Reading 24 - Question 11 - Money Duration VS Duration for a yield curve strategy

Dear all

i am a little confused with Question 11 of the reading. there maybe a misunderstanding from my side with regards to MD VS Money Duration

The Question is as follows:

Hirji reviews Canadian government bonds for a Malaysian institutional client. Prégent and Hirji expect changes in the curvature of the yield curve but are not sure whether curvature will increase or decrease. Hirji first analyzes positions that would profit from an increase in the curvature of the yield curve. The positions must be duration neutral, and the maximum position that the Malaysian client can take in long-term bonds is C$150 million. Hirji notes that interest rates have increased by 100 basis points over the past six months. Selected data for on-the-run Canadian government bonds are shown in Exhibit 2.

Exhibit 2. On-the-Run Canadian Government Bonds As of 1 July Maturity** YTM (%) Duration PVBP (C$ millions)** 2-year 1.73 1.97 197 5-year 2.01 4.78 478 10-year 2.55 8.89 889 Long-term 3.16 19.60 1,960

Based on Exhibit 2, the amount that Hirji should allocate to the 2-year bond position is closest to:

  1. C$331 million.
  2. C$615 million.
  3. C$1,492 million.

The answer i thought right is the following:

to have a Duration Neutral strategy, you will need to have the following pair of ptf:

  • Long 2y, short 5y => This couple will have a duration of (1.97 - 4.78) = -2.81years
  • Long LT, Short 10y => this couple wiill have a duration of 10.71

the maximum long position for LT Bonds is 150M hence

2 years position = 10.71 x 150M / 2.81 = 571M

The answer provided is the following:

C is correct. In order to take duration-neutral positions that will profit from an increase in the curvature of the yield curve, Hirji should structure a condor. This condor structure has the following positions: long the 2-year bonds, short the 5-year bonds, short the 10-year bonds, and long the long-term bonds. Hirji’s allocation to the 2-year bond position is calculated as follows:

The C$150 million long-term bonds have a money duration of C$150 × 1,960 = C$294,000

Allocation to 2-year bond = Money duration of long-term bonds/PVBP of 2-year bond

2-year bond position = C$294,000/197 = 1,492.39 or C$1,492 million

anyone know the answer? I am confusing why we need to calculate money duration of 10 years bond while question is asking 2 years bond.

The net money duration of the 2/5 position has to be the negative of the net money duration of the 10/LT position. 10.71 years × CAD 150M is the net money duration of the 10/LT position. So,

2.81\ years × 2/5\ amount = 10.71\ years × CAD\ 150M\\ \\ 2/5\ amount=\frac{10.71\ years × CAD\ 150M}{2.81\ years}

@S2000magician I’m going through this same question and I am having a hard time understanding the structuring assumption of the Condor. From the text “There is no single formula for allocating the funds to these positions—the relative weights of the two positions are discretionary.” Does it need to be structured such that the two longs are duration neutral, and the two shorts are duration neutral? I was under the impression that you structure the two long/short positions as duration neutral, but the answer seems to go against this?

Has anyone figure it out??? Is 571M the correct answer? I have not seen an erratum on that question.

The problem with this question is exactly this:

When I wrote my solution, I (naïvely, as it turns out) believed that they wanted the same value in the 2-year and 30-year bonds (which they call long bonds, but they’re clearly 30-year bonds), and the same value in the 5-year and 10-year bonds.

Apparently not.

Apparently they want the same money duration (technically, the same absolute money duration) in each position, so the amount of 2-year bonds you purchase will have a value roughly ten times that of the 30-year bonds you purchase.

The value is:

\frac{19.60\ years \times CAD\ 150M}{1.97\ years} = CAD\ 1,492,385,787