Interest rates and fixed income basics

Interest rate derivatives are contracts on bond prices, and bond prices move opposite to yields. Nothing else in this module makes sense until that single relationship is instinctive. This chapter builds it from the ground up: what a government security is, how its price and yield are linked, and how duration turns a yield change into a price change that you can put in a table.

Government securities and treasury bills

The Government of India borrows through securities issued by RBI on its behalf. Dated G-Secs have maturities from a few years to forty, a face value of ₹100, and pay a fixed coupon half-yearly, for example a "7.10% GS 2034" pays ₹3.55 every six months per ₹100 until 2034 and then returns the ₹100. Treasury bills are short-term instruments of 91, 182 and 364 days with no coupon; they are issued at a discount and redeemed at ₹100. States borrow through State Development Loans on similar terms. All of these are sold at RBI auctions and trade in the secondary market on NDS-OM, the RBI-owned screen, with settlement through CCIL. Retail investors can hold them through RBI Retail Direct or a demat account.

Two day-count conventions matter. Dated G-Secs use 30/360 for accrued interest; T-bills and money market instruments use actual/365. A bond's quoted price is the clean price; the buyer actually pays the dirty price, clean plus interest accrued since the last coupon.

A 91-day T-bill bought at ₹98.40 yields (1.60 ÷ 98.40) × (365 ÷ 91) = 6.52% annualised. This is the number the T-bill futures contract in the next chapter is quoted against.

Price and yield move in opposite directions

A bond's price is the present value of its future cash flows, discounted at the yield the market demands. Raise the discount rate and every present value shrinks, so the price falls; lower it and the price rises. The yield that makes the present value equal to the market price is the yield to maturity (YTM). It is the single rate that summarises the return an investor earns by holding to maturity and reinvesting coupons at that same rate.

Three relationships follow. When the coupon equals the yield, the bond trades at par (₹100). When the coupon is below the market yield, the bond trades at a discount, because the fixed coupon is less than the market now pays. When the coupon is above the yield, it trades at a premium. A 7% bond in a 6.8% market is at a small premium; the same bond when the 10-year yield rises to 7.5% drops to a discount. Current yield, coupon divided by price, ignores the pull to par and is not the same as YTM.

The yield curve plots yields against maturity. It normally slopes up (longer bonds yield more), is called inverted when short rates exceed long rates, and flat in between. Policy rates set by RBI, the repo rate and the overnight MIBOR, anchor the short end; inflation expectations and government borrowing drive the long end.

Duration: turning a yield change into a price change

Macaulay duration is the weighted average time, in years, at which a bond's cash flows arrive, each weighted by its present value. A zero coupon bond has duration equal to its maturity; a coupon bond has a shorter duration because some money comes back early. Modified duration converts that into price sensitivity: the approximate percentage change in price for a one percentage point change in yield.

The estimate says the bond should fall to about ₹96.79, and repricing it exactly at 8.25% gives ₹96.793. For small moves duration is almost exact. Duration rises with maturity, falls as the coupon rises (more cash comes back early), and falls as the yield rises. A fund manager who expects yields to fall lengthens duration; one who expects a rise shortens it or hedges with futures, which is what the next chapter is about.

PV01 (or DV01), the rupee change in value for a one basis point move, is simply modified duration × 0.0001 × price. For the bond above it is 2.598 × 0.0001 × 97.42 = ₹0.0253 per ₹100, or ₹253 per ₹10 lakh of face value. Dealers hedge in PV01 terms.

Convexity: why duration is only an approximation

The price-yield curve is not a straight line; it bows towards the origin. That curvature is convexity, and it works in the bond holder's favour: when yields fall the price rises by more than duration predicts, and when yields rise it falls by less. In the example, a full 100 basis point rise to 9% gives an actual price of ₹94.94 against a duration estimate of ₹94.89. The gap is small for a three-year bond and large for a thirty-year one. Convexity is higher for longer maturities and lower coupons, and between two bonds of equal duration the more convex one is preferred. The exam asks only for the direction: duration overstates the loss on a yield rise and understates the gain on a yield fall, and a convexity adjustment corrects both.