Definitions

# Holding period return

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)'''

$HPR_n = frac\left\{Income + \left(P_\left\{n+1\right\} - P_n\right)\right\}\left\{P_n\right\}$

## 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

$Annualized_HPR_n=\left(\left(\left[D_1 + \left(P_\left\{n+1\right\} - P_n\right)\right]/P_n\right) + 1\right)^\left\{,!1/Years\right\}-1$

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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