📊 Risk Metrics
Risk metrics provide quantitative measures of portfolio risk. Each metric captures a different aspect of uncertainty, and no single metric tells the whole story. Using multiple metrics together gives a comprehensive view of portfolio risk.
🧭 The Four Questions
Every page in this section exists to answer one of four questions. A metric earns its place by answering one of them; two cross-cutting pages explain how the answers are computed and how far they can be trusted. The two tables further down compare the four best-known of these metrics side by side and suggest when to reach for each.
📉 How Much Can It Hurt?
| Metric |
What it answers |
| Max Drawdown |
The largest peak-to-trough decline before a new peak — the worst loss an investor would actually have lived through. |
| Current Drawdown |
How far below its own historical peak a portfolio stands right now, as opposed to the worst fall it ever suffered. |
| Drawdown at Risk |
Drawdown at Risk applies the quantile idea to drawdowns rather than to returns: it is the drawdown depth that should not be exceeded at a chosen confidence level. |
| Conditional Drawdown at Risk |
Conditional Drawdown at Risk averages the drawdowns that did breach the Drawdown at Risk threshold, answering how deep the fall goes once it goes past that point. |
| Ulcer Index |
The Ulcer Index combines how deep a portfolio falls with how long it stays down, so a shallow decline that persists can score worse than a sharp one that recovers quickly. |
| Value at Risk |
A deliberately narrow question: over a given horizon and at a chosen confidence level, what is the loss that should not be exceeded? |
| Conditional Value at Risk |
Takes over exactly where Value at Risk stops: the average loss in the cases where the Value at Risk threshold was in fact breached. |
| Worst Realization |
The least favourable single-period return actually observed in the available history — an observed fact rather than an estimate. |
The first five read the path the portfolio actually took; the last three read the distribution of its returns. Shuffle the order of those returns and the last three are unchanged, while the first five can change completely.
🧩 Am I Diversified?
| Metric |
What it answers |
| Correlation |
How holdings move in relation to one another, which is why diversification depends on how positions behave together rather than on how many of them there are. |
| Risk Contribution |
How total portfolio risk is attributed back to the individual holdings — what each position contributes is generally not the same as how much of the portfolio it represents. |
| Concentration |
How far a portfolio's weight is gathered into a few positions, giving a reading that a plain count of holdings cannot provide. |
⚖️ Am I Paid for the Risk?
| Metric |
What it answers |
| Volatility |
The dispersion of returns — how much value fluctuates, and the building block of nearly every other risk metric. |
| Sharpe Ratio |
How much excess return was earned per unit of total volatility. |
| Sortino Ratio |
The same comparison, with only downside volatility in the denominator. |
| Beta & Active Return |
How strongly a portfolio tends to follow its benchmark, and which part of the result the benchmark does not explain. |
| Benchmark Selection |
Every benchmark-relative figure inherits the benchmark it was measured against, so the choice of comparison is itself part of the verdict. |
🎲 What If…?
| Metric |
What it answers |
| Historical Replay |
What the movements of a real past episode would do to the portfolio as it is composed today. |
| Hypothetical Shock |
Replaces the historical episode with a chosen one, which makes it possible to test a scenario that the available history never contained. |
| Simulation Modes |
Each mode rests on its own assumptions, and those assumptions determine as much what its results cannot say as what they can. |
🔧 Method
| Page |
What it answers |
| Observed Annualization |
How a per-period figure becomes an annual one, with the number of periods in a year measured from the data instead of assumed in advance. |
| Data Quality |
A risk figure is only as trustworthy as the observations behind it, so the amount and freshness of the underlying data belong to the reading of the result. |
📋 Comparative Overview
| Metric |
What It Measures |
Formula |
Range |
Details |
| Sharpe Ratio |
Risk-adjusted return (total vol) |
\(\frac{R_p - R_f}{\sigma_p}\) |
\((-\infty, +\infty)\) |
📖 |
| Sortino Ratio |
Risk-adjusted return (downside only) |
\(\frac{R_p - R_f}{\sigma_d}\) |
\((-\infty, +\infty)\) |
📖 |
| Max Drawdown |
Worst peak-to-trough decline |
\(\frac{Trough - Peak}{Peak}\) |
\([-100\%, 0\%]\) |
📖 |
| Volatility |
Dispersion of returns |
\(\sigma = \sqrt{\text{Var}(R)}\) |
\([0, +\infty)\) |
📖 |
🔑 When to Use Each Metric
| Scenario |
Best Metric |
Why |
| Comparing two funds |
Sharpe Ratio |
Normalizes return by total risk |
| Asymmetric return distributions |
Sortino Ratio |
Only penalizes downside volatility |
| Worst-case scenario planning |
Max Drawdown |
Shows the maximum pain point |
| General risk assessment |
Volatility |
Foundation for all other metrics |
| Portfolio optimization |
All four |
Each captures a different dimension |
⚠️ Common Pitfalls
Limitations
- Historical metrics ≠ future risk: Past volatility may not predict future volatility
- Normal distribution assumption: Sharpe and Sortino assume returns are roughly normal; financial returns have fat tails
- Lookback sensitivity: Metrics change significantly depending on the time window
- Benchmark dependency: Sharpe and Sortino depend on the risk-free rate, which changes over time