Risk in fixed-income arbitrage

[kthwow]

hi, david... i've been confused with this question from FRM handbook.

Q) identify the risks in a fixed-income arbitrage strategy that takes long positions in interest rate swaps hedged with short positions in Tresuries.
a. The strategy could lose from decrease in the swap-treasury spread
b. The strategy could lose from increase in the Treasury rate, all else fixed
c. The payoff in the strategy has negative skewness
d. The payoff in the strategy has positive skewness

 

[wolfi]

i dont understand why david didnt answer you!!

 

[David Harper CFA FRM]

Hi kthwow,

Here is the handbook answer:

c) The strategy has no exposure to the level of rates but is exposed to a widening of the swap-Treasury spread. Assume for instance that the swap and Treasury rates are initially 5.5% and 5%. If these rates change to 5.3% and 4.5%, for example, both values for the swap and the Treasury bond would increase. Because the drop in the Treasury rate is larger, however, the price of the Treasury bond would fall more than the swap, leading to a net loss on the position. The strategy should gain from decreases in the swap-Treasury spread, so a) is wrong. The strategy should gain from increases in the Treasury rate, all else equal, so b) is wrong. Finally, the distribution of the payoff depends on the distribution of the swap-Treasury spread. Because this cannot go below zero, there is a limit on the upside. The position has negative skewness, so c) is correct.

So (eg), assume Treasury yield = 5% and swap starts at 6% (pay 6% and receive floating Treasury + Spread(S)%; nevermind it probably should be LIBOR).

If the treasury (market) rate goes up by + 1%, then short treasury gains by 1%*duration; and,
the long swap (I dislike this terminology; should just say "receive fixed, pay floating") is paying T+S+1%, so value is lost here, per the hedge, of about 1%*duration. (another implicit assumption the durations match).

The intended skewness point is that your maximum gain is when S drops to 0. But, ceteris paribus, your only source of gain is this "basis" closing to zero.

On the other hand, if rates go - 1%, then short treasury position loses by 1%*duration; and the swap hedges by gaining T+S-1%. However, the spread (S) can widen without limit, so in this case (spread widening) as the pay floater you have sort of unlimited exposure.

David