How it works
Seven problems from the desks where this module's ideas meet: a treasurer, an importer, a hedge fund, a borrower, an oil trader, a pension fund and a bank. Most need two or three steps and more than one lesson. Answer each part, press Check, then walk through the worked solution. Use a calculator. Rates and prices are illustrative.
Problem 1The importer's dollar bill
L1.6.01 · L1.6.02A London furniture retailer must pay a US supplier USD 3,000,000 in 182 days. Its bank quotes GBP/USD 1.2700 / 1.2703. Dollar rates are 4.50% (ACT/360) and sterling rates 4.75% (ACT/365). The bank prices forwards off the mid spot rate, with no extra spread.
(a)If the retailer bought the dollars today at spot, how many pounds would it pay? (to the penny)
GBP(b)Instead it buys the dollars 182 days forward. How many pounds will it pay on the day? (to the nearest pound)
GBP
Problem 2Where to park ten million for three months
L1.6.03A US company treasurer has USD 10,000,000 spare for 91 days. A Treasury bill maturing on the right day is quoted at a discount rate of 4.30%. A large bank offers a 91-day CD at 4.35%, simple interest. Both use ACT/360.
(a)What is the bill's yield on the price paid, ACT/360, in %? (three decimals)
%(b)Which should a cautious treasurer choose, and why?
Problem 3A leveraged bond fund on repo
L1.6.04 · L1.4.05A hedge fund buys USD 100,000,000 face value of US Treasuries at a dirty price of 99.00 and finances them in repo: 2% haircut, 5.30% repo rate, ACT/360, for 30 days. Halfway through, the bonds fall to 97.50.
(a)How much of its own money does the fund need to put up at the start? (dollars)
USD(b)After the price fall, how much cash must the fund return (or cover with more bonds) to restore the haircut? (dollars)
USD
Problem 4A SOFR loan over a weekend
L1.6.05 · L1.3.06A company borrows USD 25,000,000 from a Wednesday to the following Monday at SOFR compounded in arrears plus a margin of 1.25%, ACT/360. The margin is simple interest on top. SOFR prints 4.30% on Wed, 4.32% on Thu, 4.35% on Fri.
(a)How much interest in total does the company pay on Monday? (to the cent)
USD
Problem 5Reading an oil curve
L1.6.06Crude oil is $80.00 a barrel for prompt delivery. Interest is 5% a year (simple, a month is 1/12 of a year) and storage costs $0.40 a barrel a month. The 3-month future trades at $79.00.
(a)What does the market price tell you?
(b)What convenience yield, in % a year, does the futures price imply? (two decimals)
%
Problem 6US bonds for a euro investor
L1.6.07 · L1.6.02A Frankfurt pension fund holds US Treasuries that return 4.5% in dollars over a year. Over the same year EUR/USD rises from 1.08 to 1.15. One-year rates were 4.5% in dollars and 2.5% in euros (annual compounding).
(a)What was the fund's return in euros if it did not hedge? (%, two decimals)
%(b)If, at the start, it had sold the whole year-end dollar value forward at the parity rate, what would its euro return have been? (%, two decimals)
%
Problem 7Which bank is more fragile?
L1.6.03 · L1.6.04Two banks each hold USD 20 billion of government bonds. Bank A funds them with overnight repo, using the bonds as collateral. Bank B funds them with overnight unsecured interbank deposits. A market panic starts, and lenders become nervous about banks.
(a)Which bank is more likely to lose its funding, and why?