Lab Test: Derivatives · RiskAtoms Academy

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Eight problems from the people who use derivatives: a jeweller, an oil producer, a finance director, a treasurer, a private investor, an options trader, a risk manager and a credit fund. Most need two or three steps and more than one lesson, and some ask which position is riskier and why. Answer each part, press Check, then step through the worked solution. Use a calculator. Prices and rates are illustrative.

Problem 1A jeweller's gold forward

L1.7.01 · L1.7.02

A jewellery maker in Dubai

A jeweller needs 1,000 ounces of gold in 6 months and wants to fix the price today. Gold is $2,400 an ounce. Dollars can be borrowed or lent at 4% a year, annually compounded. Ignore storage and other costs. A dealer quotes a 6-month forward price of $2,470.

(a)What is the fair (no-arbitrage) forward price, in dollars an ounce? (two decimals)
USD
(b)The dealer's quote is not fair. How would an arbitrageur lock in a riskless profit?
ABuy the forward from the dealer and sell gold short todayBBorrow dollars, buy gold now, and sell it forward to the dealer at the quoted priceCLend dollars and buy the forwardDThere is no riskless profit: the quote is a forecast of the future gold price
(c)How much riskless profit, in dollars, would that make on 1,000 ounces? (to the nearest dollar)
USD

Problem 2An oil producer's margin account

L1.7.03

A treasurer at a Canadian oil producer

To hedge its sales, the producer sells (goes short) 2 crude oil futures of 1,000 barrels each at $80.00. Initial margin is $6,000 and maintenance margin $4,500 per contract. After a margin call the account must be topped up to the initial margin.

Settlement prices over the next four days: $81.20, $82.50, $81.90, $83.40.

(a)On which day does the first margin call come? (1 to 4)
(b)How much cash in total does the producer pay in on margin calls over the four days?
USD
(c)The board asks: has the hedge lost us money?
AYes: the futures lost money, so the hedge was a mistakeBThe futures lost $6,800 over the four days, but the oil the producer will sell is worth about that much more. The hedge is working; the margin calls are a cash cost of hedging that must be fundedCNo: margin calls are refunded when the contract expiresDIt cannot be known until the futures expire

Problem 3Fixing a floating-rate loan

L1.7.04

A finance director at a Brazilian airport operator

The company has a USD 50 million loan paying SOFR + 1.2%. It enters a five-year interest rate swap: it pays a fixed 3.8% and receives SOFR, annually on the same notional. Two years later, 3 years remain and swap rates for all maturities have fallen to 3% (take a flat curve, annual compounding).

(a)What fixed rate does the company pay in all, on the loan and swap together? (%)
%
(b)What is the swap worth to the company now, in USD millions? (two decimals; negative if it is a liability)
USD m
(c)The chief executive says the swap was a bad decision. What is the best reply?
AAgreed: we should close it out now to stop further lossesBThe swap's value is negative because rates fell, but the loan now costs less by about the same amount. Together they still cost the 5% we set out to lock inCThe value is only a book entry and has no meaningDWe should enter a second pay-fixed swap to average down

Problem 4Dollars raised, yen needed

L1.7.05 · L1.7.01

A treasurer at a Japanese electronics group

The group issues a 5-year USD 200 million bond paying 4.5% a year, but its costs and revenues are in yen. It enters a cross-currency swap with a bank at USD/JPY 150: it swaps the dollars for yen at the start, pays the bank 0.9% a year on the yen principal, receives the bond's dollar coupons, and swaps the principals back at the same 150 at maturity. At maturity the market rate is 165 yen per dollar.

(a)How much yen interest does the group pay the bank each year, in JPY millions?
JPY m
(b)Compared with having no swap, how many yen does the swap save on repaying the bond's principal at maturity? (JPY billions)
JPY bn
(c)Which risk does the group still carry after the swap?
ANone: the swap removes all riskBYen interest rate risk on the bond's dollar couponsCCredit risk to the swap bank: if the bank fails while the swap is worth a lot to the group, the group must replace it at a worse rateDThe risk that the dollar strengthens

Problem 5A collar on a family shareholding

L1.7.06 · L1.7.07

A private investor in Singapore

An investor holds 500 shares, now at $120. She buys 110-strike puts for $3.40 and sells 135-strike calls for $2.90, one of each per share, all expiring on the same date. Measure profit at expiry against today's share price, including the premiums.

(a)What is the most she can lose on the whole holding at expiry? (dollars, as a positive number)
USD
(b)What is the most she can make on the whole holding at expiry? (dollars)
USD
(c)The share ends at $100. How much better off is she than if she had not hedged? (dollars)
USD

Problem 6A put that is too dear

L1.7.08

A trader on an options desk in Frankfurt

A share that pays no dividends trades at €80. One-year European options with strike €80 are quoted: call €7.50, put €5.50. The one-year rate is 4%, annually compounded. Each contract is on 100 shares.

(a)What should the put cost by put-call parity? (euros, two decimals)
EUR
(b)Which trades lock in a riskless profit?
ABuy the put, sell the call, buy the share, borrow the present value of the strikeBSell the put, buy the call, sell the share short, and lend the present value of the strikeCBuy the put and the share onlyDSell the put and the call
(c)How much riskless profit, today, on 100 contracts? (euros, to the nearest euro)
EUR

Problem 7Two traders, one earthquake

L1.7.07 · L1.7.09 · L1.7.12

A risk manager at a bank in Hong Kong

Two traders deal in options on a stock index at 100. Trader A buys 10,000 straddles at strike 100 (call $6.50 plus put $5.50 each). Trader B sells 10,000 of the same straddles. Then an earthquake strikes, markets swing wildly, and the index ends at 78 on expiry.

(a)Before anything happens, which trader is taking the bigger risk, and why?
AA: paying $12.00 a unit is a big outlayBB: the most B can make is the $12.00 premium, while losses grow without limit as the index moves away from 100, and rise as soon as volatility jumpsCNeither: a straddle has no direction, so both are hedgedDBoth the same: one's gain is the other's loss
(b)Below what index level does Trader B start to lose money at expiry?
(c)What is Trader B's profit or loss at expiry with the index at 78? (dollars; negative for a loss)
USD

Problem 8Credit protection, and the collateral behind it

L1.7.10 · L1.7.11

A credit portfolio manager at a fund in Toronto

The fund buys 5-year CDS protection on USD 10 million of a retailer's bonds at a spread of 250 basis points, paid quarterly (take each quarter as a quarter of a year). The expected recovery rate is 35%.

The trade is not centrally cleared, so both sides post initial margin. The fund must post USD 1.2 million and will use government bonds, which the dealer takes at a 4% haircut.

(a)What premium does the fund pay each quarter? (dollars)
USD
(b)If the retailer defaults and the recovery is as expected, how much does the protection pay? (USD millions)
USD m
(c)What market value of government bonds must the fund post as initial margin? (USD millions, two decimals)
USD m

Score 0 / 240 of 8 problems checked