VAR

[intuitive]

Q1) You are the risk manager of a fund. You are using the historical method to estimate VaR. You find that the worst 10 daily returns for the fund over the period of last 100 trading days are -1%, -0.3%, -0.6%, -0.2%, -2.7%, -0.7%, -2.9%, 0.1%, -1.1%, -3.0%. What is the daily VaR for the portfolio for 95% confidence level?

Q2)Rational Investment Inc. is estimating a daily VaR for its fixed income portfolio currently valued at $800 million. Using returns for the last 400 days (ordered in decreasing order from highest daily return to lowest daily return), the daily returns are as follows: 1.99%, 1.89%, 1.88%. 1.87%.............-1.76%, -1.82%, -1.84%, - 1.87%, -1.91%.
At 99% confidence level what is your estimate of daily dollar VaR using the historical simulation?
Need Help to solve this.

 

[ShaktiRathore]

Hi,
1)First arrange the returns from worst to best i.e. in ascending order,
-3.0%, -2.9%, -2.7%, -1.1%,-1%,, -0.7%, -0.6%,-0.3%, -0.2%, 0.1%,
now according to Dowd the [(1-CL)*n+1]th worst return is the Var for n observations at confidence level CL. Here CL=95% and n=100 therefore (1-.95)*100+1=6th highest worst return is the Var which is nothing but -.7%. we need to identify a return observation such that 5% of the returns lies to the left of Var return observation so that if we select 6th worst return then 5/100=5% of area/observations lies to its left.
2)here CL=99% so that [(1-.99)*400+1]th observation or 5th highest worst return should be the Var. Which is -1.76% hence dollar Var is $-1.76%*800= -$14.08 which is the answer.
Correct me if any of the anwsers above is wrong.(you can also use (1-CL)*n for arriving at Var but that's not used here, i used the Dowd approach)
thanks

 

[David Harper CFA FRM]

I agree, of course, with ShaktiRathore. Please note his comment about "you can also use (1-CL)*n." This is true, such that each question has two valid answers (actually more ...). In the case of the first question:

• Historically the FRM (GARP) would return -1.0% as the correct answer (i.e., the 5th worst) because, eg, this is Jorion's approach;
• But more recently, due to Dowd's approach (Dowd, after all, is the syllabus assignment), [(1-CL)*n+1]th , GARP is fully aware that -0.7% (as the 6th worth) is also correct. fwiw, I think this is the better approach b/c it locates the 5% (5/100) of outcomes "cleanly" in the outside region (tail).