Case 062Stress testing and scenariosWarm up

An insurer holds a Rs 500 crore equity portfolio with a beta of 1.1 against solvency headroom of Rs 150 crore. Apply a 25% market fall, decide whether the headroom survives, and say what else the scenario should include.

The situation

Nerival Insurance is a life insurer. Its investment portfolio includes Rs 500 crore of listed equities with a beta of 1.1 to the broad market, and Rs 600 crore of corporate bonds alongside a larger government bond book. It holds capital Rs 150 crore above its required solvency level; that surplus is its headroom.

The board's risk committee asks for a simple stress test: the equity market falls 25%. It wants to know whether the headroom survives and whether the test is enough.

Your task

Apply the 25% fall, decide whether the headroom survives, and say what else a credible scenario should include.

Quick check

After a 25% market fall, how much of the Rs 150 crore headroom is left?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The headroom survives, but only just: the portfolio loses Rs 137.5 crore, leaving Rs 12.5 crore. A beta of 1.1 turns a 25% market fall into a 27.5% portfolio fall. The headroom breaks at a market fall of 27.3%. The scenario is a floor, not a worst case: with a crisis beta of 1.3, or with credit spreads widening at the same time, the headroom is breached.

Step 1What does the simple scenario say?

A family with Rs 1.5 lakh of spare savings and a Rs 5 lakh share portfolio that moves a little more than the market would want to know whether a bad year wipes out the spare savings. Beta scales the market fall to the portfolio: 1.1 x 25% is 27.5%, a loss of Rs 137.5 crore against Rs 150 crore of headroom. Nerival keeps Rs 12.5 crore, about 8% of the cushion. The headroom would break at a market fall of 27.3%, only 2.3 points worse than the scenario, which the committee should hear as the real headline.

The relationship
loss=500×1.1×25%=137.5breakeven fall=150500×1.1=27.3%\text{loss} = 500 \times 1.1 \times 25\% = 137.5 \qquad \text{breakeven fall} = \frac{150}{500 \times 1.1} = 27.3\%
500equity portfolio, Rs crore
1.1portfolio beta to the market
150solvency headroom, Rs crore
What it says in wordsThe loss is the portfolio times beta times the market fall; the breakeven is the fall that uses up exactly the headroom.
Headroom of Rs 150 crore against the scenario, and what it leaves outEquity fall, beta 1.1137.512.5 leftSame fall, crisis beta 1.3162.512.5 shortBeta 1.1 plus spreads +100 bp137.5+24 from wider credit spreads11.5 shortheadroom Rs 150 crore0Rs crore of loss. A single-factor scenario is a floor, not a worst case.
A 25% market fall at beta 1.1 costs Nerival Rs 137.5 crore and leaves Rs 12.5 crore of its Rs 150 crore headroom, but the same fall at a crisis beta of 1.3, or combined with a 100 basis point widening in credit spreads, breaches it.
Step 2Why is a single-factor scenario only a floor?

Real sell-offs do not move one thing. A market fall of 25% usually arrives with wider credit spreads, lower rates and a higher beta, and each of those adds to the loss. Beta measured in calm years tends to rise in a crisis: at 1.3 the same fall costs Rs 162.5 crore and breaches the headroom by Rs 12.5 crore. Credit spreads widening by 100 basis points on Rs 600 crore of corporate bonds with a spread duration of 4 cost another Rs 24 crore; combined with the equity fall that is Rs 161.5 crore, Rs 11.5 crore more than the headroom.

ScenarioLoss, Rs croreHeadroom left
25% fall, beta 1.1137.512.5
25% fall, crisis beta 1.3162.5-12.5
25% fall at beta 1.1, spreads +100 bp161.5-11.5
The headroom survives the equity-only scenario with Rs 12.5 crore to spare, but a crisis beta or a simultaneous credit spread widening turns the result into a shortfall.
Step 3What else should the scenario include?

Build it from the balance sheet outwards. On the asset side: credit spreads, interest rates on the government bond book, and any property or unlisted holdings that are marked less often but fall too. On the liability side, which is where an insurer differs from a fund: lower rates raise the value of long policy liabilities, guarantees in savings products become more expensive, and policyholders may surrender at a different pace. And the requirement itself: the capital an insurer must hold can change as its assets and liabilities move, so headroom is a moving target. A stress test the committee can rely on names the joint scenario, gives the loss on each line, and says what management would do at each level of headroom left. Confirm how the current IRDAI solvency rules measure available and required capital before building the full version.

Where candidates lose it

Candidates stop at Rs 137.5 crore is less than Rs 150 crore, so it passes. The committee needs to hear how thin the margin is, that the breakeven is only a 27.3% fall, and what the test leaves out.

The other miss is applying the 25% directly to the portfolio and forgetting beta, which understates the loss by Rs 12.5 crore, the entire remaining headroom.

What the interviewer asks next

  • How would you choose the size of the market fall for the committee's scenario?
  • The insurer wants to keep the equity exposure. What could it do to protect the headroom?
  • Why do falling interest rates hurt a life insurer even when its bonds rise in value?

Company names and figures are illustrative.