Arithmetic returns and end of period value

CFA General
#1

I have a specific question which is not directly related to the CFA curriculum but maybe could be solved with. As a law student I’m stuck with the terms arithmetic return, risk, monthly sharpe ratio, Geometric returns and the ending wealth (or the end of period wealth).

I will specify: if you look at the perfomance of the Global Stock Index between 1921-1996, you will find (according to the P. Jorion and W. N, Goetznmann’s article in The journal of Finance "Global Stock Markets in the Twentieth Century) that :

Arithmetic return is 5,48

Risk is 15,83

Monthly Sharpe is 0,0999

Geometric Return is 4,32

Ending wealth is 27,3.

My question is which formula you can use to know the ending wealth (27,3 US Dollar) over that period (75 years) if you know that in the beginning (December 1920) the investment consisted in 1 US dollar?

(additional information with the table was: Arithmetic return is obtrained from the monthly average multiplies by twelve; risk is monthly volatility multiplied by square root of twelve; Geometric return uses annual compounding; Ending wealth reports the final value of 1$ invested on December 1920 at the end of the sample.)

Thanks for your help.

#2

With this, you would want to use the geometric return figure in order to calculate terminal wealth, since the arithmetic return will not take into account the compounding effects.

I would calculate this with the given information as Terminal Wealth = $1 x ((1.0432)^75), but I am getting $23.85 as an answer, not $27.30.

I am wondering if there was a typo in either the book or in your posting? Because if it were really $23.70 instead of $27.30, I would probably say that was close enough with rounding discrepancies in the likely case the geometric return was rounded by the author.

#3

there is a similar table in Goetzmann - The Equity Risk premium. It’s in google books page 356 table 16.6

The footnote includes “measured in excess of the wholesales price index inflation”

(not adjusting for inflation, the ending wealth is probably higher than $50)