PQ-external Mean Reverting model of interest rate

[frmpart2dan]

Could someone help me with this question:

Q: The Bureau of Labor Statistics has just reported an unexpected short-term increase in high-priced luxury automobiles. What is the most likely anticipated impact on a mean-reverting model of interest rates?

A. The economic information is long-lived with a low mean-reversion parameter
B. The economic information is short-lived with a low mean-reversion parameter
C. The economic information is long-lived with a high mean reversion parameter
D. The economic information is short lived with a low mean reversion parameter

 

[David Harper CFA FRM]

Hi @frmpart2dan It's not a good question in my opinion (nor FRM typical). Note (B) and (D) are identical. What quantity reflects an"increase in high-priced luxury automobiles" reported by the BLS; is it price, quantity, employment? By elimination, that answer must be (A) because the other answers are inconsistent; i.e., the pair must be either long-lived news --> low mean reversion param, or short-lived news --> high mean reversion param. But it's a little murky as to how we'd infer that an unspecific increase in high-priced luxury automobiles implies a long- versus short-lived shock to the system; I feel like I could make either argument. Here is Tuckman (emphasis mine):

The implications of mean reversion for the term structure of volatility and factor shape may be better understood by reinterpreting the assumption that short rates tend toward a long-term goal. Assuming that short rates move as a result of some news or shock to the economic system, mean reversion implies that the effect of this shock eventually dissipates. After all, regardless of the shock, the short rate is assumed to arrive ultimately at the same long-term goal. Economic news is said to be long-lived if it changes the market’s view of the economy many years in the future. For example, news of a technological innovation that raises productivity would be a relatively long-lived shock to the system. Economic news is said to be short-lived if it changes the market’s view of the economy in the near but not far future. An example of this kind of shock might be news that retail sales were lower than expected due to excessively cold weather over the holiday season. In this interpretation, mean reversion measures the length of economic news in a term structure model. A very low mean reversion parameter, i.e., a very long half-life, implies that news is long-lived and that it will affect the short rate for many years to come. On the other hand, a very high mean reversion parameter, i.e., a very short half-life, implies that news is short-lived and that it affects the short rate for a relatively short period of time. In reality, of course, some news is short-lived while other news is long-lived, a feature captured by the multi-factor Gauss+ model presented in Chapter 11. -- "Tuckman, Bruce; Serrat, Angel. Fixed Income Securities: Tools for Today's Markets (Wiley Finance) (p. 272). Wiley. Kindle Edition."