How it works
Problem 1A bad year on the cards
L2.1.01A risk analyst at a credit card lender
Your lender has £800m of card balances. It expects 3% of balances to be written off each year and builds that into its interest rates. It holds £60m of capital for the card book. This year, write-offs reach 4.8% of balances.
How much of the card book's capital does the unexpected loss use up, in %?
Problem 2Three new lines of business
L2.1.02An insurer's chief underwriting officer
Your board is asked to approve three new covers:
- A. Flight-delay cover for two million trips a year, with 15 years of detailed delay data.
- B. Cover for a warehouse in a flood zone where the records show a 4% chance of a flood each year, for a 15-year lease.
- C. Cover for losses if a new kind of computer breaks today's encryption, something that has never happened.
Which statement is the best advice?
Problem 3Which fund pays better for its risk?
L2.1.03An investment consultant to a pension fund
Two funds give you their scenario forecasts for next year. Treasury bills pay 2%. Returns in %.
| Scenario | Chance | Fund A | Fund B |
|---|---|---|---|
| Strong | 20% | 25% | 9% |
| Steady | 50% | 8% | 5% |
| Weak | 30% | −12% | 1% |
What is Fund A's Sharpe ratio, to two decimal places?
Problem 4From five days to a year
L2.1.03A junior market risk analyst
Your manager wants a quick estimate of a share's annual volatility from its last five daily returns: 0.8%, −1.2%, 0.5%, 1.4%, −0.6%. Use the sample standard deviation and 252 trading days a year.
What is the annualised volatility, in %, to one decimal place?
Problem 5Is reinsurance worth its price?
L2.1.04An insurer's chief financial officer
Your insurer has €12bn of capital and must keep at least €9bn. Next year's result is one of five equally likely outcomes: −€5.0bn, −€1.5bn, €2.0bn, €5.5bn, €9.0bn. Falling below the minimum costs a further €4bn in lost business and funding. A reinsurance programme would halve every swing around the €2bn middle result, for €0.4bn a year.
By how much, in €bn, does reinsurance raise the average result after distress costs?
Problem 6A flight to quality
L2.1.06A risk manager at a hedge fund
Your fund has $3bn of capital and runs 20× leverage across many relative-value trades. Its model says that in a bad week about 15% of the trades lose 2.5% each. You are asked to test a flight to quality in which 80% of the trades lose 2.5% each together, and forced selling costs a further 0.5% on the whole book.
What is the fund's leverage after the stress (assets ÷ capital)?
Problem 7Rates up, deposits out
L2.1.04 · L2.1.07A bank supervisor
A bank you supervise has $8bn of equity, $6bn of cash and $60bn of 8-year government bonds with a 2% annual coupon, bought at par and held to maturity. Yields have since risen by 2.5 points. Its $120bn of deposits are mostly uninsured, and you expect 20% to be withdrawn this week.
If it pays the withdrawals from cash and then by selling bonds, what equity will its accounts show, in $bn, to two decimal places?
Problem 8Your client is everybody's client
L2.1.05 · L2.1.06 · L2.1.07A counterparty risk analyst at a prime broker
A family office has a $5bn total return swap with your bank on a single stock, with 15% margin. Within your limits it looks fine. You then learn from market talk that it has similar swaps on the same stock with 4 other banks, and that together they amount to a large part of the company's shares.
What is the best response?
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