Question

In January, See Us First Bank offers a client firm a $ 100 million loan for one year with the following terms: • The interest payments are due every six months. • The interest rate is determined every six months at the rate on the 3-month commercial paper on that day. That is, the rate for the SIX-MONTH period from July 1st until December 31st will be determined on July 1st. at the 3-month commercial paper spot rate. There are no futures contracts on 3-month commercial papers, but there are futures contracts, which expire in September, on: $1 million 3-month Treasury bills, $1 million 3-month Eurodollars. On March, the BANK decides to hedge its interest risk and estimates the following regressions for the hedging period: Regression of RATES on 3-month COMMERCIAL PAPER on Regression coefficient R-squared value 0.96 Futures RATES on 3-month TREASURY BILLS Futures RATES on 3-month EURODOLLARS 0.95 0.95 0.99

Answer 1

)he concept of the minimum variance hedge ratio is used to solve this problem.

We are concerned with two variables:

$\triangle S$: change in 3-month commercial paper interest rate

$\triangle F$: change in 3-month interest rate of the instrument being used to hedge ie 3-month treasury bill or 3-month eurodollar bill

We will select that instrument which has higher beta ie regression coefficient when $\triangle S$ is regressed against $\triangle F$

Since both T-bill & eurodollar bill, have same beta (=0.95), we will choose that regression which has higher R square value (ie greater ability to explain variance in commercial paper rate.

Hence we chose 3-month eurodollar rate ie r-squared of 0.99 or 99%

Minimum variance hedge ratio (h) = beta = 0.95

Q: Optimal number contracts of 3-month euro-dollar contracts = h * (total loan amount)/(size of 1 future contract)

Bank should go long on Q number of future contract. Attached below some material for referance.

Calculating the Minimum Variance Hedge Ratio The minimum variance hedge ratio depends on the relationship between changes in the spot price and changes in the futures price. Define: AS: Change in spot price, S, during a period of time equal to the life of the hedge AF: Change in futures price, F, during a period of time equal to the life of the hedge. We will denote the minimum variance hedge ratio by h*. It can be shown that h* is the slope of the best-fit line from a linear regression of AS against AF (see Figure 3.2). This result is intuitively reasonable. We would expect h* to be the ratio of the average change in S for a particular change in F. The formula for h* is: h* = pos

Optimal Number of Contracts To calculate the number of contracts that should be used in hedging, define: Qa: Size of position being hedged (units) QF: Size of one futures contract (units) N*: Optimal number of futures contracts for hedging. The futures contracts should be on h* QA units of the asset. The number of futures contracts required is therefore given by h* QA N = OF