# Is there any relationship between investment return of a stock, for individual year (Yearly return) and multiple years (Overall annualized return)

currently, I'm calculating the return of a stock, for individual year and multiple years. I tend to answer the following question.

1. Return of a stock for end of year 2010 (Individual year)
2. Return of a stock for end of year 2011 (Individual year)
3. Return of a stock for beginning of year 2010 till end of year 2011 (Multiple years)

Assuming,

1. I purchase 1 unit of stock at 1st January 2010, at price $1 2. No further buy transaction & sell transaction in between, in beginning of year 2010 till end of year 2011 Here's my calculation ## Return for end of year 2010 (Stock price reach$2.5 at end of year)

Date            Price
01/01/2010      -$1.0 (Invest) 31/12/2010$2.5

XIRR([01/01/2010, 31/12/2010], [-1.0, 2.5]) = 1.506


## Return for end of year 2011 (Stock price reach $1.8 at end of year) We assume stock opening price at the beginning of year is$2.5.

Date            Price
01/01/2011      -$2.5 (Invest) 31/12/2011$1.8

XIRR([01/01/2011, 31/12/2011], [-2.5, 1.8]) = -0.2806


## Return for beginning of year 2010 till end of year 2011 (Multiple years)

Date            Price
01/01/2010      -$1.0 (Invest) 31/12/2011$1.8

XIRR([01/01/2010, 31/12/2011], [-1.0, 1.8]) = 0.3422


I was wondering, is there any relationship between 0.3422 (Return for multiple years) and 1.506 (Return for individual year), -0.2806 (Return for individual year).

Is there a way for me to derive 0.3422, based on value 1.506 & -0.2806 ?

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## 1 Answer

Are you sure the return for two years is 0.7214? It should be 0.3422 per year if you are using 31/12/2011, and 0.3416 if you are using 01/01/2012 as the end date.

Assuming the last number (because it makes for two full years, therefore easier to calculate), yes, there is a formula to derive it from the return of the individual years. It's the geometric average:

=SQRT((1+1.506) * (1-0.2806)) - 1

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Yup. I make a mistake on my last calculation. Thanks. I will then study on "geometric average" subject. –  Cheok Yan Cheng Jul 8 '14 at 16:58