In: Accounting
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.
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?
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