Coupon effect

Yield to maturity feels like a return. The coupon effect is the workbook's proof that it is not quite one.

Take two bonds from the same issuer, maturing on the same date. Their credit risk is identical and their maturity-related price risk is identical. Price both off the same set of zero-coupon rates, which is the correct way to value them. They come out with different YTMs.

Nothing is mispriced. The difference arises only because the bonds pay different coupons, and a YTM squeezes each bond's cash flows through a single rate of its own. The workbook names this "coupon effect" and uses it to make a sharp point: YTM is another way of quoting price, and neither price nor YTM can be used as a tool to judge whether a bond is cheap or rich.

The workbook's example: two 3-year bonds of the same issuer, Bond A with an 8% coupon and Bond B with a 9% coupon, priced off the zero rates 7.75% (1 year), 8.00% (2 years) and 8.25% (3 years).

The YTMs differ even though both prices come from exactly the same curve. Why:

1. YTM assumes a flat curve. It uses one rate for all cash flows. For Bond A that implied flat rate is 8.2242%; for Bond B, 8.2215%. The actual rates are 7.75%, 8% and 8.25%. The measure assumes two different flat curves at the same moment.
2. YTM assumes reinvestment at itself. Bond A's YTM implies reinvesting coupons at 8.2242%, Bond B's at 8.2215% — while the actual future reinvestment rates are unknown.

The bond with the larger share of its value in early cash flows (the higher coupon) leans more on the lower short-term zero rates, so its single averaged rate comes out slightly lower.

The workbook's conclusion: only if the actual market price differs from 99.4246 for Bond A or 101.9983 for Bond B is there any mispricing.

The workbook's bonds, scaled to Rs 5 crore of face value each (5,00,000 bonds of Rs 100).

A treasury analyst sees the two bonds quoted at their fair prices:

Her junior colleague argues: "A yields more and trades below par — buy A, it is cheap." Both halves are wrong as reasons. The prices are exactly what the zero curve says; there is no cheapness in either. The 0.0027 percentage point YTM gap is the coupon effect, not an opportunity.

What can legitimately separate them, per the workbook:

• Reinvestment view. If rates are expected to rise, Bond B may be preferred, because its larger Rs 9 coupon gets reinvested at higher rates. On Rs 5 crore that is Rs 45,00,000 a year of coupon against Bond A's Rs 40,00,000.
• Tax. If capital gains are taxed more lightly than income, Bond A may be preferred: less income each year, and a capital gain as its price pulls from 99.4246 up to 100.

The choice turns on tax and expectations — never on which YTM is bigger.

Chapter 1 (Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Markets), section 1.11 on yield measures, works the Bond A and Bond B example and then lists the drawbacks of YTM as a true return measure: it assumes a flat term structure, it produces different YTMs for bonds with the same maturity but different coupons (the coupon effect), and it assumes different reinvestment rates at the same time. Expect a question that asks what the coupon effect is, or which statement about YTM is a drawback.

• Different YTMs do not mean one bond is mispriced. Both bonds in the example are priced correctly off the same curve.
• Price below par is not "cheap". Bond A is below par because its coupon is below the relevant rates.
• YTM is another way of quoting price, not an independent return measure — the workbook's own words.
• YTM assumes a flat term structure and reinvestment at the YTM itself. The coupon effect is one symptom of the first.
• Mispricing exists only when the market price differs from the price implied by the zero curve.
• Preferences between such bonds come from tax treatment and reinvestment expectations.