Max Drawdown, Ulcer Index, Calmar — Three Ways to Measure "How Painful the Drop"

4-section structure: Concept / How We Compute / How to Read / Caveats.

1. Concept

Standard deviation says "how much it fluctuates". VaR/CVaR says "worst single-day loss". But for investors, the most visceral pain measurement is:

"From when I bought to now, how much did it fall from its peak?"

That's drawdown. Three complementary angles:

Metric	Answers
Max Drawdown (MDD)	What's the deepest drawdown in history?
Ulcer Index (UI)	Averaged pain across the whole period (not just the deepest)
Calmar Ratio	Annual return per unit of worst drawdown

2. How We Compute

2.1 Max Drawdown

running_max = max of price seen so far
drawdown_t = (price_t − running_max_t) / running_max_t   # negative
max_dd = min(drawdown)

Example: stock goes 100 → 150 → 90:

running_max = 150; drawdown = −40%; MDD = −40%

2.2 Ulcer Index

ulcer = √(mean(drawdown²)) × 100

Quadratic mean amplifies deeper drawdowns. Distinguishes "deep but short" from "deep and prolonged" — MDD can't.

2.3 Calmar Ratio

annual_return = (end_price / start_price) ^ (252 / n_days) − 1
calmar = annual_return / |MDD|

Answers: "do the returns justify the worst pain?"

2.4 Data & Window

Stock: past 252 trading-day close
Portfolio: daily NAV
Sample < 30 → available: false

3. How to Read

3.1 MDD Color Scale

MDD	Color	Profile
> −10%	🟢	Stable (bonds, utilities)
−10% to −25%	🟡	Mainstream large/growth
< −25%	🔴	High-vol growth, cyclicals

3.2 Ulcer Index Scale

UI	Color	Reading
< 5	🟢	Low pain
5–12	🟡	Moderate
> 12	🔴	High pain

3.3 Calmar Scale

Calmar	Color	Reading
> 1.0	🟢	Excellent (>1% ann. return per 1% MDD)
0.3–1.0	🟡	Acceptable
< 0.3	🔴	Drawdown not worth it

3.4 Combined Matrix

MDD	Ulcer	Calmar	Interpretation
Low	Low	High	🟢 Ideal — steady winners
Deep	Low	High	🟡 Flash crash survivor (deep MDD, mostly calm + high return)
Low	High	Mid	🟡 Prolonged stagnation
Deep	High	Low	🔴 Painful (deep + prolonged + low return)

3.5 Sharpe / Sortino / Calmar Comparison

Ratio	Denominator	Psychological Match
Sharpe	Total volatility	Low volatility tolerance
Sortino	Downside volatility	Only care about drops
Calmar	Single worst drawdown	Can't stomach major crashes

4. Caveats

⚠️ MDD Is Extremely Sample-Sensitive

If 252 days missed major events → MDD looks mild → Calmar inflated. Late-bull-market Calmar is the most misleading.

Mitigation:

Pair with P1C.1 VaR/CVaR
Longer windows (configurable in future)
P2.3 historical stress tests (Phase 2)

⚠️ No MDD Reset

Running-max classic approach — drawdowns don't age out. A 2008 −50% stays on record in 2024.

Pros: stable long-term view. Cons: early shocks "permanently remembered".

Rolling-window MDD is alternative but noisier at window edges; we chose stability.

⚠️ Ulcer Is Level, Not Percent

Ulcer = 8.5 doesn't mean "8.5% average drawdown". It's quadratic mean × 100.

Use for relative comparison (A=5 vs B=10: A half as painful); not for absolute interpretation.

⚠️ Calmar Inflates in Bull Markets

2021 post-2020-crash Calmar was explosive (small MDD, high returns). Doesn't guarantee future.

High Calmar ≠ low risk — it just means the past happened not to crash.

⚠️ Portfolio Legacy Compat

Old field max_drawdown_pct: positive (e.g., 35.0 for −35%)
New field drawdown.max_drawdown_pct: negative (academic convention)

Both returned to avoid breaking legacy UI.

⚠️ Short Samples Break Calmar

< 1 year: annualization distorts, MDD may not have shown yet
min_sample = 30 but recommend 252+

Try It

Stock Analysis → Risk: MDD / Ulcer / Calmar cards below VaR/CVaR/Sortino
Portfolio: portfolio version in the row below
Compare same stock's Sharpe/Sortino/Calmar; pick the one matching your psychological frame
Click 📐 for formulas and parameters

Max Drawdown, Ulcer Index, Calmar — Three Ways to Measure Drawdown Pain