multiply by p.
Saying diversification removes all risk
Students remember that diversification reduces risk and overstate it.
Fix: Say diversification removes unsystematic risk only. Systematic risk remains.
Classifying interest rate risk or inflation risk as unsystematic
They seem to affect only some securities.
Fix: Anything that affects the whole market or economy is systematic. Company or industry-specific causes are unsystematic.
Comparing risk by standard deviation alone when expected returns differ
Lower σ looks safer.
Fix: Compute CV to compare risk per unit of return when expected returns are not equal.

Worked examples

Example 1

The returns on the shares of Sundaram Ltd. under different economic conditions are: Boom: probability 0.3, return 20%; Normal: probability 0.5, return 12%; Recession: probability 0.2, return 2%. Calculate the expected return, variance and standard deviation.

Show the solution

Check probabilities: 0.3 + 0.5 + 0.2 = 1.0.
Expected return = (0.3 × 20) + (0.5 × 12) + (0.2 × 2) = 6 + 6 + 0.4 = 12.4%.
Deviations: Boom 20 − 12.4 = 7.6; Normal 12 − 12.4 = −0.4; Recession 2 − 12.4 = −10.4.
Squared deviations: 57.76; 0.16; 108.16.
Weighted: 0.3 × 57.76 = 17.328; 0.5 × 0.16 = 0.08; 0.2 × 108.16 = 21.632.
Variance = 17.328 + 0.08 + 21.632 = 39.04.
Standard deviation = √39.04 = 6.248, about 6.25%.

Answer: Expected return = 12.4%; variance = 39.04; standard deviation ≈ 6.25%.

Example 2

Security A has expected return 15% and standard deviation 6%. Security B has expected return 10% and standard deviation 5%. Which security is riskier relative to its return? Also state in one line whether the risk measured is systematic or unsystematic.

Show the solution

Standard deviation alone shows A (6%) is riskier in absolute terms than B (5%).
Expected returns differ, so use coefficient of variation.
CV of A = 6 ÷ 15 = 0.40.
CV of B = 5 ÷ 10 = 0.50.
Lower CV means less risk per unit of return, so A is better on this basis.
Standard deviation measures total risk, which is systematic plus unsystematic risk. Only beta measures systematic risk.

Answer: A has higher standard deviation but lower CV (0.40 against 0.50), so A carries less risk per unit of return and is preferable. Standard deviation measures total risk.

Exam tips

Write the table in full. Marks are given for each step, so a correct method with a small arithmetic slip still scores.
Learn the systematic and unsystematic lists with one example each. Theory questions often ask for the difference with examples.
State the formula before substituting. Add a one-line conclusion naming the less risky or preferred security.
Check that probabilities add up to 1 before starting. If they do not, note it and proceed as the question directs.
Link this topic to portfolio theory and CAPM: standard deviation is total risk, beta is systematic risk.

Practice questions from Security Analysis

Risk and Return of Securities in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Risk and Return of Securities: frequently asked questions

What is the difference between systematic and unsystematic risk?

Systematic risk affects the whole market, such as inflation or interest rate changes, and cannot be diversified away. Unsystematic risk is specific to a company or industry, such as a strike or management failure, and can be reduced by diversification.

How do you calculate expected return of a security?

Multiply each possible return by its probability and add the results. If only past returns are given with no probabilities, take their simple average.

Why is standard deviation used as a measure of risk?

It shows how widely returns are spread around the expected return. A wider spread means more uncertainty, so a higher standard deviation means higher risk. It is in the same unit as return, which makes it easy to interpret.

When should I use coefficient of variation instead of standard deviation?

Use it when you compare securities with different expected returns. It gives risk per unit of expected return, so it is a fairer comparison than standard deviation alone.