The Following Information Relates to Questions
Sanober Hirji Is

question 19

Multiple Choice

The following information relates to Questions
Sanober hirji is a junior analyst with Northco Securities, which is based in canada. Theinstitutional clients of Northco are active investors in canadian coupon-bearing government
bonds. client portfolios are benchmarked to a canadian government bond index, which is a
diverse maturity index portfolio. after reviewing the portfolio of a French institutional client,hirji evaluates yield curve strategies for canadian government bond portfolios under various interest rate scenarios. hirji's supervisor, Éliane Prégent, forecasts that canadian long-term rates will rise and short-term rates will fall over the next 12 months. Northco's chief economist forecasts that canadian interest rates will increase or decrease by 100 basis points over the next 12 months. based on the chief economist's forecast, hirji suggests increasing the convexity of the French institutional client's portfolio by selling 10- year bonds and investing the proceeds in a duration-matched barbell position of canadian government 3-year and long-term bonds. She notes that the duration of the 10-year bonds,
along with the durations of the other portfolio bonds, aligns the portfolio's effective duration with that of the benchmark. Selected data on canadian government bonds are presented inexhibit 1. $$\begin{array}{l}\text { EXHIBIT } 1 \text { Canadian Government Bonds as of } 1 \text { January }\\\begin{array} { l c c } \hline \text { Security } & \text { Effective Duration } & \text { Effective Convexity } \\\hline \text { 1-year } & 0.99 & 0.007 \\\text { 3-year } & 2.88 & 0.118 \\\text { 10-year } & 9.51 & 0.701 \\\text { Long-term } & 21.30 & 2.912 \\\hline\end{array}\end{array}$$ * There is no single convention for how convexity numbers are
presented; for example, bloomberg has historically followed a
convention of dividing the "raw" convexity number by 100
(as presented here) . however, it is important to use the raw
convexity number when estimating returns.
hirji then considers a strategy to sell some long-term bonds from the French institutional
client's portfolio and purchase short maturity at-the-money options on long-term bond fu-
tures. The portfolio's duration would remain unchanged. Prégent asks:
"how would portfolio performance be affected by this strategy if the yield curve were
to remain stable?"
hirji also proposes the following duration-neutral trades for the French institutional client:
• long/short trade on 1-year and 3-year canadian government bonds
• Short/long trade on 10-year and long-term canadian government bonds
Six months later, 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. Se-
lected data for on-the-run canadian government bonds are shown in exhibit 2. $$\begin{array}{l}\text { EXHIВГ } 2 \text { On-the-Run Canadian Government Bonds as of } 1 \text { July }\\\begin{array} { l c c c } \text { Maturity } & \text { YTM } ( \% ) & \text { Duration } & \text { PVBP } ( C \$ \text { million) } \\\hline \text { 2-year } & 1.73 & 1.97 & 197 \\\text { 5-year } & 2.01 & 4.78 & 478 \\\text { 10-year } & 2.55 & 8.89 & 889 \\\text { Long-term } & 3.16 & 19.60 & 1,960 \\\hline\end{array}\end{array}$$ hirji then considers the scenario where the yield curve will lose curvature for the Malay-
sian institutional client. She notes that a 7-year canadian government bond is also available
in the market. hirji proposes a duration-neutral portfolio comprised of 47% in 5-year bonds
and 53% in 7-year bonds.
Finally, hirji uses the components of expected returns to compare the performance of a
bullet portfolio and a barbell portfolio for a british institutional client. characteristics of these
portfolios are shown in exhibit 3. $\begin{array}{l}\text { EXHIBIT } 3 \text { Characteristics of Bullet and Barbell Portfolios }\\\begin{array} { l c c } \hline & \text { Bullet Portfolio } & \text { Barbell Portfolio } \\\hline \text { Investment horizon (years) } & 1.0 & 1.0 \\\text { Average annual coupon rate for portfolio } & 1.86 \% & 1.84 \% \\\text { Average beginning bond price for portfolio } & \mathrm { C } \$ 100.00 & \mathrm { C } \$ 100.00 \\\begin{array} { l } \text { Average ending bond price for portfolio } \\\text { (assuming rolldown and stable yield curve) }\end{array} & \mathrm { C } \$ 100.38 & \mathrm { C } \$ 100.46 \\\text { Current modified duration for portfolio } & 4.96 & 4.92 \\\begin{array} { l } \text { Expected effective duration for portfolio } \\\text { (at the horizon) }\end{array} & 4.12 & 4.12 \\\begin{array} { l } \text { Expected convexity for portfolio } \\\text { (at the horizon) }\end{array} & 14.68 & 24.98 \\\text { Expected change in government yield curve } & - 0.55 \% & - 0.55 \% \\\hline\end{array}\end{array}$
-The answer to Prégent's question is that the portfolio would most likely experience:

• A) a loss.
• B) no change.
• C) a gain.

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