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07 · Measuring risk

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Portfolio and Risk, lesson 7

Measuring risk

Volatility, VaR, expected shortfall and drawdown.

Volatility from Risk and return, and quantiles from Probability: the value below which a given share of outcomes falls.

Part 1. A bad day, in dollars

Ten thousand simulated days of profit and loss on a $10m book. Find the loss that only the worst days go past.

How bad is a bad day?Live

The cut-off tells you how bad a bad day is, and nothing about the days past it. Fat tails moved the cut-off a little and made the days beyond it much worse. Only the average of those days caught that.

Value at risk and expected shortfall

The loss that only 1% of days go past is the 99% one-day value at risk, or VaR. The average loss on those worst 1% of days is the 99% expected shortfall, or ES. VaR is a quantile; expected shortfall is the average beyond it.

Your turn

A desk's 99% one-day VaR is $2m. Which statement is right?

VaR is a threshold, not a worst case. On the 1% of days beyond it the loss can be any size, and VaR says nothing about how large.

Part 2. VaR from volatility

Keep going with Pro

You've done the first part. Pro opens the rest of this lesson, and every other one.

Still to come
  1. VaR from volatility
  2. A worked problem
  3. Falls from a peak
  4. The same thing, for real
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Next lessonEstimating covarianceNoisy estimates and why shrinkage helps. Start lesson 8

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