Formula for holding period return calculations In this post, we explain the formula for holding period return calculations 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.

Learning objectives:

• Learn the formula for holding period return calculations.
• Understand the concept of adjusted prices.

Formula for holding period return calculations

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 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:

HPR = PT / P0  1

where P0 is the initial price you paid when you bought the stock and PT is the final price you received when you sold the stock. So, we have:

HPR = £5 / £5 — 1 = 0

However, this simple formula, which is based on the initial price and the final price, works ONLY IF there were no dividends and/or stock splits during the holding period. Otherwise, we have two options as explained next.

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 = PT / P0 — 1

Now, P0 is the adjusted price you paid when you bought the stock and PT is the adjusted price when you sold it.

Option 2: Compound returns to obtain the holding period return

If you don’t have access to adjusted stock prices, we can use the following formula for holding period return calculations.

HPR = ∏(1 + Rt ) — 1

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 + Rt ) to obtain the HPR.

So, 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 P0 and the final price PT as follows:

HPR = PT / P0 — 1

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

HPR = ∏(1 + Rt ) — 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.

Recap

When investors hold an asset for multiple periods, say 10 years, they would be interested in computing their holding period return. The formula for holding period return calculations 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 return for each period (taking into account dividends, etc.) and then compound these returns to obtain the holding period return.

What is next?

This post is part of the series on investments. The next post in the series is the average return. The previous post discussed the difference between nominal returns and real returns.