Question

1. Which of the following is not the advantage of VaR?

It is easy to understand.

It shows the expected loss given that the loss is greater than the absolute VaR level.

It is the loss level that will not be exceeded with a certain probability.

It captures an important aspect of risk in a single number.

2.Which of the following bonds has the longest duration?

7-year, 7% coupon bond

7-year, 12% coupon bond

14-year, 7% coupon bond

14-year, 12% coupon bond

3.One investment project has a probability of 0.03 of a loss of $20 million and a probability of 0.97 of a loss of $2 million during a one-year period. What are the 95% VaR and expected shortfall (ES) for this project?

VaR = $2 million; ES = $20 million

VaR = $20 million; ES = $12.8 million

VaR = $2 million; ES = $12.8 million

VaR = $20 million; ES = $0.64 million

4.Suppose that you have a bond position worth $100 million. Your position has a modified duration of 8 years and a convexity of 150. By how much does the value of the position change if interest rates increase by 25 basis points?  Use the duration-convexity rule.

($1,953,125)

($1,906,250)

($2,046,875)

($2,187,500)

Answer 1

Solution 1) The correct option is B.

The other three options are advantages of the VaR, i.e.,

• It is easy to understand
• It is the loss level that will not be exceeded with a certain probability.
• It captures an important aspect of risk in a single number.

Solution 2) Duration is inversely related to the bond's coupon rate. while it is directly related with the time-to-maturity.

On the basis of maturity, 14 years bonds have more duration as compared to the 7 years bonds. Thus, options a and b will not have the highest duration.

Since lower coupon bonds have a longer duration, thus, 14 years 7% coupon bond will have the longest duration.

Thus, the correct option is (c).

Solution 4) Initial Portfolio value = $100 million = 100,000,000

% Change in the bond prices = -Modified Duration*Change in yield + 0.5*Convexity*(Change in yield)^2

% Change in the bond prices = -8*0.0025 + 0.5*150*(0.0025)^2

= -0.02 + 0.5*150*0.00000625

= -0.02 + 0.00046875

= -0.01953125

= -1.953125%

Hence, change in bond's portfolio = % Change in the bond prices*Initial Portfolio value

= -1.953125%*100,000,000

= -1,953,125

Hence, the correct option is (a)

Please post question 3 separately.