HEDGING WITH FUTURES EXAMPLE

* A Company plans to issue $10,000,000 of 20-year, semi-annual coupon, bonds

    in March 2010  (It is now September 2009) to finance its capital expenditure

    program. Interest rates would be 9% if the bonds were issued today. If interest

    rates were to go up, bonds prices would decline bringing less money. How can

    the company protect itself against rising interest rates?

*  Use short hedge, i.e. sell futures contract short!

*  Table 23-2: Future Prices (Treasury Bonds: $100,000; Pts. 32nds of 100%, semi-

    annual, 6% coupon; Last)

                 September 2010      118’25

                 March 2010              116’17

                 June 2010                115’17

*  Each March contract has the price of 116’17, or 116+17/32, or 116.53125% of

    par. The total value of one contract is thus 116.53125% of $100,000 or

   $116,531.25. Since the company wants to issue $10,000,000 of bonds, it will sell

   $10,000,000/$116,531.25 = 85.81 contracts (rounded to 86) for delivery in March.

   The total value of 86 contracts is 86x$116,531.25 = $10,021,688, which is

   very close to the bond value the company wants to issue. In addition, the 

   company will put up 86x$900 = $77,400 in margin money and pay brokerage

   commission. 

*  Should the interest rates go up by March, the company will REPURCHASE the

    futures contract at lower cost, thus offsetting the loss from financing the bond

    issue at higher interest rates! The hedge against increasing interest rates

    will work!

*  NUMERICAL EXAMPLE: In March 2010 the interest rates on bonds are up by

   100 basis points (100 basis points is 1%) to 10% (vs. 9% in September 2009).

*  What will happen to the value of company’s bonds? It will have to pay 10%

    yield on bonds with 9% coupon. The bond issue will bring only $9,142,046 for

    a LOSS of: $10,000,000 - $9,142,046 = $857,954.

    [n = 20x2 = 40; i = 10/2 = 5; PMT = 10,000,000x0.09/2 = 450,000; FV = 10,000,000;

     Calc. PV = 9,142,046]

*  Alternatively, the LOSS can be calculated as follows: 1% higher coupon will

    result in higher interest payments of $100,000 or $50,000 semi-annually.

    [n = 20x2 =40; i = 10/2 = 5; PMT = 50,000; FV = 0; Calc. PV = 857,954]

*  What will happen to the value of the futures contract? The settlement price was

    116.53125% of par, or $1,165.3125 per bond. What is the implied yield on that 

    bond?

    [n = 20x2 = 40;  PMT = 1,000x0.06/2 = 30; FV = 1,000; PV = - 1,165.3125;

     Calc. i = 2.3572]

                                     Annually   2x2.3572 = 4.7144%

*  If interest rates rise by 1%, the yield on Treasury bonds will have to increase

    from 4.714% to 5.714% and the value of the futures contract will drop to

    $103,383.17 per each contract.

    [n = 20x2 = 40; i = 5.714/2 = 2.857; PMT = 100,000x0.06/2 = 3,000; FV = 100,000; 

     Calc. PV = 103,383.17]    

    With 86 contracts, the total value of the position is 86x$103,383.17 = $8,890,953.

*  The company will now close its position, i.e. it will REPURCHASE the contract

    in the futures market for $8,890,953. The same contract was earlier sold short

    for $10,021,688. The company made the GAIN of $10,021,688 - $8,890,953 =

    $1,130,735 on its short position.

 *  OVERALL Gain = GAIN on short position – LOSS on its bond =

                               =  $1,130,735 -  $857,954 = $272,782

*  Not included here are the commissions, opportunity costs and the margin

   money.

*  NOTE: If the interest rates went down, the company would have a LOSS on

   futures position, but a GAIN on its bonds (they will be sold with lower coupon

   rate)!!    

Credits : Prof. Peter Dzadzic, and MBA Student, Lulu Mero