FRM Exam Part I · The Building Blocks of Risk Management

Risk Mitigation: Hedging, Diversification and Insurance

Q: What is the difference between hedging and insurance?

Hedging offsets an exposure with an opposite position, so gains and losses cancel and upside is given up. Insurance pays a premium to transfer a defined loss and you keep the upside. Both reduce risk but with different costs.

Q: How does diversification reduce risk?

When assets are not perfectly correlated, their losses and gains do not occur together, so portfolio volatility is below the weighted average. It removes idiosyncratic risk only. Systematic risk stays.

Q: Can diversification fail in a crisis?

Yes. Correlations tend to rise in stressed markets, so assets fall together and the benefit shrinks. This is a known limitation, and stress testing helps assess it.

Q: Is risk avoidance a mitigation technique?

It is a risk response. You stop the activity so the risk is removed, but you also lose the expected return, so it is used when risk exceeds appetite.

Updated 11 October 2026 · Fact-checked

Risk mitigation means reducing, transferring or removing a risk you face. The main tools are avoidance, hedging (offsetting exposure with a related position), diversification (spreading exposure across imperfectly correlated assets), insurance (paying a premium to transfer a loss) and retention. For each question, identify which risk is addressed and what remains.

Understand Risk Mitigation: Hedging, Diversification and Insurance

Every firm faces risks it can choose to avoid, reduce, transfer or keep. These are the basic risk responses: avoidance, mitigation or reduction, transfer and retention (accepting the risk). Mitigation tools are the ones the FRM tests most.

Hedging takes a position that moves opposite to an existing exposure. A European exporter who will receive USD in three months can sell USD forward. Losses on the exposure are offset by gains on the hedge. Hedging cuts both downside and upside. It also leaves residual risks, such as basis risk (the hedge does not track the exposure perfectly) and counterparty risk.

Diversification spreads money across assets whose returns are not perfectly correlated. The portfolio standard deviation is lower than the weighted average of the individual standard deviations whenever correlation is below 1. It removes idiosyncratic (specific) risk. It cannot remove systematic (market) risk, which affects all assets together. In a crisis, correlations often rise and the benefit shrinks.

Insurance transfers the risk of a defined loss to an insurer in return for a premium. Unlike a hedge, it usually keeps your upside: you pay for protection and still gain if things go well. An option works like insurance. A protective put sets a floor on loss while keeping the gains. Insurance has its own issues: deductibles, limits, exclusions, moral hazard (the insured takes more risk) and adverse selection (high-risk parties buy more cover). Insurer credit quality matters too.

Risk avoidance means not taking the activity at all, such as exiting a market. It removes the risk but also the return. Risk can also be mitigated by limits, collateral, netting and diversifying counterparties. Whatever you choose, ask what risk is left over.

Key formulas to remember

Two-asset portfolio variance: σp² = w1²σ1² + w2²σ2² + 2·w1·w2·ρ·σ1·σ2; Weights sum to 1. Take the square root for σp. Lower ρ means lower portfolio risk.
Perfect correlation case: If ρ = 1: σp = w1σ1 + w2σ2; No diversification benefit. For ρ < 1, σp is below this weighted average.
Equally weighted portfolio of n assets (same σ, same pairwise ρ): σp² = σ²/n + ((n − 1)/n)·ρ·σ²; As n grows, variance approaches ρσ². That floor is systematic risk.
Total risk decomposition: Total variance = Systematic variance + Idiosyncratic variance; Diversification removes only the idiosyncratic part.
Protective put payoff at expiry: Value = ST + max(K − ST, 0); Floor at K. The cost is the premium, which lowers net gains.
Net result of a hedged position: Net = Gain or loss on exposure + Gain or loss on hedge; Residual is the unhedged part, often basis risk.

How to solve Risk Mitigation: Hedging, Diversification and Insurance questions

Use this routine for any question on hedging, diversification, insurance or avoidance.

1Identify the exposure: what can lose value, in which currency, price or event.
2Classify the risk: systematic or idiosyncratic, financial or non-financial, insurable or not.
3Match the tool: diversification for idiosyncratic risk, hedging for a known price exposure, insurance for a defined loss event, avoidance when risk exceeds appetite.
4Check what is given up: hedges give up upside, insurance costs a premium, avoidance gives up return.
5If numbers appear, compute: portfolio variance with the formula, or hedge plus exposure outcomes at each scenario.
6State the residual risk: basis risk, counterparty risk, correlation breakdown, moral hazard or policy exclusions.
7Check the answer against the wording, especially words like 'eliminate', 'reduce' and 'transfer'.

