Another perspective on HPY (Annual returns)

Let’s use an example of a house. You bought a house 42 years ago for $10,000 and just sold it for $80,000.

If we use the standard way of calculating the HPR, your profit is %700. Woo Hoo! Hold on, what about the past 8 years? Didn’t you spend any money to eat?
HPR = 80,000 / 10,000 = 8.0
HPY = HPR - 1
= (8.0 -1) = 7.0 = 700%

The proper way of doing it is to do it below. Now, you’ve got a more reasonable number which is 5.08%. So, if you’re investments takes a long time, annualize them.

HPY = [(HPR)1/n - 1] x 100
= [(8.0)^1/42 - 1] x 100
= (1.050758 - 1) x 100
= (0.050758) x 100
= 5.08% Annually

Annual Holding Period Yield

Now we are getting to the nitty gritty details.

Previously, we were talking about Holding Period Return with no sense of the time factor. Now, we are going to put the time factor in with the Annual Holding Period Yield and the calculation is as below:

Annual HPY = Annual HPR - 1
Annual HPR = HPR to the power of (1/n)
Where n = number of years

Going from the previous example but with some minor modification. Let’s say that after investing $1, in two years, I get $1.50.

Therefore, HPR = 1.5/1 = 1.5
Annual HPR = HPR to the power of (1/n)
= 1.5 power (1/2)
= 1.224

Sorry for the confusion as I haven’t found out how to superscript in my computer.

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Annual Rate of Return

Continuing from the previous discussion, we will introduce a new variable called Holding Period Yield (HPY). Let’s say after investing $1 for a year, I get $1.5. Therefore HPR (Holding Period Return) is 1.5/1 = 1.5.
HPY = HPR -1
in this case
1.5-1
= 0.5
In percentage, Holding Period Yield is 50%

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