Hedging, trading and arbitrage with interest rate derivatives

This chapter puts Module 3 to work. A Debt Long-Short strategy manager has three uses for interest rate derivatives: hedge a bond book against rising yields, trade a view on rates or on the shape of the curve, and pick up arbitrage when futures drift from fair value. The exam's favourite calculation here is the hedge ratio, so it gets a complete worked check with the numbers verified both ways.

Hedging: matching PVBP

A hedge works when the rupee change in the futures position for a given yield move equals and offsets the rupee change in the portfolio. Since price sensitivity is duration times value, the number of contracts is the ratio of the portfolio's duration-weighted value to the futures contract's duration-weighted value.

D_futures is the modified duration of the underlying bond that the futures contract tracks. Futures contract value is the futures price × 2,000. Sell contracts to hedge a long bond book (a short hedge); buy contracts to lock in the price of bonds you will purchase later (a long hedge), for example when a fund expects a large inflow next month and fears yields will fall before the money arrives.

The hedge is not perfect. First, rounding: 397 rather than 396.5 leaves a small over-hedge. Second, basis risk: the portfolio may hold corporate bonds and SDLs whose yields do not move one-for-one with the 10-year G-Sec; if credit spreads widen while G-Sec yields are flat, the futures do nothing. Third, the curve may not shift in parallel; a 3-year-heavy portfolio hedged with 10-year futures is exposed to a steepening. Fourth, the hedge removes upside: if yields fall, the futures lose what the bonds gain. A cross hedge (hedging one instrument with a futures on another) is always exposed to the first three.

Adjusting duration instead of eliminating it

A manager need not hedge fully. To move portfolio duration from 5.0 to a target of 3.0 without selling bonds, sell enough futures to remove the 2.0 difference: contracts = 10 crore × (5.0 − 3.0) ÷ (1,94,000 × 6.5) = 158.6, about 159 lots. To lengthen duration ahead of an expected rate cut, buy futures with the same formula. This is the everyday use of IRFs in a Debt Long-Short SIF: a quick, cheap dial on rate exposure. A mutual fund may use it to reduce duration (hedging) but not to go net short.

Trading on a rate view

A directional trade is simply long futures if you expect yields to fall and short if you expect them to rise, with leverage of 30 times or more at typical margins. A curve trade bets on the slope. For an expected steepening (long yields rising relative to short), buy short-dated exposure (T-bill futures or short bonds) and sell 10-year futures, sized by PVBP so the position is neutral to a parallel shift. For a flattening, reverse it. A spread trade between two futures months bets on carry. The 25% unhedged cap limits how large the net short in an SIF can be, but a PVBP-neutral curve trade is mostly hedged and uses little of that budget.

Arbitrage: cash-and-carry

If the futures price is above fair value, buy the underlying bond, finance it in the repo market, and sell the futures; at expiry the cash settlement locks in the difference. The implied repo rate is the return this trade earns; if it exceeds the actual repo rate, the arbitrage is profitable.

The arbitrageur buys ₹2 crore face of the bond at ₹98.00 dirty, finances it in repo at 6.4%, and sells 100 futures at 98.10. At expiry the bond is worth whatever it is worth, but the futures settle at the same price, so the two cancel and the ₹0.33 per ₹100 (less transaction costs and the bid-ask spread) is the profit. If the futures were cheap, a reverse cash-and-carry would sell the bond (or lend it out in repo), invest the cash, and buy futures. In practice such gaps are small and close fast, which is why institutional desks rather than retail clients do this.

Overnight index swaps and FRAs

Two OTC instruments complete the picture. An overnight index swap (OIS) exchanges a fixed rate for the compounded overnight MIBOR over a period of, say, one year, on a notional principal, with only the net difference paid. A bank that pays fixed and receives floating gains if overnight rates rise; one that receives fixed gains if they fall. The one-year OIS rate is the market's view of the average repo rate over the next year and is the cleanest signal of expected RBI action. A forward rate agreement (FRA) fixes an interest rate for a future period, settled in cash on the difference between the agreed rate and the reference rate at the start of that period. Mutual funds and SIFs may use OIS and FRAs for hedging within RBI and SEBI limits; their main use in the exam is conceptual: understand the direction of gain and loss and the role of MIBOR.