VAR:FRM EXAM 1999—QUESTION 82: jorion

[[email protected]]

EXAMPLE 15.7: FRM EXAM 1999—QUESTION 82
BankLondon with substantial position in five-year AA-grade Eurobonds has
recently launched an initiative to calculate 10-day spread VAR. As a risk
manager for the Eurobond trading desk you have been asked to provide an
estimate for the AA-spread VAR. The extreme move used for the gilts yield is
40bp, and for the Eurobond yield is 50bp. These are based on the standard
deviation of absolute (not proportional) changes in yields. The correlation between
changes in the two is 89%. What is the extreme move for the spread?
a. 19.35bp
b. 14.95bp
c. 10bp
d. 23.24bp

Answer
d) VAR=
√40^2 + 50^2 − 2 × 40 × 50 × 0.89 = 23.24.
The negative sign is because the portfolio is exposed to a difference in yields.

My doubt is that : The formula used is that of portfolio variance right , where they have not used weights. But I dont undertnad why -ve sign is used?? .also extreme move for the spread means std deviation? why sqrt 10 is not multiplied??

 

[David Harper CFA FRM]

Hi snigdha - I never trust questions this old, too many errors and imprecisions (e.g., correlation is unitless 0.89 not 89%). The answer clearly calculates the standard deviation of the difference between two randoms, one with standard deviation of 40 bps and the other 50 bsp ... weights not needed because they are both effectively equally weighted ... scaling not needed because question is "What is the extreme move for the spread?" not "what is the 10-day VaR" ... Hope that helps, but i might not get trapped in questions like this (candidly)

David