J
James789
Member
I find the way value at risk is discussed in the notes and tested in previous examinations to be a bit strange.
VaR is intuitively simple. Take say a £1000 portfolio, have a distribution for the value of the portfolio value in 1 year, then compute the 5% (lower) tail value of this distribution, which gives a 'worst case' portfolio value. Then subtract this value from the initial £1000, which in this case gives the 1-year 95% VaR.
The first thing that doesn't seem quite right in the notes is the definition. We are given a formula the VaR 'of a continuous random variable' (which I don't think really makes sense in itself) as
VaR(X) = -t where P(X < t) = p
But if we are to take X (going back to the example above) as equal to the portfolio value in 1 year, t in this case would come out being the negative of the worst case portfolio value, and not the actual VaR value we want. We have to take X to be the return on the portfolio (in £), not the value of the portfolio, for this definition to make sense.
The mathematical definition above is applied in previous exam questions (e.g. April 2015 Q2) to a random variable representing a return distribution, giving a VaR that is a percentage. This also seems strange, because the VaR is then not a monetary value.
I also found a question (September 2016 Q1) where we are asked for the VaR of a Poisson distribution. The probabilities are simple to look up in the tables, the answer comes out to be -5. While this is consistent with the above mathematical definition, this again uses the idea of the 'VaR of a random variable', which I find a bit weird.
I think my gripe here is to do with how VaR is defined and used. The portfolio value example seems to make sense and is, I believe, the standard definition of VaR, but everything else seems to be various degrees of muddled.
VaR is intuitively simple. Take say a £1000 portfolio, have a distribution for the value of the portfolio value in 1 year, then compute the 5% (lower) tail value of this distribution, which gives a 'worst case' portfolio value. Then subtract this value from the initial £1000, which in this case gives the 1-year 95% VaR.
The first thing that doesn't seem quite right in the notes is the definition. We are given a formula the VaR 'of a continuous random variable' (which I don't think really makes sense in itself) as
VaR(X) = -t where P(X < t) = p
But if we are to take X (going back to the example above) as equal to the portfolio value in 1 year, t in this case would come out being the negative of the worst case portfolio value, and not the actual VaR value we want. We have to take X to be the return on the portfolio (in £), not the value of the portfolio, for this definition to make sense.
The mathematical definition above is applied in previous exam questions (e.g. April 2015 Q2) to a random variable representing a return distribution, giving a VaR that is a percentage. This also seems strange, because the VaR is then not a monetary value.
I also found a question (September 2016 Q1) where we are asked for the VaR of a Poisson distribution. The probabilities are simple to look up in the tables, the answer comes out to be -5. While this is consistent with the above mathematical definition, this again uses the idea of the 'VaR of a random variable', which I find a bit weird.
I think my gripe here is to do with how VaR is defined and used. The portfolio value example seems to make sense and is, I believe, the standard definition of VaR, but everything else seems to be various degrees of muddled.