What you will learn
- Calculate drawdown and the gain needed to recover.
- Explain what value at risk shows and what it leaves out.
Drawdown and recovery
Drawdown is the fall from a previous peak to a later trough, measured as (trough - peak) ÷ peak. Maximum drawdown is the worst such fall in the sample, and time under water measures how long recovery took.
Recovery is asymmetric. After a fall of d, the gain needed to regain the peak is 1 ÷ (1 - d) - 1: 25% after a 20% fall, 100% after a 50% fall. Maximum drawdown depends on the sample period and may understate future declines.
Value at risk and its limits
Value at risk estimates a loss that should be exceeded on only a stated share of days, such as 5% for a 95% one-day figure. It can come from historical returns or from volatility under a normal assumption.
It says nothing about how large losses are beyond the threshold, and it relies on past data that may exclude crises. Fat tails and rising correlations make the worst days larger than a normal model suggests.
Stress scenarios
A stress test applies hypothetical shocks, such as equities falling 30% while correlations rise toward 1, and computes the portfolio loss. It needs no probability, so it can examine events outside the sample.
Scenarios reveal concentrations that volatility figures hide, such as many positions relying on one currency. Their weakness is that someone must imagine the shock, and real crises often surprise.
Worked example: Drawdown and recovery arithmetic
A fictional portfolio rises from 100 to a peak of 130, falls to 91, then recovers to 117. The drawdown is (91 - 130) ÷ 130 = -30.0%. Regaining 130 from 91 needs a gain of 130 ÷ 91 - 1 ≈ 42.9%. At 117 it is still 10.0% below the peak.
Check your understanding
A portfolio worth 500,000 has daily volatility of 1.5%. Using a normal assumption with zero mean and a 95% multiplier of 1.645, what is the one-day value at risk? What does it not tell you?
Show answer and explanation
Value at risk is 1.645 × 1.5% × 500,000 = 1.645 × 7,500 = 12,337.50. On roughly one day in twenty, losses could exceed that, but the figure sets no limit on how much more. It also assumes normal returns and stable volatility, which can fail in stress.