The following questions refer to this graph.
1. Compute the duration and modified duration of each of the four bonds. If each bond'syield to maturity immediately increases by 1 percentage point, approximately how many dollars willeach price decline? (For the coupon bond, use the no-arbitrage price computed in 3.)Hint: Use the approximations of bond value changes based on duration.
a) Bond #1:‐1.91%; Bond #2: ‐2.89%; Bond #3: : ‐0.96%; Bond #4: ‐1.87%
b ) Bond #1: ‐1.91%; Bond #2: ‐2.89%; Bond #3: ‐1.87%; Bond #4: ‐0.96%
c) Bond #1: ‐0.96%; Bond #2: ‐1.91%; Bond #3: ‐2.89%; Bond #4 : ‐1.87%
2.
Suppose that you believe that the 1-year interest rate will be 4% in one year from now (based
on your views on central bank policy). What trade would you consider as a result of the difference between your view and the forward rate?
Question 6 options:
a) You go long one 2-year zero-coupon bond. You finance this by shorting 0.95 1-year bonds.
b ) You go long one 1-year zero-coupon bond. You finance this by shorting 0.95 2-year bonds.
3. What is your profit or loss (change in the value of your butterfly strategy, which is a portfolio with the three bonds) if the yields of the three zero-coupon bonds immediately change to 4.82%, 4.87%, and 4.92%? Hint: Use the approximations of bond value changes based on duration.
a) -$0.5
b) $0.5
c) $1.28
d) -$1.28
4. What is average of the yields of the 1-year and 3-year zero-coupon bonds? Suppose that you view the 2-year interest rate as abnormally high relative to this average. Your view that the 2-year rate is too high is supported by information that several pension funds and banks have been forced to sell large positions of 2-year bonds, pushing down the price, hopefully only temporarily.
Structure a long-short trade between 1, 2, and 3-year zero coupon bonds which reflects thisview while being relatively immune to changes in the level of yield curve (i.e., the modifiedduration of long side is equal to that of the short side) and relatively immune to changes in theslope of yield curve. Specifically, go long one 2-year bond and decide on your positions in 1-yearand 3-year bonds. Hint: as discussed in the book, you can try having a dollar duration in each"wing" bond that is equal to half the dollar duration of the "body" bond. For instance, with positions (thenumber of bonds) denoted by x, prices by P, modified duration by
, and bonds indicated by
their maturity (1, 2, or 3), we have
and
and
can be computed from the following equations:
Which are the positions in the "wings" of the butterfly?
a) Long 0.94 1‐year bonds and 0.34 3‐year bonds
b) Long 0.34 1‐year bonds and 0.94 3‐year bonds
c) Short 0.94 1‐year bonds and 0.34 3‐year bonds
d) Short 0.34 1‐year bonds and 0.94 3‐year bonds