Question

In: Accounting

On February 24 a company decides to issue $5 million face value in new bonds on...

On February 24 a company decides to issue $5 million face value in new bonds on May 24. They desire to issue them at their current coupon rate of 13.76%. They will be priced at par value with a 20-year maturity and duration of 7.22 years. However, if rates rise while due diligence is occurring, the market will factor that into the bonds’ value, resulting in less funds being raised. To deal with this, they decide to hedge the issue.

  1. June futures contracts are trading at 68-11.
  2. The CTD bond underlying the futures contract has a yield of 13.60% and a projected duration of 7.83 years.

c. The optimal number of contracts is given by:

N* = (Pb X Db) (1+YTMctd)    where

                (Pf X Df ) (1+YTMb)

Pb = dollar value of bond portfolio at par

Db = duration of bond portfolio

Pf = dollar value of one futures contract at current price

Df = duration of CTD bond for futures contract

YTMctd = Yield to Maturity of CTD bond

YTMb = Yield to Maturity of the portfolio

Face value of TBond futures contract = $100,000

d. Should they take a short or long position and why? Compute N* for the hedge.

e. On May 24 the bonds are issued and the futures position closed out. The yield on comparable bonds is now 15.25%, so the bonds are issued at a 13.76 coupon but at a price of 90.74638/100 face. Compute the new value of the portfolio and how much it lost in value because of the rate change.

f. The futures price at close is now 60-25. Compute the gain on the futures position based on this and N*.

g. Compute the performance of the hedge. Did the hedged portfolio gain or lose value?

Solutions

Expert Solution

June Futures Contract 68-11
Price of Futures $ 68.34375
Dollar Value of Bond Portfolio at Par $ 5,000,000
Duration of Bond Portfolio 7.22 Years
Dollar Value of One Futures Contract at Current Price                     68,343.75
Duration of CTD Bond for Futures Contract 7.83 Years
Yield to Maturity of CTD Bond 13.60%
Yield to Maturity of the Portfolio 13.76%

1. Computation of N for Hedge:

(Pb X Db) * (1+YTMctd) /  (Pf X Df ) * (1+YTMb)
(5,000,000 * 7.22) * (1.136) / (68.343.75 * 7.83) * (1.1376)
67.37 Contracts

2. Should they take a short or long position ?

The company should take a Short Position because the speculation that Bond Interest Rate may Rise in Future will Lead to bond being issues At Price Lower than its Par Value.

3. New Value of the Portfolio and How much it lost its Value due to Rate Change ?

No. of Units Issued : Value of Bond Portfolio at Par / Par Value of Bond
5,000,000 / 100
50,000 Units

New Value of the Portfolio : No. of Units Issued * Issue Price
50,000 * 90.74638
$ 4,537,319

Value Lost : Value of Bond Portfolio at Par - New Value of Portfolio
5,000,000 -  4,537,319
$ 462,681

4. Gain or Loss on Futures Position :

Price of 1 Future Contract
Contract Price of Futures 68-11                68.34375                                   68,343.75
Price on May 24 60-25 60.78125 60781.25
                                    7,562.50

(Contract Price of Futures - Price on May 24) * No. of Futures Contracts
(68,343.75 -  60,781.25) * 67.37
7,562.50 * 67.37
$ 509,485.63

g) DId Hedged Portfolio Gain or Lose Value ?

The Hedged Portfolio performed well as there is a increase in its Overall Value.

Gain on Futures - Value Lost on Bond Portfolio
$ 509,485.63 -  $ 462,681
$ 46,804.63


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