Interepreting VAR

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johntavv

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An example for interpreting VAR reads:
A $100m portfolio has a 1.37% VAR at the 5% probability over one week.
So there is a 5% chance that more than $1.37m will be lost and a 95% chance that less than this will be lost.
Similarly, at the 1% VAR, there is a 1% chance that more than $1.37m will be lost and a 99% chance that less will be lost.
The text says: a 1% VAR would be expected to show greater risk than a 5% VAR.
But at 1% VAR, doesn’t it mean there is lower probability (compared to 5% VAR) of greater losses? Why does the 1% VAR show greater risk?
 
johntavv wrote:
The text says: a 1% VAR would be expected to show greater risk than a 5% VAR.
Click to expand...
Interesting question.
i THINK what it’s saying is the odds (risk) losing 5m of value is lower than the odds of losing $1m.
 
You’re reading it wrong. It’s saying the VAR is greater at 1% probability than the VAR at 5% probability.
 
Here’s the sort of thing you would see:
  • 20% VAR = $0.1 million
  • 10% VAR = $0.8 million
  • 5% VAR = $1.37 million
  • 1% VAR = $8.2 million
All they’re saying is that the 1% number ($8.2 million) is bigger than the 5% number ($1.37 million).
 
Why is the loss at 1% VAR higher than at 5% VAR?
5% chance of a loss is a higher probability than a 1% chance of a loss, so not clear on this concept…
 
You have to think about 1% as the outliers or Balck swan events in the tail.
 
johntavv wrote:Why is the loss at 1% VAR higher than at 5% VAR?
5% chance of a loss is a higher probability than a 1% chance of a loss, so not clear on this concept…
Click to expand...
Here are the possible outcomes for 100 weeks of an investment:
  • You lose $8.2 million 1 week
  • You lose $5 million 3 weeks
  • You lose $1.37 million 1 week
  • You lose $1.1 million 4 weeks
  • You lose $0.8 million 1 week
  • You lose $0.7 million 3 weeks
  • You lose $0.3 million 5 weeks
  • You lose $0.1 million 2 weeks
  • You break even 15 weeks
  • You gain $0.1 million 25 weeks
  • You gain $1 million 40 weeks
What’s your 1% 1-week VAR?
$8.2 million: 1% of the time you’ll lose $8.2 million or more.
What’s your 5% 1-week VAR?
$1.37 million: 5% of the time you’ll lose $1.37 million or more.
And so on.
(These numbers are consistent with the VARs I gave a few posts above.)
 
What I do is picture the bell curve in my head of possible returns. VAR is just saying in the worst X% of outcomes your loss will be Y.
The “X” would be the shaded in area under the curve. The Y would be the return.
If you can still picture that bell curve, moving to a smaller and smaller cumulative distribution (the more extremem of a number you would get (in my head it’s on the left side)
 
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