Holding Period Return (Definition, Formula)

What is Holding Period Return (HPR)?

Holding period return refers to total returns over the period for which an investment was held, usually expressed in percentage of initial investment, and is widely used for comparing returns from various investments held for different periods of time. It also captures any additional income from the investment apart from helping calculate the growth or decline in value over multiple periods.

Holding Period Return Formula

Here’s the formula –

Holding Period Return Formula = Income + (End of Period Value – Initial Value)/Initial Value

An alternative version of the formula can be used for calculating return over multiple periods from an investment. It is useful for calculating returns over regular intervals, which could include annualized or quarterly returns. Here, t = number of years

Annualized HPR = [Income + (End of Period Value – Initial Value)/Initial Value+1] * 1/t_-1

Alternatively, returns for regular time intervals can be calculated thus:

(1 + HPR) = (1+r₁) x (1+r₂) x (1+r₃) x (1+r₄)

Here, r₁, r₂, r₃, r₄ are periodic returns.

It can also be represented thus:

HPR = [(1+r₁) x (1+r₂) x (1+r₃) x … (1+r_n)] – 1

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Here, r = return per period

n = number of periods

Basic Examples

You can download this Holding Period Return Excel Template here – Holding Period Return Excel Template

Suppose if an individual bought a stock which paid dividends of $50 and its price reached $170 from the initial price of $140 at which it was bought a year ago.

Now, we can calculate the HPR as follows:

HPR = [$50 + ($170 – $140)] / $140 = 57.14%

Now, we would try to calculate the annualized returns for the same stock over a period of 3 years. Let us suppose the stock paid dividends worth $50 each year, and returns varied with 21% growth for the first year, followed by 30% returns for the second year and -15% returns for the third year.

Now, we would calculate the annualized HPR as below:

HPR = [(1 + 0.21) x (1 + 0.30) x (1 – 0.15)] – 1
= [(1.21) x (1.30) x (0.85)] -1 = 33.70%
The result would be HPR of 33.71 for all 3 years.

The advantage of using this method is that it would help take into account the effect of compounding over the years, which would lead to a realistic outcome.

Interpretation

HPR can be used to calculate total returns for an investment for a single or multiple periods, including various forms of returns, which might be added improperly otherwise when calculating total returns. For instance, if someone holds a stock for a certain amount of time, and it pays dividends periodically, these dividends also need to be taken into account along with changes in stock prices. It would also require keeping in mind that a rise in the value of the investment during multiple periods of return leads to a compounding effect, which might be left out in simpler calculations.

For instance, if an investment grew by 10% annually, it would be erroneous to assume that in two years, the growth on initial value would be 20%. It has to be calculated, taking into account 10% growth for the first year and then calculating 10% growth over ‘this’ amount for the 2nd year, leading to a total return of 21.1% in two years, instead of 20%.

Relevance and Use of HPR Formula:

As we already explained, one of the key applications of the holding period return formula is inaccurately calculating the effect of compounding while estimating total returns on investment for multiple periods. Apart from that, it has great utility in comparing various investments held for different time intervals in terms of their total returns over these periods.

Calculator

You can use the following Calculator.

Income
End of Period Value
Initial Value
Holding Period Return Formula =

Holding Period Return Formula =

Income+

(End of Period Value − Initial Value)
	=
Initial Value

(0 − 0)
	=	0
0

Holding Period Return Formula in Excel (with excel template)

Let us now do the same example above in Excel. This is very simple. You need to provide the three inputs of Income, end of the period value, and initial value.

You can easily calculate the Holding Period in the template provided.