Calculate maximum drawdown for investment portfolios. Analyze downside risk with historical or simulated return data.
Maximum Drawdown Formula: MDD = max(Pi - Pj) / Pi
Where: Pi is the peak value, Pj is a subsequent trough value (j > i)
Maximum drawdown (MDD) is a key risk metric used in finance to measure the largest single drop from peak to trough in the value of an investment portfolio, before a new peak is achieved. It's expressed as a percentage of the peak value.
Mathematical Definition:
For a time series of portfolio values P0, P1, ..., Pn:
MDD = maxi ∈ (0,n) maxj ∈ (i,n) (Pi - Pj) / Pi
Where Pi is a peak value and Pj is a subsequent trough value.
Risk Assessment: MDD measures the worst-case loss an investor would have experienced if they invested at the worst possible time. It helps investors understand the downside risk of an investment.
Recovery Time: A large drawdown requires an even larger percentage gain to recover. For example, a 50% loss requires a 100% gain just to break even.
Strategy Comparison: Investors can compare the maximum drawdowns of different investment strategies to assess which has historically been less risky during market downturns.
| Maximum Drawdown | Risk Level | Typical Investments |
|---|---|---|
| 0% to -10% | Low Risk | Money market funds, short-term bonds |
| -10% to -20% | Moderate Risk | Balanced funds, dividend stocks |
| -20% to -35% | High Risk | Growth stocks, equity funds |
| -35% to -50% | Very High Risk | Small-cap stocks, sector funds |
| -50% or more | Extreme Risk | Leveraged investments, cryptocurrencies |
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