In this post, we explain the holding period return formula with examples and offer an easy-to-use holding period return calculator.

When investors buy securities (e.g., stocks), they may hold them for months or years before selling them. The duration during which an investor holds on to a particular security is known as the **holding period **and the return over that period is referred to as the **holding period return**. This is typically abbreviated as **HPR**.

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## Holding period return formula

Imagine that you bought a stock for £5/share in September. Afterward, the share price increased to £8 in October but went back down to £5 in November. What is your holding period return (HPR) over this 2-month period?

Intuitively, you know that your holding period return is zero because you bought the stock for £5 back in September and it is still worth £5 in November. In general, you can calculate the holding period return as follows:

where *P _{0}* is the initial price you paid when you bought the stock and

*P*is the final price you received when you sold the stock. So, we have:

_{T}*HPR = £5 / £5 — 1 = 0*

However, this simple formula works ONLY IF there were no dividends and/or stock splits during the holding period. Otherwise, there are two ways of calculating holding period returns as explained next.

### Option 1: Use adjusted prices

The first option is to use what we call **adjusted prices**, which account for dividends and splits. Various data providers such as Yahoo! Finance offer free access to adjusted stock prices. If you’re using adjusted prices, you can still use the same formula for holding period return computations:

*HPR = P _{T} / P_{0} — 1 *

Now, *P _{0}* is the

*adjusted*price you paid when you bought the stock and

*P*is the

_{T}*adjusted*price when you sold it.

### Option 2: Compound returns to obtain the holding period return

If you are unable to use adjusted stock prices, you can use the following formula for holding period return calculations.

With this formula, we first compute the return for each period and then compound them to find the holding period return. Note that *∏ *is the product symbol and is telling us to compound gross returns *(1 + R _{t} )* to obtain the

*HPR.*

Going back to our example, the net return for October is £8 / £5 − 1 = 60% and the one for November is £5 / £8 *− *1 = *−*37.5%. Then, the holding period return is:

*HPR = (1 + 60%) (1 *− 37.5%) *− 1 = 0*

This is the same result as before.

### Summary

In summary, if you’re working with adjusted prices, *HPR *can easily be calculated based on the initial price *P _{0}* and the final price

*P*as follows:

_{T}*HPR = P _{T} / P_{0} − 1*

Otherwise, you need to calculate the *HPR *by compounding gross returns as follows:

*HPR = ∏(1 + R _{t} ) − 1*

## Holding period return calculator

We offer a holding period return calculator that computes holding period returns up to 10 periods (10 days, 10 months, etc.). All you need to do is to enter the return observations for each period. If you are computing a holding period return over, say, 7 months, leave the fields for Return 8, Return 9, and Return 10 as zero.

Also, make sure to enter net returns (not gross returns). If you don’t know the difference between the two, you can read our post on basic return calculations.

##### summary

When investors hold an asset for multiple periods, say 10 years, they would be interested in computing their holding period return (HPR). The holding period return formula depends on whether you are working with adjusted prices or raw prices. In the case of adjusted prices, the holding period return is simply the return computed using the adjusted purchase price and the adjusted selling price. In the case of raw returns, you have to first compute the gross return for each period (taking into account dividends, etc.) and then compound these returns to obtain the holding period return.

##### What is next?

This lesson is part of our free course on investments.

**Next lesson**: We will introduce arithmetic average return as a simple metric for evaluating average investment performance across multiple periods.**Previous lesson**: We discussed the difference between nominal returns and real returns.

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