Holding-period return and the valuation premise

◈ 6 cards

Income plus price change over cost — the holding-period return for a bond and a share — and why it is not enough: the premise that every price is the PV of promised cash flows at the market’s rate, never the coupon.

The simplest return there is

Buy something, collect what it pays, sell it. The holding-period return (HPR) is everything you got back, over what you paid:

$H P R = \frac{P _{1} - P _{0} + income}{P _{0}}$

Price change plus income, divided by cost. It works for any security, and every later return in this course is a refinement of it.

Worked example — a Prairie Grid bond, then a Tamarack share

Halton Dairy Co-op buys Prairie Grid Energy's bond at 96.20 per 100 of par, collects the two semi-annual coupons of 2.75 each (5.50 for the year), and sells a year later at 98.10:

$H P R = \frac{98.10 - 96.20 + 5.50}{96.20} = \frac{7.40}{96.20} = 7.69 %$

=(98.10-96.20+5.50)/96.20 → 0.076923. Of the 7.40 earned, 1.90 is price gain and 5.50 is coupon income — the bond version of the two pieces every return has.

The same investor buys a Tamarack Foods common share at 42.00, receives a $1.20 dividend, and sells at 45.30: =(45.30-42+1.20)/42 = 10.71 %. Same formula; the income is a dividend instead of a coupon.

Why HPR is not enough

HPR has two blind spots. It ignores when the income arrived — a coupon in month one and a coupon in month twelve count the same, though the first could have been reinvested. And it ignores how long the holding was — 7.69 % over one year and 7.69 % over three years print the same number. The fix for both is a rate that discounts each cash flow to the day it arrives: the yield to maturity (Lesson 10.4). HPR is what you got; yield is what the price implies.

The valuation premise

Behind every price in this module sits one idea, and the paper tests it as a definition: a security's price is the present value of its promised cash flows, discounted at the return the market currently requires. For a bond, the promised flows are the coupons and par; the discount rate is the market yield for its term and credit — not the coupon rate, which merely sizes the coupons, and not the bank rate or the issuer's return on equity. When the market's required yield rises, the same promised dollars are worth less today, so the price falls. Module 7's PV of an annuity plus a lump sum is exactly this calculation; Lesson 10.2 does it in one Excel call.

Recompute

The Tamarack share bought at 40.00 instead, same $1.20 dividend and 45.30 sale: =(45.30-40+1.20)/40 = 16.25 %. A lower cost lifts both the gain and the yield on the dividend; the formula does not care which.

The holding-period return is what you got back over what you paid. It counts the dollars; it does not care when they arrived or how long you waited.