An Approach to Assessing Yield Curve Strategies

Scenario Analysis

As described earlier, many factors can change the return of a fixed-income portfolio, including changes in the yield curve. These changes can involve the curve’s slope, level, shape, and underlying currencies. Scenario analysis refers to a set of tools used to measure the changes in multiple inputs into a fixed-income portfolio value, all happening simultaneously. For example, a manager may use scenario analysis to measure the impact of a curve that slopes upward, and simultaneously appreciates underlying currency. The scenario analysis would allow viewing the impact on the portfolio’s price under the new conditions without recalculating all of the offsetting effects one by one.

$$ \begin{align*} & \text{Expected } \Delta \% \text{ Bond Price} \\ & = (-\text{Mod Duration} \times \Delta \text{Yield}) + \left[ \frac {1}{2} \times \text{Convexity} \times (\Delta \text{Yield})^2) \right] \end{align*} $$

$$ \begin{array}{c|c|c}
\textbf{Maturity} & \textbf{ModDuration} & \textbf{Convexity} \\ \hline
2yr & 2.15 & 7.0 \\ \hline
5yr & 4.08 & 20.4 \\ \hline
10yr & 7.22 & 33.98
\end{array} $$

A manager considering scenario analysis could use the equation listed above in conjunction with the portfolio bond data to calculate a final portfolio value under two different circumstances, such as:

• A flattening of the yield curve (No change in the 2-year yield, a 50bp fall in the 5-year yield, and a 75bp fall in the 10-year yield.).
• A steepening of the yield curve (No change in the 2-year yield, a 50bp rise in the 5-year yield, and a 75bp rise in the 10-year yield.)

If the portfolio is a bullet portfolio, made up of all 5-year notes, the final portfolio would be calculated as:

Flattening of the yield curve:

$$ \begin{align*} & \text{Expected } \Delta \% \text{ Bond Price} \\ & = (-\text{Mod Duration} \times \Delta \text{Yield}) + \left[\frac{1}{2} \times \text{Convexity} \times (\Delta \text{Yield})^2)\right] \end{align*} $$

5-year Bonds:

$$ \begin{align*} (-4.08 \times -0.005) + \left[\frac {1}{2} \times 20.4 \times (-0.005)^2 \right] & = + = 0.0204 + 0.005202 \\ & = 2.5602\% \end{align*} $$

Steepening of the yield curve:

$$ \begin{align*}
(-4.08 \times 0.005) + \left[\frac{1}{2} \times 20.4 \times (0.005)^2 \right] & = + = -0.0244 + 0.005202 \\ & = -1.9198\% \end{align*} $$

Question

Based on the information in the provided table, what is the anticipated effect of a yield curve flattening on a portfolio consisting of equally-weighted 2-year and 10-year notes?

1. 5.51%.
2. 2.75%.
3. -3.15%.

Solution

The correct answer is B.

$$ \begin{array}{c|c|c}
\textbf{Maturity} & \textbf{ModDuration} & \textbf{Convexity} \\ \hline
2yr & 2.15 & 7.0 \\ \hline
10yr & 7.22 & 33.98
\end{array} $$

A flattening involves – (No change in 2-year yields, a 50bp fall in the 5-year yield, and a 75bp fall in the 10-year yield.)

$$ \begin{align*} & \text{Expected } \Delta \% \text{ Bond Price} \\ & = (-\text{Mod Duration} \times \Delta \text{Yield}) + \left[\frac{1}{2} \times \text{Convexity} \times (\Delta \text{Yield})^2)\right] \end{align*} $$

10-year Bonds

$$ \begin{align*} & (-7.22 \times -0.0075) + \left[ \frac{1}{2} \times 33.98 \times (-0.0075)^2 \right] \\ = & 0.05415 + 0.0009556875 \\ = & 5.51\% \end{align*} $$

Given the equal-weighted allocation of the portfolio between the 2-year and 10-year notes, the projected price adjustment will be the average of the changes in the 2-year and 10-year notes. As a result, the correct choice is B \(\left(\frac {5.51\%}{2} \right)\).

A is incorrect. The correct answer is B based on the above workings.

C is incorrect. It should be rejected since it implies an anticipated loss in the portfolio. This option contradicts the portfolio’s exposure, which involves either an unchanged rate in the 2-year portion or a decreasing rate in the 10-year portion. Thus, a positive portfolio change is to be expected, not a negative one.

Reading 21: Yield Curve Strategies

Los 21 (g) Evaluate the expected return and risks of a yield curve strategy