- Holding period return
In

finance ,**holding period return**(HPR) is a measurement of return on anasset or portfolio. It is one of the simplest measures ofinvestment 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 andcapital 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**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)

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