Question

1. Risk. Suppose you are evaluating the risk of 10 year US Treasury bonds. The returns from the previous five years are listed below.

Year	2011	2012	2013	2014	2015
10−Yr T−Bond’s Return	16.04%	2.97%	−9.10%	10.75%	1.28%

1. Calculate the average annual return. (5 points)
2. Calculate the variance of returns. (5 points)
3. Calculate the volatility of returns. (10 points)
4. Calculate the range of values we can be 95% sure returns will fall within. (5 points)

Answer 1

a

	T bond
2011	16.04%
2012	2.97%
2013	-9.10%
2014	10.75%
2015	1.28%
Average=	4.39%

Average or Mean = Sum of all observations/Count of all observations

b

Sample Variance =((∑k=1 to N (observationk – average))/(N-1))

Variance=

0.009246

c

Sample Standard deviation =((∑k=1 to N (observationk – average))/(N-1))^(1/2)

Standard dev=

9.62%

d

As per 95% rule

range = average+/- 2 std dev

= 4.39+/-2*9.62

=4.39-2*9.62 to 4.39+2*9.62

=-14.85% to 23.63%