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2013-12-19T04:40:11Z

124.197.98.124:

{{Unreferenced|date=December 2009}}

In [[finance]], '''holding period return''' (HPR) is the total return on an [[asset]] or [[Portfolio (finance)|portfolio]] over the period during which it was held. 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 [[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 e.g. Dividends) - (Initial Value)) /(Initial Value)'''

<math>HPR_n \ = \ \frac{Income + (P_{n+1} - P_n)}{P_n}</math>

==Example==

{| class="wikitable" style="text-align:center" align="right"
|+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

[[AHPR|Annualized HPR]] = (((Present Value, or face Value, End-Of-Period Value) + (Any Intermediate Gains e.g. Dividends) - (Initial Value)) /(Initial Value)) + 1 ) ^ ( 1 / (Years) ) - 1

<math>\mathrm{Annualized\, HPR}_{n}=\left(\frac{D+(P_{n+1}-P_{n})}{P_{n}}+1\right)^{\frac{1}{t}}-1</math>

t 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:

<math>1+HPR=\left(1+HPR_{1}\right)\left(1+HPR_{2}\right)\left(1+HPR_{3}\right)\left(1+HPR_{4}\right)</math>

{{DEFAULTSORT:Holding Period Return}}
[[Category:Basic financial concepts]]
[[Category:Mathematical finance]]

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