In finance, holding period return (HPR) is a measurement of return on an asset or portfolio. It is one of the simplest measures of investment performance.

HPR is the percentage by which the value of a portfolio (or asset) has grown for a particular period. It is the sum of net income and capital gains divided by the initial period value (asset value at the beginning of the period).

HPR = ((Present Value, or face Value, End-Of-Period Value) + (Any Intermediate Gains eg. Dividends) - (Initial Value)) /(Initial Value)'''

$HPR\_n\; =\; frac\{Income\; +\; (P\_\{n+1\}\; -\; P\_n)\}\{P\_n\}$

Example

Example: Stock with low volatility and a regular quarterly dividend

End of:	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
Dividend	$1	$1	$1	$1
Stock Price	$98	$101	$102	$99
Quarterly ROI	-1%	4.08%	1.98%	-1.96%
Annual ROI				3%

To the right is an example of a stock investment of one share purchased at the beginning of the year for $100. At the end of the first quarter the stock price is $98. This is a capital loss. The stock share bought for $100 can only be sold for $98, which is the value of the investment at the end of the first quarter. The first quarter return is:

($98 - $100 + $1) / $100 = -1%

Since the final stock price is $99, the annual ROI is:

($99 ending price - $100 beginning price + $4 dividends) / $100 beginning price = 3% ROI. If the final stock price had been $95, the annual ROI would be:

($95 ending price - $100 beginning price + $4 dividends) / $100 beginning price = -1% ROI.

Annualizing the holding period return

Over multiple years

To annualize a holding period return (translate it into percentage per year), then

Annualized HPR = (((Present Value, or face Value, End-Of-Period Value) + (Any Intermediate Gains eg. Dividents) - (Initial Value)) /(Initial Value)) + 1 ) ^ (1 / (Years) ) - 1

$Annualized\_HPR\_n=(([D\_1\; +\; (P\_\{n+1\}\; -\; P\_n)]/P\_n)\; +\; 1)^\{,!1/Years\}-1$

Years being number of years that have passed. For example, if you have held the item for half a year, year would equal 1/2.

From quarterly holding period returns

To calculate an annual HPR from four quarterly HPRs:

If HPR1 through HPR4 are the holding period returns for four consecutive periods, the annual HPR is calculated as follows:

(1 + HPR)= (1 + HPR1)(1 + HPR2)(1 + HPR3)(1 + HPR4)