Yield to Maturity

A bond promises you a fixed set of payments: some coupons, then your money back. You do not have to pay face value to get them — in the secondary market you pay whatever the bond happens to cost that day.

So the real question is not "what is the coupon?" but "what return do I earn on the price I am actually paying?" That is Yield to Maturity.

YTM is the one interest rate which, used to discount every future rupee the bond will pay, gives back exactly today's market price. Nothing more mysterious than that. It is the bond market's equivalent of the effective rate on a fixed deposit, and when a dealer quotes "7.18 per cent" for a government security, YTM is what is being quoted.

The workbook builds it in four steps: list the coupon payments, add the redemption amount at maturity, discount each of those inflows at the market yield, and add them up. That gives the price from a known yield.

YTM runs the same machine backwards. The price is the number you can see on the screen; the yield is the unknown. There is no algebra that isolates it — you have to try a rate, see whether the resulting price is too high or too low, and close in. A spreadsheet does this in a millisecond; in the exam you either interpolate between two trial rates or use the approximation formula below.

The consequence to carry away is the one Chapter 2 hammers: price and yield move in opposite directions. Raise the discount rate and every future rupee is worth less today, so the price falls. A 10 per cent bond discounted at 8 per cent is worth Rs 107.98; discount the identical cash flows at 12 per cent and it is worth well under par.

YTM is the rate y that solves:

Price = C/(1+y)^1 + C/(1+y)^2 + ... + (C + Face value)/(1+y)^n

where C is the coupon in rupees and n the years to maturity. Solved by trial and error.

The examinable shortcut, good to within a few basis points:

Approximate YTM = [ C + (Face value − Price) ÷ n ]
                  ÷ [ (Face value + Price) ÷ 2 ]

A corporate bond: face value Rs 100, coupon 9 per cent paid annually, 3 years left to maturity, trading at Rs 95.

You receive Rs 9, Rs 9, and Rs 109. Find the rate that prices those at Rs 95.

Try 11 per cent:

Rs 95.11 is a shade above Rs 95, so the true yield is a shade above 11 per cent.

Try 12 per cent: 8.04 + 7.17 + 77.58 = Rs 92.79. Now we have overshot.

Interpolating between the two: (95.11 − 95.00) ÷ (95.11 − 92.79) = 0.05, so YTM ≈ 11.05 per cent. Check it: discounting at 11.05 per cent gives 8.10 + 7.30 + 79.59 = Rs 95.00. Exact.

The approximation formula gets you close without the table: [9 + (100 − 95) ÷ 3] ÷ [(100 + 95) ÷ 2] = 10.67 ÷ 97.5 = 10.94 per cent.

Now line the three measures up, because the ordering is itself an exam answer:

The bond is bought at a discount to face value, so YTM > current yield > coupon. Buy the same bond at a premium — say Rs 104 — and the order reverses exactly.

Chapter 2 (Securities: Types, Features and Concepts of Asset Allocation and Investing) introduces bond valuation, then "Yield and Price", "Current Yield" and "Yield to Maturity (YTM)" in sequence, and notes that yield quotations in the debt market usually refer to YTM. Chapter 2's own sample questions test the inverse relationship directly — "interest rates in the market have increased subsequently, this bond is likely to quote..." with "at a price below face value" as the answer. Expect the conceptual inverse-relationship item for certain, the coupon-versus-yield ordering very often, and occasionally a short discounting table to total.

• Coupon is not yield. The coupon is fixed in rupees the day the bond is issued and never changes. The yield changes every time the price changes. The workbook is explicit that the coupon "merely helps in computing the cash flows".
• Bought below face value → yield above coupon. Bought above face value → yield below coupon. Candidates reverse this under time pressure. Sanity-check it: paying less for the same cash flows must mean earning more.
• YTM assumes you hold to maturity and that every coupon is reinvested at the YTM itself. Sell early, or reinvest coupons in a savings account, and your realised return will not be the YTM.
• YTM is not a promise for a corporate bond. It is the return if the issuer pays. That is why corporate bonds yield more than government bonds of the same maturity — the gap is the credit spread, and it widens in a recession.
• Current yield and YTM are different questions. Current yield ignores the capital gain or loss you book at redemption; YTM includes it. They only coincide when the bond trades exactly at par.