Value at Risk

Value at Risk is a way of expressing a portfolio's risk as a single monetary figure: how much can be lost over a chosen period, such that a deeper drawdown remains a rare outcome. The estimate always comes with two parameters without which it cannot be read: the horizon (a day, a week, a month) and the confidence level. The same portfolio produces different VaR figures over a daily and a monthly horizon, so only estimates built on identical settings can be compared.

Where the figure comes from

VaR is calculated in several ways. The historical method takes the actual daily changes in portfolio value over a past period, ranks them from worst to best and cuts off the tail at the chosen probability; the cut-off point is the estimate. The parametric method assumes that returns are normally distributed and derives the answer from the portfolio's volatility, multiplied by a coefficient for the confidence level. The Monte Carlo method simulates a large number of scenarios from given parameters and examines the tail of the resulting distribution. For a portfolio of several securities, correlation plays the decisive role: as long as the assets do not move in step, the combined VaR is smaller than the sum of the individual ones, and that difference is the numerical measure of the benefit that diversification provides.

An example using the site's data

Historical VaR for a position in a single security is built directly from its series of daily changes — the same series shown on the one-year chart:

Take the daily changes over the year, sort them, cut off the worst tail and convert the relative change at the boundary into roubles at the current value of the position. The resulting amount is the daily VaR at the chosen confidence level.

Where VaR is misunderstood

The first substitution is treating VaR as a property of the security rather than of the position. It is a monetary amount: it grows with the size of the investment and rises sharply when leverage is used, even though the asset itself does not change.

The second is the unspoken assumption that the position can be closed at the market price within the calculation horizon. For illiquid securities this is not true: the actual time needed to exit is set by the liquidity horizon, and when it is longer, the estimate refers to a period over which the position could not in fact be sold.

The third is trusting the model in a regime that was absent from the sample. Historical VaR knows nothing of events that fell outside the calculation window, while parametric VaR understates the tail, because real return distributions have fatter tails than the normal one. This is model risk: the error comes not from the market but from the assumptions behind the calculation.