Yield to Call

A callable bond lets the issuer repay early. Issuers use that right when interest rates have fallen — they retire the expensive old bond and borrow again more cheaply. That is exactly when an investor least wants the money back, because it has to be reinvested at lower rates.

So a callable bond has two possible yields:

• Yield to maturity — if it runs its full life.
• Yield to call — if it is redeemed at the call date for the call price.

When a bond trades well above its face value, a call is likely, and yield to call is the more realistic number.

The workbook's method: take the YTM formula and make two substitutions.

1. Replace face value (redemption value) with the call price.
2. Replace n with the number of periods to the first call date.

The call price and call date are fixed at issue. The call price may be higher or lower than face value. Where the issuer gives a schedule of call dates and prices, and nothing specific is said, the first call date is assumed.

The workbook's illustration: a bond paying a 12% coupon semi-annually, face value ₹1,000, trading at ₹1,180. The first call is 8 years away at ₹1,050.

In a spreadsheet, the YIELD function works if you enter the call date as "maturity" and the call price (per ₹100) as "redemption": settlement 01-01-2022, maturity 01-01-2030, rate 12%, price 118, redemption 105, frequency 2, basis 0 → YTC = 9.21%.

P₀ = Σ [Coupon ÷ (1 + r/cf)^t]  +  Call price ÷ (1 + r/cf)^(n × cf)
      t = 1 to n × cf

cf = coupon frequency per year, n = years to first call

For the workbook's bond: 1,180 = Σ 60 ÷ (1 + r)^t + 1,050 ÷ (1 + r)^16, with r a half-yearly rate.

The workbook's Chapter 4 caselet. A bond with face value ₹1,000 trades at ₹950. It pays a 12% coupon once a year and has 10 years to maturity. It is callable at the end of 7 years at a 5% premium — ₹1,050.

950 = Σ 120 ÷ (1 + r)^t  (t = 1 to 7)  +  1,050 ÷ (1 + r)^7

Spreadsheet: YIELD(settlement, call date, 12%, 95, 105, 1, basis) → YTC = 13.62%

Why is YTC this high? The investor pays ₹950 and could receive ₹1,050 in seven years — a ₹100 gain over a short horizon on top of the ₹120 coupon.

Now the premium case, illustrative: a PMS holds ₹5 crore face value of the workbook's first bond, bought at ₹1,180. Quoting yield to maturity would assume the issuer keeps paying a 12% coupon for the bond's full remaining life. But an issuer whose bonds trade at a hefty premium — a sign that market rates have fallen well below 12% — has every reason to call in year 8. Reporting the 9.21% yield to call is the prudent figure; a higher yield assumes the issuer will leave money on the table.

Chapter 4 (Investing in Fixed Income Securities), section on yield measures, derives yield to call from the YTM formula, shows the spreadsheet method (Illustration 4.3), and tests it in a caselet (13.62%). Chapter 4 also explains why callable bonds carry higher reinvestment risk. Expect a computation and a conceptual question on when an issuer calls.

• Two substitutions, not one: call price for face value, and periods to the first call for n.
• Frequency matters. A semi-annual bond uses half the coupon and twice the periods; the workbook's first example has 16 half-years, its caselet 7 annual periods.
• Spreadsheet prices are per ₹100 — enter 118 and 105, not 1,180 and 1,050.
• Issuers call when rates fall. A callable bond therefore carries more reinvestment risk than a non-callable one, and investors are the ones exposed.
• If nothing is said, assume the first call date.
• The call price can be above or below face value; do not assume par.