How it works
Problem 1Four plans for a flood
L2.6.01A risk manager at a logistics firm
Your firm's main warehouse sits near a river. Engineers put the chance of a flood at 5% a year, and a flood would cost about €8,000k. The board's appetite: no single event may cost the firm more than €2,000k. You have two tools, which can be combined:
- Flood barriers cost €120k a year and cut the chance of a flood to 1%.
- Flood insurance with a €500k deductible. The insurer charges 1.3 times the expected loss it covers.
Which plan has the lowest expected annual cost while staying within the board's appetite?
Problem 2How many copper futures?
L2.6.02A treasury analyst at a copper wire maker
Your company will buy 1,500 tonnes of copper in three months at the local spot price. It hedges with exchange futures of 25 tonnes each. From the last three years of monthly data: the standard deviation of changes in the local spot price is 6%, that of the futures price is 5%, and their correlation is 0.9.
How many futures contracts give the minimum-variance hedge? Round to a whole number.
Problem 3The price actually paid
L2.6.02The same treasury analyst, three months later
Your company bought futures at $8,500 a tonne. Three months later it buys its copper locally at $9,100 a tonne and closes the futures at $9,020. Assume one futures tonne for every tonne bought.
What is the effective price per tonne, in $, after the futures gain?
Problem 4A floor and a cap
L2.6.03An adviser to a founder with a concentrated holding
A founder holds 50,000 shares of her company, now at €80. She wants protection for a year without paying much. You propose a collar: buy one-year puts with a strike of €72 at €3.45 a share and sell one-year calls with a strike of €100 at €2.77 a share.
What is the largest possible loss per share over the year, in €, after the net premium?
Problem 5Sizing the swap
L2.6.04A bank's ALM analyst
Your bank holds $150m face of a 7-year bond paying a 3.5% annual coupon. At today's 4.0% yield it is priced at 97.00 per 100, with a modified duration of 6.073. The ALCO wants the interest rate risk hedged with a new 7-year pay-fixed swap, whose DV01 is $600.21 per $1m notional.
What swap notional matches the bond's DV01, in $ millions?
Problem 6Diversified, until it is not
L2.6.05A portfolio risk analyst
Your fund holds 25 shares in equal weights. In calm markets each has a volatility of 28% and each pair has a correlation of 0.2. Your stress scenario, based on past crises, raises each volatility to 40% and each correlation to 0.7.
What is the fund's volatility in the stress scenario, in %?
Problem 7The morning margin call
L2.6.06A collateral manager at a bank
Your bank has five derivatives with one counterparty, all under one ISDA Master Agreement with a CSA. Their values to your bank this morning, in € millions:
| Trade | A | B | C | D | E |
|---|---|---|---|---|---|
| Value | 9.0 | −4.0 | 6.0 | −3.5 | 1.5 |
The CSA has a threshold of €3m and a minimum transfer amount of €0.5m. You already hold €4.2m of collateral from the counterparty.
How much collateral do you call today, in € millions?
Problem 8Which treaty keeps less?
L2.6.07A reinsurance buyer at a property insurer
Last year your insurer had three large claims: €1.5m, €6m and €14m. You are comparing two treaties for next year on the same claims: a 50% quota share, or a per-risk excess of loss of €8m xs €2m.
Under the excess of loss treaty, how much would your insurer have kept in total, in € millions?
Your score
0 / 8
0 of 8 problems checked.