An analyst manages an active fixed-income fund that is benchmarked to the Bloomberg Barclays US Treasury Index. This index of US government bonds
currently has a modified portfolio duration of 7.25 and an average maturity of 8.5 years. The yield curve is upward-sloping and expected to remain unchanged.
Which of the following is the least attractive portfolio positioning strategy in a static curve environment?
A Purchasing a 10-year zero-coupon
bond with a yield of 2% and a price of 82.035
B Entering a pay-fixed, 30-year USD interest rate swap
C Purchasing a 20-year Treasury and financing it in the repo market
B is correct. The 30-year pay-fixed swap is a “short” duration position and
also results in negative carry (that is, the fixed rate paid would exceed MRR received) in an upward-sloping yield curve environment; therefore, it is the least attractive static curve strategy. In the case of a.), the manager enters a “buy-and-hold” strategy by purchasing the 10-year zero-coupon
bond and extends duration, which is equal to 9.80 = 10/1.02 since the Macaulay duration of a zero
equals its maturity, and ModDur = MacDur/(1+r) versus 7.25 for the index.
Under c.), the manager introduces leverage by purchasing a long-term bond and financing it at a lower short-term repo rate.
Could someone please explain this solution? I don´t get it 
Hi,
In a static yield environment, the difference between a 2 year fixed rate bond right now and the expectations of the future level of the same 2 year fixed rate bond is about nothing. And this relation doesn’t change with time. The curve is the same now and in 2 years. It means that floating rates are closed to fixed rates on the period.
When you enter a pay-fixed 30 year swap, you pay a fixed interest rate and received a floating rate based on a 30 year bond. It has a negative duration because if rates go down you paid something relatively more expensive (the fixed rate) than what you receive (the floating rate) NOW and you suffer from a decrease in rates when you should have profited from it, if you had been long duration (when rates go down price of the bond increase). Conversely if (floating) rates go up you will profit from this increase because you receive NOW the relatively higher rate (floating rate) compared with what you paid (fixed rate) when you should have suffered from this situation if you had been long duration (when rates go up price go down).
Hence in a static yield environment you would be better off riding down the yield curve by being long a bond whose price is negatively correlated with the yield curve shape (upward and static) more than your benchmark (8.5 vs 10 and 20) than being long a swap whose payoff is positively correlated with the yield curve shape.