Mean Reversion of Interest rates

[notjusttp]

Pls consider the following question

The monthly VaR of a fixed income portfolio of treasuries is $1,000,000 and you believe that the Vasicek interest-rate model offers a good representation of the evolution of interest rates. The annual VaR is:
Choose one answer. a. Likely to be higher than (12)½ × $1,000,000
b. Likely to be lower than (12)½ × $1,000,000
c. Correctly estimated to be (12)½ × $1,000,000
d. Correctly estimated to be $12,000,000

The correct answer is: Likely to be lower than (12)½ × $1,000,000.

This is due to mean reversion in interest rates.

Doubt

1) What do you mean by mean reversion in interest rates?

2) Usually we take the Monthly VAR and multiply by root of 12. How would we know in exam when to not solve in this way?

Thanks & Rgds :roll:

 

[David Harper CFA FRM]

Hi notjusttp,

Same logic as with the other question. Scaling with square root assumes i.i.d.

Although mean reversion has a few definitions, for exam purposes, we can think of mean reversion as negative autocorrelation; i.e., a positive return is likely to be followed by a negative return. (Note this is different than mean reversion term in GARCH!).
This is a sort of "gravitation pull" which dampens the "diffusion" of the scaling...

...and, again, perhaps playing with this XLS will give a good sense:
http://www.bionicturtle.com/premium/spreadsheet/1.a.1._intro_to_var/
if you make the autocorrelation positive (>0), cell c9, the scaled VaR will be greater than the i.i.d. VaR, and
if you make the autocorrelation negative (<0), you simulate this "mean reversion in returns", and the scaled VaR will be less than the i.i.d. VaR, and

Exam point:
* As Linda Allen shows, we can refer to (at least) two different meanings of mean reversion:
1. As in GARCH(1,1), mean reversion toward a long-run average variance, or
2. Mean-reversion between returns over time, which is negative autocorrelation (some refer to this as "mean reversion in asset dynamics").

GARCH(1,1) is a good example of (i) mean-reverting toward a long run variance, but (ii) not mean reverting in regard to asset dynamics

David

 

[notjusttp]

Hi david,

Thanks this is crystal clear due to your link on mean reversion and due to the playing in the excel..Hope GARP allows us to take your excel sheet in exam and we would all come with flying colours... ;-P