Question

# Risk. Suppose you are evaluating the risk of 10 year US Treasury bonds. The returns from...

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)

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%