Holding period return

Yield to maturity tells you what a bond pays if you hold it to the end. Most investors do not. They buy somewhere in the middle of a bond's life and sell somewhere else in it, and what they want to know is simple: how much did I make on what I put in?

Holding period return answers exactly that. Add up the three things that came in — the coupons, whatever those coupons earned once reinvested, and the gain or loss on the sale — and divide by what you paid.

Three income streams, one denominator:

1. Coupons received while the bond was held.
2. Reinvestment income — coupons do not sit idle; they are reinvested at whatever rate prevails when they arrive.
3. Capital gain or loss — sale price minus purchase price, which can be negative.

The workbook is blunt about what this measure is not. It calls HPR a crude return: it is the excess generated over the initial investment in percentage terms, over a horizon that is usually longer than one year, and it does not consider compounding. So an HPR of 33% earned over three years is not an 11% annual return, and it must not be compared with any annualised figure. The fixed income markets use a variant called realised yield for that, which does compound and is expressed as an annualised percentage.

        Coupon + Reinvestment income + (Sale price − Purchase price)
HPR = ───────────────────────────────────────────────────────────────
                             Purchase price

An investor buys a government security at Rs 98 per Rs 100 of face value. Over the next year it pays a coupon of Rs 7.50, which is reinvested at 6%, and the bond is sold at Rs 101.

HPR = [ 7.50 + (7.50 × 6%) + (101 − 98) ] ÷ 98
    = [ 7.50 + 0.45 + 3.00 ] ÷ 98
    = 10.95 ÷ 98 = 11.17%

Scale it to a treasury desk holding Rs 200 crore of face value: the outlay is Rs 196 crore, the coupon is Rs 15 crore, reinvestment adds Rs 0.90 crore and the sale adds Rs 6 crore — Rs 21.90 crore on Rs 196 crore, the same 11.17%.

Now the trap the workbook warns about. Suppose the same desk had held for three years and the total came to 33.5% of cost. Dividing by three gives 11.17% a year, which looks like the one-year figure. The compounded equivalent is

(1.335)^(1/3) − 1 = 10.11%

The simple division overstates the annual return by 106 basis points. On Rs 196 crore, that is the difference between claiming Rs 21.9 crore a year and actually earning Rs 19.8 crore.

Chapter 3 (section 3.2.7) introduces HPR in the debt market terminology block, immediately before current yield and yield to maturity. The exam tests the three-part numerator — most candidates forget the reinvestment income — and the conceptual point that HPR is not an annualised return and cannot be compared with YTM.

• The reinvestment income is a separate term. Coupon plus capital gain alone is not the workbook's HPR.
• HPR is not annualised and does not compound. Dividing a multi-year HPR by the number of years is not an annual return; that is what realised yield is for.
• Do not compare HPR with YTM. YTM assumes the bond is held to maturity and that every coupon is reinvested at the YTM itself; HPR assumes neither.
• The denominator is the purchase price, not the face value. A bond bought at Rs 104 has Rs 104 in the denominator.
• A capital loss is allowed in. Sell below cost and the third term is negative, which can pull HPR below the coupon rate or below zero.
• The workbook cross-references HPR to "section 3.2.6" while HPR is in fact section 3.2.7; 3.2.6 is redemption of a bond. Read the content, not the pointer.