Quickest way: Match the tool to the risk, then check for a trap

When to use it: For conceptual multiple-choice questions where you must pick the correct statement.

Underline the risk type in the stem.
Remember: diversification cannot remove systematic risk.
Remember: hedging fixes the outcome, insurance keeps the upside for a premium.
Eliminate options using 'eliminates', 'always' or 'guarantees'.
If asked about portfolio volatility, test ρ = 1 first as the upper bound, then compute.

Common mistakes in Risk Mitigation: Hedging, Diversification and Insurance

Saying diversification can eliminate all risk.
Students remember that diversification lowers risk and extend it too far.
Fix: It removes only idiosyncratic risk. Systematic risk remains.
Treating hedging and insurance as the same thing.
Both protect against loss.
Fix: A hedge offsets gains and losses, so upside is lost. Insurance pays a premium and keeps the upside. Options behave like insurance, forwards like hedges.
Forgetting the cross term 2·w1·w2·ρ·σ1·σ2 in portfolio variance.
Rushing and averaging the standard deviations.
Fix: Always write all three terms. Square root only at the end.
Reporting variance as the answer when the question asks for standard deviation.
Stopping before the square root.
Fix: Take σp = √(σp²) and check the units.
Assuming a hedged position has no risk.
The hedge looks like a perfect offset.
Fix: Name the residual risks: basis risk, counterparty risk, imperfect hedge ratio and liquidity.
Ignoring moral hazard and adverse selection when discussing insurance.
Students focus only on the risk transfer.
Fix: Link deductibles, limits and monitoring to these two problems.

Worked examples

Example 1

A portfolio is 60% in Asset A (σ = 20%) and 40% in Asset B (σ = 30%). The correlation is 0.25. Calculate the portfolio standard deviation.

Show the solution

w1 = 0.6, σ1 = 0.20, w2 = 0.4, σ2 = 0.30, ρ = 0.25.
w1²σ1² = 0.36 × 0.04 = 0.0144.
w2²σ2² = 0.16 × 0.09 = 0.0144.
Cross term = 2 × 0.6 × 0.4 × 0.25 × 0.20 × 0.30 = 0.48 × 0.25 × 0.06 = 0.0072.
Variance = 0.0144 + 0.0144 + 0.0072 = 0.0360.
σp = √0.0360 = 0.18974, about 18.97%.
Check: the weighted average σ = 0.6×20% + 0.4×30% = 24%. The portfolio is lower, as expected for ρ < 1.

Answer: About 18.97%, compared with 24% if the assets were perfectly correlated.

Example 2

A firm holds 10,000 shares priced at USD 50. It buys 10,000 put options with strike USD 48 at a premium of USD 2 each. At expiry the share price is USD 40. What is the net value of the position after the premium, and the loss versus today's USD 500,000 value?

Show the solution

Shares value at expiry = 10,000 × 40 = USD 400,000.
Put payoff = max(48 − 40, 0) = USD 8 per share, so 10,000 × 8 = USD 80,000.
Premium paid = 10,000 × 2 = USD 20,000.
Net value = 400,000 + 80,000 − 20,000 = USD 460,000.
Loss = 500,000 − 460,000 = USD 40,000.
Check the maximum loss: floor value 48 × 10,000 = 480,000, less premium 20,000 gives 460,000, so the loss is capped at USD 40,000 for any price at or below 48.

Answer: Net value USD 460,000; loss USD 40,000, which is also the maximum loss. The firm keeps all gains above the price, less the premium.

Exam tips

Expect conceptual statements with absolute words. 'Eliminates' about diversification is almost always wrong.
Know the contrast: forward hedge fixes the outcome, put option protects the downside and keeps the upside at the cost of a premium.
For portfolio variance, write the full formula, then take the square root. Use the calculator memory for the three terms.
Link insurance questions to moral hazard, adverse selection, deductibles and limits.
In scenario questions, name the residual risk after mitigation.

Practice questions from The Building Blocks of Risk Management