Question

question 2

1) An asset had returns of +20 % , + 18 % , +13 % , -7 %, + 2% , and + 8% over the previous six years. What is the standard deviation of this asset over the past six years? i) 10.24% ii) 9.35% ii) 1.05% iv) 13.21% 2) Based on Q1 above and a normal curve distribution, what is your estimate for the expected return for next yea (with a 95% confidence that the asset will fall within your range)? Because this is multiple choice, please use t z-score of 1.96 for your answer. iii)-11.1% to 29.1% iv) -7.0% to 20.0% ii) -11.5% to 28.7% i) -9.3% to 27.3%

Answer 1

a. Standard deviation = square root of (variance)

variance = (difference between return and mean return) ^ 2/ (no of observations -1)

mean return = sum of the return / no of observations

using this formulas for the given return values,

yrs	returns	square of differences
1	0.2	0.0121
2	0.18	0.0081
3	0.13	0.0016
4	-0.07	0.0256
5	0.02	0.0049
6	0.08	0.0001
mean return	0.09

the standard deviation = 0.102372.

b. for normal distribution, z = (expected value - mean )/standard deviation , using z value , we find the % of confidence interval for expected value. here its is mentioned that 95% of confidence interval and also mentioned z value.

expected value = z*standard deviation + mean value = 1.96*0.102372+0.09 = 0.29064 = 29.064%