Hedging Bond Positions

A hedge is a position in a cash or off-balance-sheet instrument that removes the market risk exposure of another position. For example, a long position in 10-year bonds can be hedged with a short position in 20-year issues or with futures contracts. The concept is straightforward. Implementing it effectively, however, requires a precise calculation of the amount of the hedge needed, and that can be complex. 

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For example, let us assume that an investor holds a bond with a price, Pbond that the recovery on this bond in the event of default is bond- The loss to the investor is (Pbond bond) result of the default. Flowever, the investor can hedge the bond position by buying CDS protection, for an amount equal to the default neutral hedge ratio multiplied by the standard CDS contract. 

The payoff from the standard CDS contract is (1 - PcDs) nd the default neutral hedge ratio multiplied by (1 - Rqds) would provide the hedging cash flow to offset the loss on the bond position. 

For bond positions hedged via CDSs in a default neutral hedge ratio, the profit and loss generated will depend on the recovery values actually obtained for the bond and the CDS contract. The assumptions regarding recovery are crucial for hedge effectiveness. 

Impose no-arbitrage conditions, based on the principle of hedging a position in one bond with a position in another bond (for a one-factor model a two-factor model requires two bonds as a hedge) of a different maturity, to derive the partial differential equation of the zero-coupon bond price. 

Bond traders wishing to hedge the interest rate risk of their bond positions have several tools to choose from, including other bonds, bond futures, and bond options, as well as swaps. Swaps, however, are particularly efficient hedging instruments, because they display positive convexity. As explained in chapter 2, this means that they increase in value when interest rates fall more than they lose when rates rise by a similar amount—just as plain vanilla bonds do. 

BPVp Change in yield for primary bond position BP V/j Change in 5deld for hedge instrument... 

Intuitively, if the value of the portfolio is to be hedged against potential adverse market movements, the long position in bonds would need to be set against a short position in the futures contracts. A negative value for h indicates the number of contracts that will need to be shorted. 

To maintain a neutral position AV must equal zero so that any loss on the bond side of the portfolio will be offset by a gain on the futures side of the hedge and vice versa. If that is the case then equation (16.2) can be rewritten as ... 

An example would be that a protection buyer holding a fixed-rate risky bond and wishes to hedge the credit risk of this position via a credit default swap. However, by means of an asset swap the protection seller (e.g., a bank) will agree to pay the protection buyer LIBOR +/-spread in return for the cash flows of the risky bond. In this way the protection buyer (investor) may be able to explicitly finance the credit default swap premium from the asset swap spread income if there is a negative basis between them. If the asset swap was terminated, it is common for the buyer of the asset swap package to take the unwind cost of the interest rate swap. 

The first picture that comes to mind when someone talks of leverage in the bond markets is that of hedge funds and LTCM and all that happened in the summer of 1998. Contrary to popular perceptions, financing and leverage play an important and often positive role in influencing portfolio performance. 

For a hedge to be effective, the price change in the primary instrument should be equal to the price change in the hedging instrument. To calculate how much of a hedging instrument is required to get this type of protection, each bonds BPV is used. This is important because different bonds have different BPVs. To hedge a long position in, say, 1 million nominal of a 30-year bond, therefore, you can t simply sell 1 million of... 

Say a trader holds a long position of 1 million of the 8 percent bond maturing in 2019. The bond s modified duration is 11.14692, and its price is 129.87596. Its basis point value is therefore 0.14477. The trader decides to protect the position against a rise in interest rates by hedging it using the zero-coupon bond maturing in 2009, vi/hich has a BPV of 0.05549. Assuming that the yield beta is 1, what nominal value of the zero-coupon bond must the trader sell ... 

To hedge 1 million of the 20-year bond, therefore, the trader must sell short 2,608,940 of the zero-coupon bond. Using the two bonds BPVs, the loss in the long position produced by a 1 basis point rise in yield is approximately equal to the gain in the hedge position. 

BPVf = the basis point value of the primary bond (the position to be hedged)... 

Bond investors can use credit options to hedge against rating downgrades and similar events that would depress the value of their holdings. To ensure that any loss resulting from such events will be offset by a profit on their options, they purchase contracts whose payoff profiles refiect their bonds credit quality. The options also enable banks and other institutions to take positions on credit spread movements without taking ownership of the related loans or bonds. The writer of credit options earns fee income. 

Hedges can be made more accurate by adjusting their weightings according to the standard relationship for correlations and the effect of correlation. Consider two bonds with nominal values and Afj. If the bonds yields change by A.r and r2, the net change in the position s value is given by equation (17.4)... 

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