On August 2. a securities dealer. Ms. Cindy Zaicko. responsible for a $10 millio
ID: 2714288 • Letter: O
Question
On August 2. a securities dealer. Ms. Cindy Zaicko. responsible for a $10 million bond portfolio is concerned that interest rates are expected to be highly volatile over the next 3 months. The fund manager decides to use Treasury bond futures to hedge the value of the bond portfolio. The current price on a December T-bond futures is 91-22. During the period August 2 to November 2. interest rates climbed rapidly causing the bond portfolio value to drop as prices of T-Bonds declined from 100-00 to 95-11. On November 2. the December T-Bond futures contract was priced at 88-26. The portfolio was sold at its market value on Nov. 2. The minimum contract size for the T-Bond futures contract is SI00.000 and the minimum price change is $31.25 per tick of 1/32. State what kind of hedge could Ms. Zaicko take and why. Compute the opportunity cost of waiting to sell the portfolio. Describe all transactions clearly. Compute gain or loss in the futures market after describing the transactiExplanation / Answer
Total Value of the Portfolio = $ 10 Million
Current Price of T-Bond futures = 91.22
Price of T-Bond on August 2 = 100.00
Price of T-Bond on November 2 = 95.11
Price of T-Bond Futures on November 2 = 88.26
Minimum Future contract size = $ 100,000
Minimum Price change = $ 31.25 per tick of 1/32
Answer (a)
Since the investor has a portfolio of $ 10 Million in bond portfolio, he is currently holding the bonds or long on the T-bonds. The hedge the portfolio, he can go short on futures. That is he needs to sell the futures contracts so that he can have a guaranteed amount receivable on sale of the portfolio.
Answer (b)
Value of Portfolio on August 2 = $ 10 Million
Price of T-Bonds on August 2 = 100.00
Price of T-Bonds on November 2 = 95.11
As per the given problem, during the period August 2 to November 2, the interest rates climbed rapidly. When interest rates rise, the prices of the existing bonds which were issued at a lower yield to maturity compared to the current high interest rates fall. The alternative available to the bond holder is to replace the bonds with lower ytm with those providing higher interest rates now. The difference in prices of the existing bonds before and after change of interest rates would be the opportunity cost of holding the bonds for a longer term. In this case
Opportunity cost = current price - purchase price = 95.11 – 100 = -4.89
In percentage terms = -4.89/100 * 100 = -4.89%
Answer (c)
Total number of futures contracts to be sold = Total Amount of Portfolio / Future contract size
= $ 10 Million / $ 100,000 = 100
Price of December Futures contracts on August 2 = 91.22
Price of December Futures contracts on November 2 = 88.26
As we sold the Futures contracts on August 2, we buy future contracts of same maturity on November 2 to square off the position. That is
August 2 - Sold December Futures contracts at a price = 91.22
November 2 – Bought December Futures contracts at a price = 88.26
Change in Prices = 91.22 – 88.26 = $ 2.96
Number of ticks involved in the price change = ($2.96*100 cents) / 32 = 296/32 = 9.25 ticks
Price change per tick of (1/32) = $ 31.25
Profit per contract = 9.25 * $ 31.25 = $ 289.0625
Total profit for 100 contracts = Number of contracts * profit per contract
= 100 * $ 289.0625 = $ 28,906.25
Total gain in futures market = $ 28,906.25
Answer (d)
Total Investment = $ 10 Million = $ 10,000,000
Total Number of Bonds Purchased at a Price $ 100.00 = $ 10,000,000 /$100 = 100000
Sale Proceeds received from sale of 100000 bonds at a price 95.11 = $ 9,511,000
Revenue on bond portfolio without hedge = $ 10,000,000 - $ 9,511,000 = - $ 489,000
Total gain in futures market = $ 28906.25
Effective revenue on bond portfolio with hedge = -$ 489,000 + $ 28,906.25 = - $ 460,093.75
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