Question

A stock has had returns of 9 percent, 10 percent, 22 percent, -12 percent, and 25...

A stock has had returns of 9 percent, 10 percent, 22 percent, -12 percent, and 25 percent over the last five years.

1, What is the geometric return for the stock?

2. What is the standard deviation of this stock?

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Answer #1

Average return=Total return/Total time period

=(9+10+22-12+25)/5=10.8%

Return (Return-Average return)^2
9 (9-10.8)^2=3.24
10 (10-10.8)^2=0.64
22 (22-10.8)^2=125.44
-12 (-12-10.8)^2=519.84
25 (25-10.8)^2=201.64
Total=850.8%

Standard deviation=[Total (Return-Average return)^2/(Time period-1)]^(1/2)

=[850.8/(5-1)]^(1/2)

=[850.8/4]^(1/2)

=14.58%(Approx)

Geometric return=[(1+rate 1)(1+rate 2)(1+rate 3)(1+rate 4)(1+rate 5)]^(1/5)-1

=[(1+0.09)(1+0.1)(1+0.22)(1-0.12)(1+0.25)]^(1/5)-1

=9.98%(Approx).

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