HPY for multiple years product, multiple, correct

bluejazzy

Hi,

On page 318 in Volume IV, the three year HPY for three annual returns is calculated as R=(1+R1)*(1+R2)*(1+R3)-1

where R1,R2,R3 are the three annual returns.

Is this formula correct? I was thinking that the product of the returns should be raised to (1/3) to calculate it correctly.

Please help if you know the answer! Thanks.

lunarfollies

The book is correct. Taking the (1/nth ) root gives you the CAGR. For example, if you have $100 and it grows by 10% to $110 in year one and 10% again in year two to $121, your HPY is (1+10%)*(1+10%)-1 = 21%, which is correct. Since (121-100)/100 = 21%

If you take ((1+10%)*(1+10%))^.5-1, that gives you 10% which is just the CAGR.

I answered my own question. Hope it helped clarify this for others who were wondering as well.