# Holding Period Return

Holding period return is the total return earned on an investment over its whole holding period expressed as a percentage of the initial value of the investment. It is calculated as the sum of total return (i.e. capital gain (i.e. ending value of investment minus opening value of investment) and any interest or dividends) divided by the opening value of investment.

There are two sources of return for any bond, common stock, real estate, etc.: (a) capital gain and (b) income. The capital gain or loss results from the movement in bond or stock or real estate price/value from the date of purchase to the date on which the holding period return is calculated. The income results from coupon payments, dividends, rents, etc.

Holding period return is not a standardized measure of return. A given holding period return might be for a single day or a 5-year period and we won’t know. Comparison between holding period return on different investments directly is not appropriate. We need to find out the total time over which the return is calculated and then convert it to annualized holding period return.

Holding period returns for multiple periods can be connected using the time-weighted rate of return or money-weighted rate of return.

## Formula

Holding period return can be calculated as follows:

$$ Holding\ Period\ Return\\=\frac{P_1−P_0+I}{P_0} $$

Where *I* stands for income i.e. interest or dividend or rent, *P _{1}* is the closing value of investment and

*P*is the beginning value of investment.

_{0}Let’s learn how we arrived at the above equation.

Holding period return in absolute dollar amount equals the capital gain plus income. This can be expressed as follows:

$$ Holding\ Period\ Return\ (in\ dollars)\\=Capital\ Gain\ +\ Income $$

Capital gain equals closing value of investment minus beginning value of investment i.e. purchase value.

$$ Holding\ Period\ Return\ (in\ dollars)\\=P_1−P_0+I $$

Dividing both sides by the beginning value of investment, we get:

$$ \frac{Holding\ Period\ Return\ (in\ dollars)}{P_0}=\frac{P_1−P_0}{P_0}+\frac{I}{P_0} $$

$$ Holding\ Period\ Return\ (\%)=\frac{P_1−P_0}{P_0}+\ \frac{I}{P_0} $$

The above equation can also be written as follows:

$$ Holding\ Period\ Return\ (\%)\\=Capital\ Gain\ Yield+Income\ Yield $$

As we highlighted earlier, the holding period return is not a standardized yield measure. However, it can be converted to an annualized rate for comparison purposes. Annualized holding period return can be calculated as follows:

$$ Annualized\ Holding\ Period\ Return\\=\left(1+\frac{P_1−P_0+I}{P_0}\right)^\frac{1}{N}−1 $$

Where N is the total number of years for which the holding period return is available.

## Example

You invested $10,000 in a Stock A on 1 January 2015. The stock’s value as at 31 December 2016 is $11,000 and you earned a dividend of $500 over the two-year period.

You want to compare its return with another investment in Stock B made on 1 January 2014. The stock returned 5% till 31 December 2014 and in the subsequent 2-years (i.e. 1 January 2015 to 31 December 2016), it returned 15%.

Calculate each stock’s holding period return and identify which investment did better.

First, we need to work out the holding period return for Stock A:

$$ Holding\ Period\ Return\ (Stock\ A)\\=\frac{$11,000−$10,000+$500}{$10,000}=15% $$

In case of Stock A, we already have holding period returns for the initial 1 year and subsequent 2-years, which can be linked as follows:

$$ Composite\ Holding\ Period\ Return\\=(1+5\%)\times(1+15\%)−1=20.75\% $$

Because there is difference in holding period i.e. total duration of time, we can’t compare the returns directly. We must calculate annualized holding period returns:

$$ Annualized\ Holding\ Period\ Return\ (Stock\text{-}A)\\=\left(1+15\%\right)^\frac{1}{2}−1\\=7.24\% $$

$$ Annualized\ Holding\ Period\ Return\ (Stock\text{-}B)\\=\left(1+20.75\%\right)^\frac{1}{3}−1\\=6.49\% $$

Stock A did better.