Bonds, returns and business math Updated November 2026

Holding period return

Holding period return (HPR) is the total return over the time you held an investment: HPR = (P_end - P_start + income) / P_start, where income is dividends or coupons received. It is not annualized; to compare holdings of different lengths, annualize with (1 + HPR)^(1/years) - 1.

Syntax

HPR = (P_end - P_start + income) / P_start   annualized = (1 + HPR)^(1/t) - 1

Part	What it is
`P_start`	Purchase price
`P_end`	Sale price or current value
`income`	Dividends, coupons or rent received during the holding period
`t`	Holding period in years (for annualizing)

Examples

Bought at 100, sold at 110, dividends 3
(110 - 100 + 3) / 100

Result: HPR = 13%

Bought at 50, sold at 45, dividends 2
(45 - 50 + 2) / 50

Result: HPR = -6%

Bond bought at 1,000, sold at 1,200 after 3 years, coupons 40 in total
(1,200 - 1,000 + 40) / 1,000

Result: HPR = 24%; annualized = 1.24^(1/3) - 1 = 7.43%

Common mistakes

Dividing the HPR by the number of years to annualize (13% / 2 = 6.5%); use the geometric formula, which gives 6.30%.
Leaving out dividends or coupons, which understates the return, sometimes by more than the price change.
Comparing a 6-month HPR with a 3-year HPR without annualizing both.

Practice Holding period return

These drills check your answer on live data, free, no account needed.

Holding period returnYou buy 490 shares at $12.00 each, collect dividends of $2.90 per share, and sell all of them a year later at $9.50. Ignoring commissions, what is your holding period return? (Enter a negative number for a loss.)
Compound annual growth rateA company's revenue was $70,000 in 2012 and $135,000 in 2015. What was its compound annual growth rate over that span?

Questions

How do I annualize a holding period return?

(1 + HPR)^(1/t) - 1, with t in years. A 10% return over 6 months annualizes to 1.10^2 - 1 = 21%, not 20%.

What is the difference between HPR and CAGR?

CAGR is the annualized HPR of an investment with no interim cash flows. HPR is the raw total return over the actual holding period.

CAGRCAGR = (ending value / beginning value)^(1/years) - 1. Examples for investments and revenue growth, Excel RRI, and why CAGR differs from the average return.
Real vs nominal returnThe real return strips inflation out of a nominal return: real = (1 + nominal) / (1 + inflation) - 1. Examples, the quick approximation and its errors.
Current yieldCurrent yield is the bond annual coupon divided by its current price. Examples for discount and premium bonds, how it compares with YTM and mistakes to avoid.
IRR (internal rate of return)The IRR is the discount rate that makes NPV zero. How to find it by trial, what Excel IRR returns, worked examples, the accept rule and where IRR fails.