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What is the most I can lose on this investment?

This is a question that almost every investor who has invested or is considering investing in a risky asset asks at some point in time. Value at Risk tries to provide an answer, at least within a reasonable bound. It gives the likelihood that a portfolio will suffer a large loss in some period of time, or the maximum amount that you are likely to lose with some probability (say, 99%).

It finds this by:

  1. Looking at historical data about asset price changes and correlations
  2. Using that data to estimate the probability distributions of those asset prices and correlations
  3. Using those estimated distributions to calculate the maximum amount you will lose 99% of the time.

But things are not as simple as that. Real markets don’t go by statistics or rules of probability. You must read this article by Joe Nocera which talks about VaR in light of the sub-prime mortgage crisis.

Here is an interesting excerpt:

"At the height of the bubble, there was so much money to be made that any firm that pulled back because it was nervous about risk would forsake huge short-term gains and lose out to less cautious rivals. The fact that VaR didn’t measure the possibility of an extreme event was a blessing to the executives. It made black swans [unlikely events] all the easier to ignore. All the incentives, profits, compensation, glory; even job security went in the direction of taking on more and more risk, even if you half suspected it would end badly. After all, it would end badly for everyone else too."

So, here is what’s wrong with the approach:

  • There is a tendency to assume normal distributions, and thus a low probability of extremes. Reality is that financial returns are more skewed than normality suggests – excessively high and low return days are far more common than would be expected.
  • There is often an assumption that history repeats itself, or, the past can predict the future.
  • VaR does not describe the losses in the extreme left of the distribution. (Conditional VaR can help to measure the expected loss, given the loss exceeds VaR)
  • VaR does not distinguish portfolio liquidity; very different portfolios can have the same VaR i.e. VaR is a static measure of risk and does not capture the dynamics of possible losses if a portfolio were to be unwound
  • Computations can be very complex; there is model risk; precision should not be assumed
  • VaR-constrained traders can game the system i.e. maximize risk subject to keeping VaR steady. The game repeats itself at several levels; and can trigger an avalanche, because everyone misjudges risk in the same way.

Is VaR the Right Methodology?

In many situations, VaR may not be the correct risk-management methodology. If we pick a specific loss such as $1 million, VaR allows us to estimate how often we can expect to experience this particular loss. For example, using VaR we might estimate that we will lose at least $1 million on one trading day in 20, on average. During some 20-day periods, we might lose less than $1 million. During other 20-day periods, we might lose more than $1 million on more than one day. VaR tells us how often we can expect to experience particular losses. It doesn’t tell us how large those losses are likely to be.

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