As an introduction to hedging, let's consider some examples. First, consider the hedging of the Ginnie Mae (GMNA). Because we are holding the Ginnie Mae security long, the hedge is set up to sell a combination of T-Bonds and Euros that will provide offsetting cash flows. If interest rates go up, the Ginnie Mae price goes down and we incur losses in the cash position. Because we are shorting the T-Bond and Euros, money is transferred into our account as the price of these instruments heads down. We observe that the price--yield function for the Ginnie Maes could be concave at some points. This provides a considerable complication to our hedged position. Consider the situation in early 1986. The investment bankers that had set up hedged positions lost a huge amount of money because of imperfect hedges. The estimated losses were $500 million and some large houses lost over $100 million in a few days.
What exactly happened? The investment bankers were using T-Bonds and short term interest rate futures to hedge their holdings of mortgage backed securities. In the first part of 1986, interest rates dropped considerably. As interest rates drop, bond prices go up. So the firms were taking losses on their short futures position. Usually, with a hedged position, the losses on the short position are offset by gains in the financial instrument that you are holding. That is, if I was holding a corporate bond, as interest rates went down the bond price would go up and there would be gains in the cash position that offset the losses in the short position. With the mortgage backed securities, this did not occur. As rates dropped, people began to prepay their mortgages. Mortgage holders were exercising their call option with the exercise price of the par value of the mortgage plus the prepayment fee. As a result, the duration of the mortgage backed securities dropped and the price did not go up and in some cases the prices actually fell. So the investment bankers were faced with losses on the futures and losses in the cash. This is why Wall Street took such a bath in early 1986.
It happened again in 1994, when interest rates rose sharply. Mortgage holders slowed down the rate at which they prepaid their mortgages. Bonds lose value as rates go up, because the cash flows are discounted at a higher rate. Mortgage backed securities lose value at an even faster rate, since cash flows from expected prepayments are pushed back. In early 1994, Kidder Peabody & Co had $16 billion worth of mortgage backed securities in their inventory which were not hedged properly. This contributed to the demise of the firm, which was sold at the end of the year.
Short Hedges (1)
The purpose of the short hedge is to offset risk in a cash position. Consider the case of a bank with a $500 million holding of government securities. It is January 1, 1996. The bank investment committee expects a rise in the yield on government bonds within the next two months and a leveling off thereafter. That is, the investment committee expects a capital loss on the bank holdings of the government bonds (a rise in interest rates causes the bond prices to drop). You have recently been hired into the finance group. Your job is to set up a hedge.
To simplify this example, suppose the bank is holding 8% Treasury bonds with 20 years to maturity. The going rate in the market is 8.2%. So the bonds are worth approximately par value. The hedge will involve agreeing to sell Treasury bonds in the future. You call up your broker and sell 5000 March T-Bond contracts on the Chicago Board of Trade. The face value of the contract is
5000 x $100,000=$500,000,000.
Since the going rate in the market is close to the coupon on the underlying asset, the futures are trading close to par.
The next step is to follow the daily cash flows. If the bank's investment committee is correct and the rates go up, the value of the bonds that the bank holds will go down. At the same time on the futures side, you will be making money. As the rates go up, the settlement prices on the T-Bond futures will go down. Money will be transferred into your account. This money will help offset the losses on the cash market.
Since the investment committee believes that the rates will level off by March, you should execute a reversing trade in March -- or deliver your bonds. Since the bank wants to keep the Treasury bonds, buy 5000 March T-Bond contracts on March 1, 1996.
This was a very simple example. The hedge worked quite well because we were holding an instrument that was assumed to be the deliverable instrument. Note the T-Bond futures contract is a very good hedge against 8% 20 year bonds, it is not as good for other coupons. If the bank was holding $500 million in corporate bonds, the quality of the hedge would be determined by the correlation between changes in corporate yields and changes in the Treasury yields.
