A stock has had returns of 19 percent, 16 percent, 14 percent, -13 percent, 17 percent, and 3 percent over the last six years. The arithmetic and geometric returns for the stock are ______ and _______, respectively
Arithmetic mean=Sum of observations/Number of observations
=(19%+16%+14%+(-13%)+17%+3%)/6=9.33%
Geometric mean=((1+r1)*(1+r2)+(1+r3)*...*(1+rn))^(1/n) -1
Here, r1 to rn refers to the returns from year 1 to year n
Here, geometric
mean=((1+19%)*(1+16%)*(1+14%)*(1-13%)*(1+17%)*(1+3%))^(1/6)
-1
=(1.649879176)^(1/6) -1
=1.087031235-1
=0.087031235 or 8.70% (Rounded to two decimal places)
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