## historical var

vandana.jain
Finance Junkie
Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### historical var

Hi,
I just want to ask which value should we take as a var in historical simulation like in this ques
Assume that a risk manager wants to calculate VAR for an S&P 500 futures contract using the historical simulation approach. The current price of the contract is 935 and the multiplier is 250. Given the historical price data shown below for the previous 300 days, what is the VAR of the position at 99% using the historical simulation methodology?
Returns: -6.1%, -6%, -5.9%, -5.7%, -5.5%, -5.1% …… 4.9%, 5%, 5.3%, 5.6%, 5.9%, 6%

here we used -5.9 which is third worse observation

but in Pristine Notes
we have question no 15 page no 522 where we used 6th value as a var out of 500 days at 99% confidence

which one is correct ?

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vandana.jain
Finance Junkie
Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### Re: historical var

Hi pristine,

praghavan039
Posts: 4
Joined: Tue Aug 14, 2012 3:59 pm

### Re: historical var

I think for the first question, we should user -5.7 instead of -5.9%... Because 99% of 300 is 297th data. So we expect VAR to go anything below -5.7%. There is a similar question in page 65 of VAR-I ppt.

swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Re: historical var

Hi,
I think, if we use 1% significance level with 300 data sets, then for calculating the historial VaR, we should arrange the data in an desending order & to choose last 1% of data, which is here 3 data set (as 300*1% = 3, such as -6.1%, -6% & -5.9% & to select highest among those i.e. -5.90%.
Please comment if i am wrong.

Regards
Swarnendu

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: historical var

There seems to be a lot of discussion and confusion on this topic, but as a matter of fact, all of you are correct. I’m referring to the core readings material (Allen, Boudoukh and Saunders, “Undertstanding Market, Credit, and Operational Risk” Chapter 2) in response to this question. When there is an infinitely large data set (for our case let’s take a sample size of 100,000), then the 95% VaR is straight forward. It is the 5,000th data sample. However, in most our questions, the sample sizes are small, and with fat tails, the fifth percentile is not so accurate.
They have added a small technical point where they said “an observation itself can be thought of as a random event with a probability mass centered where the observation is actually observation, with 50% of the weight to the left and 50% to the right.” What this means is in the example of 100 data samples, the 5th observation corresponds to the 4.5 percent. Hence to get the 95% VaR, you need to interpolate the 5th and 6th observation.
Hence, for the exam point of view, there can be two correct answers:
1) For 100 data sample, taking the 5th value for the 95% VaR
2) For 100 data samples, Interpolating the 5th and 6th values for the 95% VaR
I hope this helps!