The last thing to realize is that if the rates went down, then you would make money on the cash side. Those gains, however, would be wiped out by losses on the futures side. So the hedge reduces both the downside and upside potential for your investment. Many portfolio managers do not use interest rate futures because of the limitation on the upside. Those managers that do use futures do not necessarily hedge 100% of the exposed assets like we did in this example. If you hedge 50% of your asset base, you cut the downside risk but still leave some upside potential.
The next example shows how a short hedge can be used to manage the liability side of the balance sheet. Suppose that a bank expecting to issue $100 million in one year certificates of deposits (CDs) three months from now is concerned with rising interest rates. In order to lock in today's CD rate, the bank could enter the following transactions:
|January 14||No Transaction
CD Rate = 9%
|Sell 100 90-day June U.S. Tbill on IMM
(current settlement price = 92.00)
Proceeds* = 100,000,000-(91/360x8/100 x 100,000,000) = $97,977,778.00
|April 5||Issue $100 million of CDs at 10% Additional annual interest
1/100 x 100,000,000 =
|Cover the short position
(June contract quoted at 90.00)
Costs = 100,000,000 - (91/360 x 10/100 x 100,000,000) =
Profit on the short position = $97,977,778-$97,472,223 = $505,555
*The funds are not actually received. In fact, the short seller would have to pay the margin requirement on the contracts. We use this concept to simplify the presentation.
This example shows why it is often difficult to learn finance from the textbook. What is wrong with this hedge? Should 200 contracts have been taken? Why?
This hedge is what I call the "naive hedge". Because $100 million in CDs are involved, the hedger elects to take a position in the futures market with underlying principal equal to $100 million. There is a major flaw in this logic. The size of the position (number of contracts taken should depend on the relative sensitivities of the cash position and the futures position to changes in interest rates. The CDs are 1 year to maturity. The hedging instrument is 3 months to maturity. A quick calculation of the modified duration shows that the CD is 4 times more interest rate sensitive than the T-bill. Actually, the correct hedge involves 400 contracts.
Long Hedge [Textbook example]
The long hedge is the opposite of a short hedge. The intent is the same; however, the long hedge is established in order to offset risk in an actual or prospective cash position. A pension fund manager expecting to receive $5 million in three months is concerned about falling yields requiring him to invest at a much lower rate in the future than he presently could. In order to lock in today's rate, the manager decides to go long 50 T-bond futures contracts.
|January 15||No transaction. Average yield on long-term bonds is 10.25%||Buy 50 June T-bond futures contracts on the CBT. Settlement
price = 76 10/32. This price is based on the delivery of an 8% coupon bond.
Assuming that such a bond is available and cheapest to deliver, the cost
of 50 contracts is 50 x 0.763125 x $100,000 = $3,815,625
The pension fund manager is only obligated to pay the margin requirement per contract and is expected to be ready to meet the margin calls. The cost is the financial committment required if the manager takes delivery of the bonds when the futures contract matures.
|April 5||Invest $5 million at 9.5%. Opporunity lost = 0.75% or
0.0075 x $5,000,000 = $37,500
This opportunity loss will be incurred over the life of the investment, which can well exceed a year in the case of the pension fund.*
|Sell 50 June T-bonds futures contracts at 80. The proceeds
are = 50 x $100,000 x 0.80 = $4,000,000
Profits = $4,000,000 - 3,815,625 = $184,375
*Assuming a 20 year time horizon, we can work out the present value by multiplying $37,500 times the annuity factor for 10.25% which is 8.4. Hence, the present value is $315,000.
What is wrong with this hedge? Obviously, the loss exceeds the gain on the hedge. But why? This is also another example of the naive hedge. There is no reference to interest rate sensitivity. However, there is even a more serious problem. Why hedge $5 million in bonds with $3.8 million in futures (even assuming the modified durations are identical)? This is what I call the 'double naive hedge'. The person doing the hedging has confused principal value with the market value. We always hedge using market value.
Much of the materials for this lecture are from Douglas Breeden, Futures Contracts, Markets and Deliveries.