The factors that contribute to a bond futures valuation versus the bond curve have different impacts on the future pricing versus the swap curve. In the following article we shall outline the elements composing the future price and then analyze their influence on the futures swap margin. We will use as our example the March 2000 Japanese Government Bond future before the roll-over into June started, as it provides the best illustration.
In general, the JGB future is cheap compared to the bond curve. This is due to the overall bearish market sentiment, which at times generates heavy selling pressure on the hedging instrument to which many Japanese accounts are restricted. This cheapness of the future consists of three elements. First of all, the cheapest-to-deliver (CTD) bond can be cheap on a spot basis. We measure the CTD spot cheapness by its spread versus the fair JGB curve (spline model) rather than its swap margin.1 Secondly, specialness in repo can make the CTD issue at delivery date even cheaper versus neighboring bonds than on a spot basis. The CTD repo element of the future's cheapness is the value of the general collateral--CTD spread in repo (in cents) until delivery. Thirdly, the liquidity premium or an overestimation of the delivery option may cause a deviation of the future price from the converted CTD forward price. The last element of the future's cheapness is therefore the CTD net basis. The chart shows the historic evolution of these three elements in the March JGB future (figure 1).
As with the time to delivery, the share of the CTD repo factor decreases naturally, leaving the other two elements to account for a larger part of the future's cheapness. However, from a theoretical point of view, both the CTD spot cheapness and the CTD net basis should be zero.2 If the CTD becomes too cheap versus other JGBs, investors will tend to purchase this bond versus surrounding issues, thereby causing the bond to richen. Net basis arbitrage puts a cap on the spread between the future and the forward CTD price. Thus, the future's cheapness will depend on the relative strength of the CTD spot cheapness and CTD net basis. The composition of the contract cheapness can hence be regarded as result of the equilibrium of arbitrage forces in the cash and basis market. If investors seeking cheap assets are the stronger force, the CTD net basis will have to bear the lions share of the future's mispricing. If, on the other hand, basis arbitrage is very active, the spline spread of the CTD will rise abnormally.
Obviously, all three components of the contract's cheapness affect its asset swap margin.3 In case of the CTD cheapening versus the spline (and swap) curve, the CTD richening in repo or the net basis widening, the swap spread of the future will decrease. However, the strength of the impact on the contract's swap spread is different for the three factors. The table below shows the results of a regression of the March future's swap spread versus each of the elements of the future's valuation.
The table suggests that the CTD spline spread has a much bigger impact than the other factors. Not only is the R2 higher, but the beta also is greatest for the CTD spot cheapness factor. This means that if the future's cheapness remains overall the same, but its source shifts from a wide net basis to a positive CTD spline spread, the contract will cheapen versus swaps. For example, if a future's cheapness of 100 cents is entirely due to the CTD net basis, the contract's swap margin will be 11 basis points wider than if the 100 cents cheapness were the result of CTD spot underperformance. Consequently, not only the quantity but also the quality of the future's cheapness determines the future's swap margin, which narrows when the importance of the CTD spot cheapness factor increases. One is able to exploit this strategy by buying the March future versus swaps when the CTD spot cheapness factor reached maximal share. Even though the continued selling pressure kept the contract cheap versus the bond curve for quite some time, its swap spread widened when the share of the CTD spot cheapness criterion decreased.
A further enhancement of this trading strategy is possible by exploiting mismatches between the implied volatilities in the future option and swaption markets. This means, instead of buying the March contract versus swaps, one creates a synthetic position by selling a March put on the JGB future and buying a seven-year payer swaption with the same profile.5 In the example of Japan, where implied swaption volatility is usually too cheap, this yielded a premium take-out of 4bps for an ATMF (at-the-money forward) put spread.
1 We know the fair spline spread (0) but not the fair swap spread as precisely. Thus, if the CTD trades at spline plus 5.4bps we can infer directly that it is 5.4bps cheap, whereas the swap spread of LIBOR minus 24.3bps does not provide such information.
2 Assuming a zero value of the delivery option. This is a permissible assumption for the Japanese future, but not for all markets.
3 By asset swap margin of the contract, we understand the implied forward swap spread of the CTD at delivery date. This corresponds to the swap margin an investor obtains by buying the contract versus a forward starting swap and taking delivery.
4 These are single variable regressions. A multiple regression over all three components has a R2 of 74%. This means that the future cheapness versus the JGB curve is the more important determining factor of the futures swap margin than the general JGB swap spread level.
5 This means a seven-year swap, forward starting on March 21, 2000, as fixed on March 1 and expiring as JGB 192 on March 20, 2007.
