Bond portfolio hedging

At the time, the June 2003 Euro-BUND future is trading at 116.42, and the cheapest-to-deliver (CTD) bond for the June 2003 futures contract is the 5% bond maturing on 4 January 2012, and having a conversion factor of 0.9341. The PVBP (or DVOl) for the CTD bond is 0.0788, while that for the bond actually held is 0.0840. The hedge ratio for the bond portfolio is therefore... 

Unhedged, the bond portfolio will lose 500,000 for every 1% fall in the bond price. The ATM put hedges this loss, while allowing the bond portfolio to profit if bond prices rise. However, the up-front cost of 627,480 may seem onerous. 

An alternative is to hedge with cheaper OTM puts, for example, the 115 puts priced at only 0.64, costing 318,720—half the price of the ATM options. As the revised payoff diagram of Exhibit 17.21 shows, however, while the investor benefits more when bond prices rise (because the premium wasted is smaller), the maximum loss is greater when bond prices fall. This is because the bond portfolio remains unhedged while bond prices fall 1.42%, until the put strike is reached, losing around 700,000. Together with the premium of around 300,000, the investor could lose more than 1 million, as the chart shows. 

On the surface, MV analysis is not especially difficult to implement. For example, it is very easy to guess at future stock and bond returns and use historical variances and correlations to produce an optimum portfolio. It is not so simple to create a multidimensional portfolio consisting of multiple equity and fixed income instruments combined with tiltemative assets such as private equity, venture capital, hedge ftmds, and other wonders. Sophisticated applications require a lot of groundwork, creativity, and rigor. 

The primary advantage of hedge fund portfohos is that they have provided double-digit returns going back to the 1980s with very low risk. Indeed, hedge fund portfolio volatility is close to that of bonds. With much higher returns and low correlation compared with traditional asset classes, they exhibit the necessary characteristics required to enhance overall portfolio perfotmance. 

Note that the unspanned stochastic volatility models are contradictory to the stochastic volatility models of Fong and Vasicek [31], Longstaff and Schwartz [56] and de Jong and Santa-Clara [24], where the bond market is complete and all fixed-income derivatives can be hedged by a portfolio solely... 

How does an investor measure the modified duration of linkers It sounds like a straightforward question and there is an easy answer, but it is sadly not the answer that people generally want. The easy answer is that a linker s modified duration is the (normalised) first derivative of price with respect to real yield, just as a conventional bond s modified duration is that with respect to nominal yield. This answer is a flippant one, because what people really want to know is some empirical rule about the sensitivity of a linker s price with respect to nominal yields, either for hedging purposes or in order to calculate aggregate duration statistics for portfolios holding both nominal and real bonds. 

Questions such as the uses to which European bond futures can be put, contract specifications and trading volumes are discussed with illustrative examples. Technical issues, which surround the use of bond futures, are also examined and presented with numerical examples. The issues include the calculation of gross and net basis, identifying the cheapest-to-deliver (CTD) cash market bond, different approaches to measuring relative volatility, calculating hedge ratios, and portfolio duration adjustment. Bloomberg screen output is used to provide a real world flavour to the topics covered. 

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 ... 

Hedging the underlying portfolio hence requires the relative volatility that exists between the cash market bond(s) held in the portfolio and the futures contract. Dollar duration can assist in this search since modified duration can help predict the effect of small changes in yield on the price of a bond ... 

The action undertaken by the portfolio manager is then as follows. Assume that the cash market bond held in the portfolio is deliverable into a futures contract and is a natural candidate for hedging using the Euro-Bund futures contract on Eurex-Deutschland. The contract specification appears in Exhibit 16.6. 

It is clear that the bond identified as being the CTD is actually that bond that the portfolio manager wishes to hedge. 

This, however, is only part of the picture. Even though the bond held in the portfolio is the CTD, the cash market bond s behaviour relative to the notional bond described in the futures contract needs to be taken into account. The following equation illustrates how, in general, the appropriately adjusted hedge ratio can be estimated. 

Consider the case where the CTD bond is priced at 104.28 and has a modified duration of 6.874 while the bond held in the portfolio is priced at 104.32 and has a modified duration of 7.491. Since bond to be hedged is not the CTD, then an adjustment needs to be made to the number of contracts shorted. This is the case where the relationship between the CTD and the bond to be hedged plays an important role. 

The portfolio is valued at 100,000,000 and has been constructed to track a bond index for which the Euro-Bund Future is a very good hedge instrument. The basis point value (BPV) of the Euro-Bund futures contract is 72.03 and the yield is 5.595% calculated on an annual 360-day year basis. The bond index, which the portfolio has been designed to track, is quoted at 117.80. 

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. 

The other side of credit selection is to short names that are deemed to be dear or expensive. This is problematic in the cash market, as bonds have to be short-covered, and is virtually impossible in the loan market. However, it is straightforward to short a name using CDS. So in this instance, the fund manager would run a portfolio of short credits and hedge this using sold protection in the relevant iTraxx index. 

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