Sortino & Downside Deviation — Only Penalizing Down Moves

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

1. Concept

Sharpe Ratio is the most common risk-adjusted return metric. But it has a questionable assumption: it treats upside volatility as risk.

A rocketing stock has high standard deviation. Its Sharpe gets dragged down by upside moves — but upside is good for investors, not a risk to be punished.

Sortino fixes this:

Sortino = Excess Return / Downside Deviation Downside Deviation = √(mean(min(Rt − target, 0)²))

Only considers days when returns fall below target. Typically:

target = 0 → only loss days
target = Rf → below risk-free days

Upside volatility no longer pollutes the denominator, aligning better with intuitive "risk" perception.

2. How We Compute

Formula

Sortino = (annual return − annual Rf) / annual downside deviation
  annual return  = mean(daily_return) × 252
  annual Rf      = rf_daily × 252
  annual dd      = sqrt(mean(min(Rt − 0, 0)²)) × √252

Target Choice

We use target = 0 (distinguishing "loss day" vs "non-loss day"). Benefits:

Easier cross-stock comparison
Most intuitive for retail investors

MAR-based version with target = Rf_daily is supported in backend (UI toggle planned).

Rf Source

Reuses v2.43 dynamic Rf chain:

^IRX (US 13W T-Bill latest yield)
Taiwan CBC 10Y bond yield
1.5% fallback

Annual Rf is shown on card hover.

Individual vs Portfolio

Stock: past 252 trading days' simple daily returns
Portfolio: NAV-derived daily returns
Identical formula, target, Rf — directly comparable

Insufficient Sample

Sample < 60 days or downside deviation = 0 → available: false.

3. How to Read

Level Table

Sortino	Interpretation
> 2.0	🟢 Excellent
1.0 – 2.0	🟢 Good
0.5 – 1.0	🟡 Acceptable
0 – 0.5	🟠 Borderline
< 0	🔴 Below Rf

Sharpe vs Sortino Comparison (Most Useful Trick)

Sharpe	Sortino	Interpretation
1.0	1.0	Symmetric up/down (normal)
1.0	2.0	Upside big, downside small → Sharpe underrates
1.0	0.5	Many down days → Sharpe missed the risk
neg	neg	Bad fundamentals, move on

Rule of thumb: stocks with Sortino/Sharpe > 1.3 tend to "drop less" — worth prioritizing.

Portfolio Sortino Usage

1.0 → strategy sustainable
< 0.5 → consider rebalancing (add negative-correlation assets, reduce high-vol positions)

Pair with P0.2 correlation matrix: low Sortino + high correlation → must rebalance.

4. Caveats

⚠️ Sharpe vs Sortino Aren't "Right vs Wrong"

Sharpe: overall risk profile (including total vol)
Sortino: investor-pain perspective (downside only)

Look at both. Modern portfolio management leans toward Sortino, but Sharpe remains academic standard.

⚠️ Pure Uptrend Inflates Sortino

If a stock only rises in the sample window (e.g., AI stocks 2023-2024), downside σ approaches zero and Sortino becomes extremely high (we show unavailable if σ=0). Don't treat such Sortino as sustainable — market reversals rebuild the denominator quickly.

⚠️ Most Sample-Sensitive of All Metrics

More reliant on tail events than Sharpe. If 252 days missed major downturns:

downside σ too small
Sortino inflated
Actual drawdown will crash the number

Mitigate: combine with P1C.1 VaR/CVaR. VaR doesn't fake-high when sample has no big drops — it just says "can't compute" (insufficient sample).

⚠️ Not for Short Horizons

< 3 months → too few samples, unstable
Minimum 60 days; recommend 252 days

⚠️ Target Philosophy

Using target = 0 per above rationale. Some institutions use target = Rf (MAR) — meaning "losses are returns below X%". Both valid, different perspectives:

target = 0 → sensitivity to absolute losses
target = Rf → sensitivity vs risk-free baseline

Backend supports target = Rf; UI toggle not yet exposed.

Try It

Stock Analysis → Risk: Sortino card beside VaR/CVaR
Portfolio: Portfolio Sortino below Rolling Sharpe
Click 📐 for formula, target, Rf source, sample size
Compare same stock's Sharpe vs Sortino — big gap means asymmetric up/down behavior