Interest rate risk

A bond is a promise to pay fixed amounts on fixed dates. Nothing about that promise changes when market interest rates move. What changes is what the promise is worth.

If you hold a bond paying 8% and new bonds start paying 9.5%, nobody will buy yours at the price you paid — they can get more elsewhere. Your bond's price has to fall far enough that a buyer earns 9.5% from the remaining coupons and the redemption amount. The issuer is perfectly healthy; the coupon still arrives; you have still lost money on paper.

That is interest rate risk, and it runs in the direction people find counter-intuitive: rates up, prices down.

The price of a bond is the present value of its remaining cash flows, discounted at the market yield. Raise the yield and every term in that sum shrinks.

Two things decide how much it shrinks:

• How far the yield moved, and
• How long the money is tied up — a bond with fifteen years of coupons left has far more cash flow sitting deep in the future, where discounting bites hardest, than one maturing next year. This is what macaulay-duration measures.

The consequence for a fund is that interest rate risk is not only a bond-book problem. Chapter 7 puts it more broadly: changes in rates affect an AIF's investments and the income earned on them by moving the spread between interest income and interest expenditure, and macro-economic factors acting through rates can substantially move the fund's Net Asset Value. A leveraged Category III AIF funding positions at a floating rate feels a rate rise on both sides of its book at once.

Price = Σ  Coupon ÷ (1 + y)ᵗ  +  Redemption ÷ (1 + y)ⁿ

For a quick estimate of the damage from a small move in yield:

% change in price ≈ − Modified duration × Δy

The minus sign is the whole point. Yields and prices move in opposite directions.

A Category II debt AIF holds Rs 100 crore face value of a five-year non-convertible debenture with an 8% annual coupon, bought at par. Six months later the RBI has tightened and comparable paper now yields 9.5%.

Discount the remaining cash flows at 9.5%:

(1.095)⁵ = 1.5742      →  PV factor on redemption = 0.6352
Annuity factor        = (1 − 0.6352) ÷ 0.095 = 3.8397

PV of coupons     = 8 × 3.8397    = Rs 30.72 crore
PV of redemption  = 100 × 0.6352  = Rs 63.52 crore
                                    ─────────────────
Market value                        Rs 94.24 crore

The holding is marked down from Rs 100 crore to Rs 94.24 crore — a loss of Rs 5.76 crore, or 5.76%, from a 150 basis point move. That is roughly 3.8% of value per 100 basis points, which is this bond's modified duration.

The coupon has not been missed. The issuer has not defaulted. The fund's NAV is still Rs 5.76 crore lighter, and an investor redeeming this month bears it.

Hold to maturity and the Rs 100 crore comes back — but the fund has spent five years earning 8% in a 9.5% world, which is the same loss arriving slowly instead of all at once.

Chapter 1, section 1.4.3 gives the one-line definition among the types of risk, and Chapter 7, section 7.5 lists it as risk factor 5 in an AIF's disclosure, with the spread-and-NAV framing. Expect the direction question — what happens to the value of existing debt when rates rise — and a question separating interest rate risk from credit-risk, since both hit a bond's price but only one involves the borrower failing.

• Rates up, prices down. Every year some candidates answer this backwards. The coupon is fixed; only the price can adjust.
• Interest rate risk is not credit risk. A rate-driven fall assumes the issuer pays in full. A credit-driven fall assumes it may not. A government security has no credit risk and plenty of interest rate risk.
• Longer maturity means more interest rate risk for the same yield move. A 91-day treasury bill barely moves; a fifteen-year bond moves a lot.
• "Hold to maturity" does not cancel it. It converts a mark-to-market loss into years of below-market income, and it does nothing for an investor who redeems in the meantime.
• Floating-rate instruments reprice, so their price risk is small — but the income risk moves to the holder instead. The risk shifts, it does not vanish.
• Chapter 7 frames it at fund level as a spread problem. A question about a leveraged fund is asking about both sides of the balance sheet, not just the bond book.