NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return

Portfolio Risk, Diversification and CAPM Explained

Updated 11 October 2026 · Fact-checked

Diversification lowers portfolio risk because assets do not move perfectly together, so their ups and downs partly cancel. Only market (systematic) risk remains. CAPM prices that remaining risk: Expected return = Rf + β × (Rm − Rf). Plot it against beta and you get the security market line.

Understand Portfolio Risk, Diversification and CAPM

A portfolio is a collection of assets. Its expected return is the weighted average of the returns of its assets. Its risk is not the weighted average of their risks. It is usually lower, and this gap is the benefit of diversification.

Why? Assets do not all move together. When one falls, another may rise or fall less. The measure of this co-movement is correlation, from −1 to +1. At +1, there is no risk reduction. The lower the correlation, the greater the reduction. Adding more securities lowers unsystematic risk (company or sector specific). It cannot remove systematic risk (market-wide risk such as interest rates, inflation, recession), which is measured by beta.

The efficient frontier is the set of portfolios that give the highest expected return for each level of risk (or the lowest risk for each level of return). Portfolios below the frontier are inefficient, since you can get more return for the same risk. Which efficient portfolio you choose depends on your risk tolerance. When a risk-free asset is added, the line from the risk-free rate tangent to the frontier is the capital market line (CML).

CAPM says investors are paid only for systematic risk. Expected return equals the risk-free rate plus beta times the market risk premium. Drawn with beta on the x-axis, this is the security market line (SML). A security above the SML is undervalued (expected return higher than required). One below is overvalued.

CML versus SML: the CML uses total risk (standard deviation) and applies to efficient portfolios only. The SML uses systematic risk (beta) and applies to any security or portfolio.

Key formulas to remember

Portfolio expected return: E(Rp) = w1 × R1 + w2 × R2 + ... + wn × Rn; Weights add up to 1. This is a plain weighted average.
Two-asset portfolio variance: σp² = w1²σ1² + w2²σ2² + 2 × w1 × w2 × ρ12 × σ1 × σ2; Standard deviation is the square root of this. Lower ρ means lower risk.
Covariance and correlation: ρ12 = Cov(1,2) ÷ (σ1 × σ2); Correlation lies between −1 and +1.
CAPM: E(Ri) = Rf + βi × (Rm − Rf); (Rm − Rf) is the market risk premium. Beta of the market is 1 and of the risk-free asset is 0.
Portfolio beta: βp = Σ wi × βi; Beta is a weighted average, unlike standard deviation.
Capital market line: E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp; Risk is total risk (σ). Applies to efficient portfolios.
Alpha (excess return): Alpha = Actual or expected return − CAPM required return; Positive alpha means the security plots above the SML.

How to solve Portfolio Risk, Diversification and CAPM questions

Use this order for any question on portfolio risk, diversification or CAPM.

1Identify what is asked: expected return, risk, beta, or a valuation judgement.
2Note the risk measure in the question. Beta means systematic risk and the SML. Standard deviation means total risk and the CML.
3Write the data down: Rf, Rm, beta, weights, correlation.
4If weights are given, compute the weighted average for return and beta. Do not average standard deviations.
5For CAPM, first find the market premium (Rm − Rf), then multiply by beta, then add Rf.
6Compare required return with expected return. Expected above required means undervalued, above the SML, positive alpha.
7Check the answer: a beta above 1 should give a return above Rm, and a beta below 1 should give a return below Rm.

Quickest way: Premium first, then beta, then Rf

When to use it: Any numerical CAPM question, or a conceptual question with options that differ on systematic versus unsystematic risk.

Subtract Rf from Rm to get the premium.
Multiply by beta.
Add Rf.
For concept questions, remember: diversification removes unsystematic risk only; beta measures systematic risk; SML uses beta; CML uses standard deviation.
Eliminate options that say diversification removes all risk or that CAPM rewards total risk.

Common mistakes in Portfolio Risk, Diversification and CAPM

Adding Rf to beta times Rm instead of beta times (Rm − Rf).
Students forget that the premium is the excess over the risk-free rate.
Fix: Always compute Rm − Rf first as a separate step.
Saying diversification eliminates all risk.
The word 'reduces' is mixed up with 'removes'.
Fix: Diversification removes only unsystematic risk. Systematic risk stays.
Taking portfolio standard deviation as the weighted average of individual standard deviations.
It works for return and beta, so students assume it works for risk.
Fix: It holds only when correlation is +1. Otherwise portfolio risk is lower.
Mixing up the SML and the CML.
Both are lines starting at the risk-free rate.
Fix: SML: beta on the x-axis, any asset. CML: standard deviation on the x-axis, efficient portfolios only.
Judging a security as undervalued when it plots below the SML.
Students confuse the direction of the comparison.
Fix: Above the SML means expected return exceeds the required return, so undervalued. Below means overvalued.

Worked examples

Example 1

The risk-free rate is 7%, the expected market return is 12% and a stock has a beta of 1.4. What is the required return under CAPM?

Show the solution

Market risk premium = 12% − 7% = 5%.
Beta × premium = 1.4 × 5% = 7%.
Required return = 7% + 7% = 14%.

Answer: 14%

Example 2

Using Rf = 6% and Rm = 11%, a stock has beta 0.8 and an analyst's expected return of 9.5%. Is it undervalued or overvalued?

Show the solution

Premium = 11% − 6% = 5%.
Required return = 6% + 0.8 × 5% = 6% + 4% = 10%.
Expected return 9.5% is below the required 10%.
Alpha = 9.5% − 10% = −0.5%. The stock plots below the SML.

Answer: Overvalued, because its expected return of 9.5% is below the CAPM required return of 10%.

Exam tips

Questions are mostly conceptual: systematic versus unsystematic, SML versus CML, what the efficient frontier shows. Learn the one-line distinctions.
For numerical questions, do the CAPM in three short steps and check the sign of the premium.
Watch for trap options that say diversification reduces market risk or that beta measures total risk.
Remember that a negative mark of 25% of the question's marks applies to wrong answers, so skip only if you cannot narrow to two options.

Practice questions from Fundamentals of Risk and Return

Portfolio Risk, Diversification and CAPM in other exams

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

Portfolio Risk, Diversification and CAPM: frequently asked questions

How does diversification reduce portfolio risk?

Assets are not perfectly correlated, so losses in one are partly offset by gains or smaller losses in another. This cuts unsystematic risk. Systematic risk remains because it affects all assets.

What is the efficient frontier?

It is the curve of portfolios offering the highest expected return for each level of risk. Portfolios below it are inefficient because a better return is available for the same risk.

What is the difference between the SML and the CML?

The SML plots required return against beta and applies to any security or portfolio. The CML plots expected return against standard deviation and applies only to efficient portfolios that combine the risk-free asset and the market portfolio.

What does CAPM assume about risk?

It assumes investors are rewarded only for systematic risk, measured by beta. Unsystematic risk can be diversified away, so it earns no extra return.