Economic Modelling · Measures of investment risk

Other Risk Measures and Practical Choice of Measure

Updated 11 October 2026 · Fact-checked

Beta measures how strongly an asset moves with the market, so it captures systematic risk. Duration measures sensitivity of value to interest rates. Liability volatility shows the risk of the obligations. You choose the measure by asking what the investor must achieve: absolute value, a liability match, or a benchmark.

Understand Other Risk Measures and Practical Choice of Measure

Variance and standard deviation treat all variation as risk. They look at total risk of a portfolio on its own. Real investors have other worries, so other measures exist. Each one answers a different question.

Beta measures systematic risk. It is the sensitivity of an asset's return to the return on the market. In the single-factor view, beta = Cov(R_i, R_m) ÷ Var(R_m). A beta of 1 means the asset tends to move one for one with the market. Above 1 means it amplifies market moves. Below 1 means it dampens them. Beta ignores specific risk, which diversification can remove. So it suits an investor who already holds a well-diversified portfolio. It is not suitable for a single asset held alone.

Duration measures how much the value of a fixed-interest asset or a liability changes when interest rates change. Higher duration means larger price changes for the same yield move. Volatility of liabilities matters because a pension fund or insurer cares about assets relative to liabilities, not assets alone. If assets and liabilities have the same duration and similar features, the surplus is protected against small parallel yield changes. A fund with a mismatch carries risk even if its assets look safe in isolation.

Choosing a measure depends on the investor. A pension fund with long-term, partly inflation-linked liabilities should look at risk relative to the liabilities, such as the volatility of the funding ratio or surplus, shortfall risk, and duration mismatch. A fund manager judged against an index cares about tracking error. An investor wanting protection from large losses may prefer shortfall probability, Value at Risk or Tail Value at Risk. A well-diversified equity investor may use beta. Variance is simple and widely understood, but it treats gains and losses alike and assumes returns are roughly symmetric.

No single measure is best. In the exam, state the investor's objective first, then justify the measure, then note its limits.

Key rules to remember

Beta: β_i = Cov(R_i, R_m) ÷ Var(R_m) = ρ_im × σ_i ÷ σ_m; Measures systematic risk relative to the market. ρ_im is the correlation between asset i and the market.
Beta of a portfolio: β_p = Σ w_i β_i; Beta is a weighted average of the asset betas, using portfolio weights that sum to 1.
Systematic and specific variance (single-factor model): σ_i² = β_i² σ_m² + σ_ei²; Assumes the residual risk is uncorrelated with the market. The first term is systematic, the second is specific.
Approximate price change using modified duration: ΔP ÷ P ≈ −D_mod × Δy; Valid for small changes in yield. D_mod is modified duration, with yield y.
Macaulay duration and modified duration: D_mod = D_mac ÷ (1 + y); Applies when y is an effective annual yield and cash flows are annual.
Surplus: S = A − L; Risk for a liability-driven investor is the variability of S, or of the funding ratio A ÷ L.

How to solve Other Risk Measures and Practical Choice of Measure questions

Use this method for both calculation questions and 'which measure would you recommend' questions.

1Identify the investor and the objective: absolute return, meeting liabilities, beating a benchmark, or avoiding large losses.
2Note the time horizon and any liability features, such as inflation linkage, guarantees or uncertain timing.
3List the data given: betas, correlations, standard deviations, weights, yields or durations.
4Pick the measure that matches the objective and write its formula in standard notation.
5Calculate carefully, keeping units consistent (percent as decimals, yields as annual rates).
6State the result in words, saying what it means for the investor.
7Comment on limits: what the measure ignores, its assumptions, and a complementary measure that would help.
8For a recommendation, give a clear choice and a short reason, then link it to the objective.

Quickest way: Match the investor to the measure

When to use it: Use this in multiple-choice questions and when you need a fast opening for a written answer.

Diversified equity investor judging market sensitivity: beta.
Fixed-interest asset or liability facing yield changes: duration.
Pension fund or insurer: risk relative to liabilities, such as surplus volatility and duration mismatch.
Manager measured against an index: tracking error.
Concern about big losses or a target return: shortfall probability, VaR or TVaR.
If the question gives betas and weights, just take the weighted average.

