Question

Calculate standard deviation

Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return, and a 10% chance of losing 3%. What is the standard deviation of this investment?

A.

8.43%

B.

5.14%

C.

9.29%

D.

7.59%

Expected return and volatility of a portfolio

An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 5%, and she puts 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively

A.

10%; 35%

B.

12%; 22.4%

C.

10%; 6.7%

D.

12%; 15.7%

You have the following rates of return for a risky portfolio for several recent years:

ans

If you invested $1,000 at the beginning of 2008, your investment at the end of 2011 would be worth ___________.

A.

$1,645.53

B.

$1,247.87

C.

$1,785.56

D.

$2,176.60

Answer 1

1)

p(x)	X	p(x) * X	p(x) * (X - Xi)^2
40%	15%	6.00%	0.00074
50%	10%	5.00%	0.00002
10%	-3%	-0.30%	0.00188
	Sum	10.70%	0.00264
		Std. Dev.	5.14%

Standard Deviation = Square of Variance

Variance = Sum of p(x) x (Xi - X)^2 = 40% x (15% - 10.7%)^2 + 50% x (10% - 10.7%)^2 + 10% x (-3% - 10.7%)^2 = 0.00264

Standard Deviation = (0.00264)^(1/2) = 5.14%

2) Expected Return = 70% x 15% + 30% x 5% = 12%

Variance = 70% x 5% = 3.5%

Std. Dev. = 3.5%^0.5 = 18.7%

Hence, D appears plausible.