You’ve observed the following returns on INTC Corporation’s stock over the past five years: -25%, -16%, -9%, 11%, and 18%. Answer Questions
average return on stock over five years : 9.6%
variance of returns: 0.04878
a) What is the standard deviation of returns over this period?
b)What range of returns would you expect to see 95% of the time?
c)What is the geometric average return on the stock over this five-year period?
a)Standard Deviation of the return =Square Root of Variance =SQRT(0.04878)=0.220862
Standard Deviation in percentage =22.0862%
b)As per 68-95-99.7 rule, Probability of range of returns between (Mean-2*Standard Deviation ) and (Mean+2*Standard Deviation) will be 95%
Hence , the lower bound of the range is( Mean-2*Standard Deviation )=9.6-(2*22.0862)=-34.5724%
The Upper bound of the range is( Mean+2*Standard Deviation )=9.6+(2*22.0862)=53.7724%
We can expect return in the range of -34.57% and 53.77%, 95% of the time (returns are rounded two two decimals.
c)Geometric Average Return of n period=R
(1+R)^n=((1+r1)*(1+r2)*.......(1+rn)
r1,r2 ,...rn are returns for period 1,2..n respectively.
In this case , returns of 5 periods are given
n=5, R=Geometric Average Return
(1+R)^5=(1-0.25)*(1-0.16)*(1-0.09)*(1+0.11)*(1+0.18)=0.75*0.84*0.91*1.11*1.18=0.750908
1+R=0.750908^(1/5)=0.944316
Geometric Average Return =R=0.944316-1=-0.05568
Geometric Average Return in percentage =-5.568%
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