u/Ill-Let-8024

I prefer arbitrage-free models. Even though equilibrium models require fewer parameters to be estimated relative to arbitrage-free models, arbitrage-free models allow for time-varying parameters. In general, this allowance leads to arbitrage-free models being able to model the market yield curve more precisely than equilibrium models.

"A is correct. Consistent with Jones’s statement, equilibrium term structure models require fewer parameters to be estimated relative to arbitrage-free models, and arbitrage-free models allow for time-varying parameters. Consequently, arbitrage-free models can model the market yield curve more precisely than equilibrium models".

Arbitrage free models basically require to estimate only thetta and volatility, while equilibrium models require to estimate long-run equilibrium rate, speed of mean reversion and volatility. Is my literal interpretation of formulas incorrect, and there's some philosophical aspect to this?

The task:

“Consider a portfolio of zero-coupon bonds that mature at different times in the future. Changes in interest rates are not always parallel across maturities, so let’s analyze what happens as rates change across the yield curve. Let’s assume that the portfolio has sensitivities to factors as provided in Exhibit 3. The portfolio has equal weightings in each key rate duration and an effective duration of 4.7. I would like you to assess the impact on the return of the portfolio if rates rise evenly across the curve and also when the curve flattens but does not twist.”

Exhibit 3 Factor Movements per One Standard Deviation Shift and Portfolio Key Rate Durations

Year	5	10	30
Parallel	1	1	1
Steepness	1	0.5	–1
Curvature	0.5	0	1
Key rate curations	1.8	3.6	8.7

Supposedly correct answer:

a loss from changes in level and a loss from changes in steepness.

Correct Answer Feedback: 

Correct. A parallel shift of the yield curve would result in a loss across each key rate duration given a sensitivity of 1. For example, a 100 basis point (bp) parallel shift would generate an approximately 4.7% loss in value. A flattening of the yield curve in the long end would result in a loss given a sensitivity of –1. For example, a 100 bp decline in the 30-year key rate duration would result in a loss of approximately 2.9% (–100 × –1 × –8.7 × 0.333). There is no impact from curvature, since the curve did not “twist.”

So problem assumes level increase while the curve flattens, which means that long-term rates do not increase as much. Logically this would make me think that answer A should be right (I chose B for the wrong reasons).

Because flattening = less steepness, and less steepness = negative change in steepness. And negative change in steepness times negative sensitivity to steepness means gain, right? They even appeal to that -1 sensitivity in their commentary, but tell that it should produce loss.