Common mistakes in Other Risk Measures and Practical Choice of Measure

Saying beta measures total risk.
Students link beta with volatility and forget the market model splits risk into two parts.
Fix: Say beta measures only systematic risk. Specific risk is not in beta and can be diversified away.
Averaging betas without using weights, or using weights that do not add to 1.
Rushing under time pressure.
Fix: Write β_p = Σ w_i β_i and check that the weights sum to 1. Include any cash, which has a beta of 0.
Using duration for large yield changes as if the result were exact.
The linear formula looks precise.
Fix: State that the result is an approximation for small changes. Convexity matters for larger moves.
Judging a pension fund by asset volatility only.
Students carry over portfolio theory without thinking about liabilities.
Fix: Discuss risk relative to liabilities, such as surplus volatility, funding ratio and duration mismatch.
Mixing Macaulay and modified duration.
The two names look similar.
Fix: Use modified duration for the price change formula. Divide Macaulay duration by (1 + y) to convert.
Recommending one measure without a reason or limitation.
Students memorise a list instead of reasoning.
Fix: Tie the measure to the objective in one sentence and add one limitation.

Worked examples

Example 1

A portfolio holds 50% in equity fund A (β = 1.2), 30% in equity fund B (β = 0.8) and 20% in cash (β = 0). Calculate the portfolio beta and interpret it.

Show the solution

Use β_p = Σ w_i β_i.
Fund A contributes 0.50 × 1.2 = 0.60.
Fund B contributes 0.30 × 0.8 = 0.24.
Cash contributes 0.20 × 0 = 0.
Sum: 0.60 + 0.24 + 0 = 0.84.

Answer: β_p = 0.84. The portfolio is expected to move about 0.84% for each 1% move in the market, so it is less sensitive than the market. This captures systematic risk only.

Example 2

A pension fund has liabilities of ₹500 crore with modified duration 14 years. Its assets are ₹500 crore with modified duration 9 years. Yields rise by 0.5% in parallel. Estimate the change in surplus and comment.

Show the solution

Use ΔV ≈ −D_mod × V × Δy, with Δy = 0.005.
Change in assets: −9 × 500 × 0.005 = −₹22.5 crore.
Change in liabilities: −14 × 500 × 0.005 = −₹35 crore.
Change in surplus = ΔA − ΔL = −22.5 − (−35) = +₹12.5 crore.
The surplus rises because liabilities fall more than assets when yields rise. If yields fall by 0.5%, surplus falls by about ₹12.5 crore.

Answer: Surplus rises by about ₹12.5 crore. The duration mismatch of 5 years exposes the fund to falling yields. Matching durations would reduce this risk. The result is approximate and assumes a small parallel yield change.

Exam tips

Start any 'which measure' answer with the investor's objective, then name the measure.
For pension funds and insurers, always bring in liabilities and the idea of matching.
Show the formula, the working and a one-line interpretation. Examiners award marks for each.
Give at least one limitation for each measure you mention, such as beta ignoring specific risk.
In computer-based papers, keep units consistent: use decimals for rates and state the assumptions.

Practice questions from Measures of investment risk

Other Risk Measures and Practical Choice of Measure: frequently asked questions

What does beta measure?

Beta measures how sensitive an asset's return is to the market return. It captures systematic risk only. It equals the covariance with the market divided by the market variance.

Which risk measure suits a pension fund?

A pension fund should focus on risk relative to its liabilities. Useful measures include the volatility of the surplus or funding ratio, duration mismatch and shortfall risk. Asset volatility alone gives an incomplete picture.

Is duration a risk measure?

Yes, it measures sensitivity of value to interest rate changes. It is most useful for bonds and for liabilities. The linear estimate works best for small yield changes.

Why not always use standard deviation?

It treats gains and losses equally and may misstate risk when returns are skewed or have fat tails. It also ignores liabilities and benchmarks. Other measures fit those cases better.