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You manage a broadly diversified fixed income portfolio. Your fund management mandate requires that you be fully invested always. That is, you cannot sell securities and simply sit on the cash you...

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You manage a broadly diversified fixed income portfolio. Your fund management mandate requires that you be fully invested always. That is, you cannot sell securities and simply sit on the cash you generate, nor do you have cash on hand to invest: the fund is now and must remain fully invested. You are also not permitted to take leveraged positions (i.e. you cannot borrow). Suppose you believe the yield curve is going to become steeper in the coming weeks, but you do not have any firm opinion on the question of if the overall yield curve will shift up or down. The portfolio you manage has positions in all 3 bonds listed above. A. Construct a trade using these 3 bonds that is largely insensitive to small parallel shifts in the yield curve, but will provide a profit if the yield curve becomes steeper. Assume you transact in 20 million (face value) of the 10-year bond. What position in the 2-year and 30-year bonds must you take? For each of the 3 bonds, state if you will buy or sell it and provide the correct par value amount needed to construct the trade. B. Suppose you do the trade you describe in part a). Immediately, the yield curve shifts upward, but not all yields move the same amount. Specifically, the yield on the 2-year rises to 1.60%, the yield on the 10-year rises to 2.20%, and the yield on the 30-year rises to 2.65%. In dollar terms, how much better or worse off is your portfolio for having done this trade (as opposed to having done nothing)?
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Before moving to the case, it is more significant that one should have idea of yield curve parallel and non-parallel shifts. Yield curve take on various shapes which has been historically observed from through various maturities treasury instrument. To be very precise, yield curve undergoes two types of shifts such as parallel shifts and non-parallel shifts. Following are the suitable explanation for both aforementioned shifts which are taken up by yield curve as follows: Parallel Shifts Figure 1: Under parallel shifts, yield curve goes under any of three directions mentioned above and rates for all maturities (interest rates) change by same amount and in same direction. Normal: When yield curve undergoes normal shift, then long term rates are more than short term rates which depict that the interest rate environment is going to be broaden. Under such scenario, interest rates (Discount Rates) for long maturity tend to be higher and in such case, bonds with shorter maturities tend to outperform the long maturity bonds in general circumstances. Flat: Under flat term structure, yield is same on almost all maturities and there is very little evidence of outperforming or underperforming either by shorter or longer maturity bond. Inverted: Under such scenario, long term rates are less than short term rates which depict that the interest rate environment is going to be narrower. Under such scenario, interest rates (Discount Rates) for long maturity tend to be lower and in such case, bonds with shorter maturities tend to underperform the long maturity bonds in general circumstances. Important Point: When the yield curve undergoes parallel shift, then yields on all maturities change in the same direction and by the same amount. Non-parallel Shifts Under non-parallel shifts, yield curve takes shape such that yields on all maturities change by different amounts. The yield curve would not remain the same as it was before the shift of the curve....

Answered Same Day Dec 27, 2021

Solution

Robert answered on Dec 27 2021
113 Votes
Consider the following 3 Government of Canada bond issues, all of which are standard semi-annual
coupon-paying bonds with bullet maturities. :
Nickname Coupon Maturity Date Quoted Yield
The 2-year 0.75% 1-Aug-2019
1.554%
(Settles 2-Oct-17)
The 10-year 1.00% 1-Jun-2027
2.142%
(Settles 2-Oct-17)
The 30-year 2.75% 1-Dec-2048
2.521%
(Settles 2-Oct-17)
You manage a
oadly diversified fixed income portfolio. Your fund management mandate requires that you be
fully invested always. That is, you cannot sell securities and simply sit on the...
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