1. Leticia has to hedge the interest rate risk of her holdings of $6,480,000 in Treasury bonds by buying or selling futures contracts. Determine the type of transaction and the price of each contract if Leticia buys/sells 48 contracts. 
2. Suppose you buy a call option on a $100,000 Treasury bond futures contract with an exercise price of 105. If the price of the Treasury bond is 115 at expiration, is the option at the money, in the money or out of the money? Determine the premium if the profit equals $8,000.

 

1. A bank issues a $100,000 variable-rate, 30-year mortgage with a nominal annual rate of 4.5%. If the required rate drops to 4.0% after the first six months, what is the impact on the interest income for the first 12 months? Assume the bank hedged this risk with a short position in a 181-day T-bill future. The original price was and the final price was on a $100,000 face value contract. 
   Did this work?
2. Laura, a bond portfolio manager, administers a $10 million portfolio. The portfolio currently has 
   a duration of 8.5 years. Laura wants to shorten the duration to 6 years using T-bill futures. T-bill futures have a duration of 0.25 years and are trading at $975 (face value = $1,000). How is this accomplished?
3. Suppose you buy a futures contract at a price of 107 and that the margin requirement is 2 points. Determine the settlement price at which you will receive a margin call if the maintenance margin requirement is 1 point.             
4. Chicago Bank and Trust has $100 million in assets and $83 million in liabilities. The duration of the assets is 5.9 years, and the duration of the liabilities is 1.8 years. How many futures contracts does this bank need to fully hedge itself against interest rate risk? The available Treasury bond futures contracts have a duration of 10 years, a face value of $1,000,000, and are selling for $979,000.

 

1. A bank issues a $3 million commercial mortgage with a nominal APR of 8%. The loan is fully amortized over 10 years requiring monthly payments. The bank plans on selling the loan after
   2 months. If the required nominal APR increases by 45 basis points when the loan is sold, what
   loss does the bank incur?
2. Assume the bank in the previous question partially hedges the mortgage by selling three 10-year
   T-note futures contracts at a price of Each contract is for $1,000,000. After 2 months, the futures contract has fallen in price to What was the gain or loss on the futures transaction?
3. Springer Country Bank has assets totaling $180 million with a duration of 5 years, and liabilities totaling $160 million with a duration of 2 years. Bank management expects interest rates to fall from 9% to 8.25% shortly. A T-bond futures contract is available for hedging. Its duration is 6.5 years and is currently priced at How many contracts does Springer need to hedge against the expected rate change? Assume each contract is has a face value of $1,000,000.
4. From the previous question, rates do indeed fall as expected, and the T-bond contract is priced at If Springer closes its futures position, what is the gain or loss? How well does this offset the approximate change in equity value.
5. A bank issues a $100,000 fixed-rate, 30-year mortgage with a nominal annual rate of 4.5%. If the required rate drops to 4.0% immediately after the mortgage is issued, what is the impact on the value of the mortgage? Assume the bank hedged the position with a short position in two 10-year T-bond futures. The original price was and expired at on a $100,000 face value contract. What was the gain on the futures? What is the total impact on the bank?
6. The bank customer will be going to London in June to purchase £100,000 in new inventory. The current spot and futures exchange rates are:

Exchange Rates Dollars/Pound
Period	Rate
Spot	1.5342
March	1.6212
June	1.6901
September	1.7549
December	1.8416

 

The customer enters into a position in June futures to fully hedge her position. When June arrives, the actual exchange rate is $1.725 per pound. How much did she save?

1. Suppose a bank has an income gap of - $15 million. How can this bank use interest rate swaps to hedge against interest rate increases? Determine the amount of the notional principal and propose an interest rate swap.
2. Liverpool Bank has an income gap of - $10 million, Alur Finance Co has an income gap of $25 million and TLBR Bank has an income gap of - $15 million. Propose an interest rate swap that will benefit all three institutions. Determine the amount of notional principal for each interest rate swap.
3. A banker commits to a two-year $5,000,000 commercial loan and expects to fulfill the agreement in 30 days. The interest rate will be determined at that time. Currently, rates are 7.5% for such loans. To hedge against rates falling, the banker buys a 30-days interest rate floor with floor rate of 7.5% on a notional amount of $10,000,000. After 30 days, actual rates fall to 7.2%. What is the expected interest income from the loan each year? How much did the option pay?
4. A trust manger for a $100,000,000 stock portfolio wants to minimize short-term downside risk using Dow put options. The options expire in 60 days, have a strike price of 9,700, and a premium of $50. The Dow is currently at 10,100. How many options should she use? Long or short? How much will this cost? If the portfolio is perfectly correlated with the Dow, what is the portfolio value when the option expires, including the premium paid? 
5. Dickey Bank anticipates an increase in interest rates in 2016 and has therefore decided to engage in an interest rate swap in which it pays 3% over a notional principal of $4 million annually. Fuller Finance Company pays Dickey Bank the interest income generated by applying the T-bill rate plus 2%. Can you determine if the income gap of Dickey Bank is negative or positive? Determine the amount paid by each institution if the T-bill rate is 0.5% or 1.5%
6. North-Northwest Bank has a differential advantage in issuing variable-rate mortgages, but does not want the interest income risk associated with such loans. The bank currently has a portfolio of $25,000,000 mortgages with an APR of prime + 150 basis points, reset monthly. Prime is currently 4%. An investment bank has arranged for NNWB to swap into a fixed interest payment of 6.5%  on a notional amount of $25,000,000 in return for its variable interest income. If NNWB agrees 
   to this.
7. What interest is received and given in the first month? What if prime suddenly increased  200 basis points?