Question

1. A stock has the following returns over the past 5 years: 18%, 37%, 10%, -12%, 22%.

The sample standard deviation is:

		15.00%
		36.00%
		18.00%
		38.07%
		16.10%
		0%

2. A stock has an average HPR of 7.5% and a standard deviation of returns of 25%. What are the two next most typical returns an investor may expect?

		0%, 7.5%
		-17.5%, 32.5%
		17.5%, 32.5%
		-42.5%, 57.5%
		7.5%, 25%

3. A sample of asset returns has 7 observations (N=7). Percent expressions are used to calculate the sum of the squared differences from the mean equal to 9,780. Dividing this number by N-1, 9,780/6 = 1,630. Based on this information, the variance of returns is:

		9,780
		1,630
		40.37
		0.163
		0.4037
		Cannot determine from the information provided

Answer 1

1.

Year	GR(%)	AR(%)	(GR-AR)	(GR-AR)^2
1	18	15	3	9
2	37	15	22	484
3	10	15	-5	25
4	-12	15	-27	729
5	22	15	7	49
TOTAL	75		TOTAL	1296
	Average return (AR) = 75/5 = 15%
	Standard deviation = square root of (1296/5) = 16.10%

2.

Since standard deviation is 25% so HPR i.e. 7.5% either will increase or decrease by 25%

So two next most typical returns an investor may expect :

(a) 7.5% + 25% = 32.5%

(b) 7.5% - 25% = -17.5%

So answer is -17.5% , 32.5%

3. Variance = sum of the squared differences from the mean equal to 9,780 divided by (N - 1)

so Variance = 9780 / 7 -1 = 1630