How to measure an investment: return, risk and portfolio metrics
Educational and methodological content. The formulas and examples explain how to measure an investment, not which to choose. Past performance does not guarantee future results.
Why metrics, and why these
A return alone says almost nothing: +30% earned by risking half your capital is not the same +30% earned with mild swings. Measuring well means separating return, risk, and the quality of the process behind them. These are also the metrics we use in the monthly updates and the model monitor.
1. CAGR vs arithmetic mean — the return that actually counts
The arithmetic mean of returns misleads. The CAGR (compound growth rate) is the only one that reflects real wealth:
CAGR = (V_end / V_start)^(1/n) − 1
Example: +50% one year, −50% the next. Arithmetic mean = 0%. But 100 → 150 → 75: you lost 25%. CAGR is (0.75)^(1/2) − 1 ≈ −13.4%. The gap is volatility drag.
2. Drawdown, semivariance, time to recovery — how bad it can get
- Maximum drawdown (MDD): the worst peak-to-trough decline. 100 to 60 → MDD = −40%.
- Semivariance / downside deviation: measures only deviations below a threshold:
σ_down = √( mean( min(r − MAR, 0)² ) ). - Time to recovery (TTR): a −50% needs +100% to recover; at 7% annual compounding that's about 10 years. Loss is asymmetric.
3. Sharpe, Sortino, Calmar — risk-adjusted return
- Sharpe =
(R_p − R_f) / σ_p. With 8% return, 2% risk-free, 12% volatility → Sharpe = 0.5. - Sortino = like Sharpe, but the denominator uses only downside deviation:
(R_p − R_f) / σ_down. - Calmar =
CAGR / |MDD|. With 12% CAGR and −40% MDD → Calmar = 0.3. - Pitfall: Sharpe assumes ~normal returns; with fat tails and skew it can mislead. Three lenses, not one.
4. Capture ratio, alpha and beta — skill or just market exposure?
The CAPM decomposes return: R_p = R_f + β·(R_m − R_f) + α.
- Beta (β) = sensitivity to the market:
β = Cov(R_p, R_m) / Var(R_m). β = 1.2 → you move 20% more than the market. - Alpha (α) = the return not explained by the market. The (claimed) skill.
- Capture ratio: a good strategy has up-capture > 100% and down-capture < 100%.
- Meaning: don't pay "alpha" fees for what is just beta. More in Alpha and Beta.
5. Honest backtesting — out-of-sample, walk-forward, capacity
- Out-of-sample: test on data not used to build the strategy.
- Walk-forward: re-fit and test "forward" on rolling windows.
- Multiple testing / deflated Sharpe: try 100 strategies and some will look great by luck; the Sharpe must be "deflated" (López de Prado; Harvey-Liu-Zhu).
- Capacity: a strategy that works on €100k may break at €100M. A backtest without costs and capacity is a drawing, not a proof.
6. Tax, costs and capacity — the real enemy of net returns
Costs (TER, spread, commissions) and tax (26% on capital gains in Italy) compound against you year after year. High turnover realizes gains and pulls tax forward. Always measure net.
In short
Return (CAGR), risk (MDD, semivariance, TTR), risk-adjusted return (Sharpe, Sortino, Calmar), skill vs market (alpha/beta, capture), process honesty and net return. Try the concepts with the ETF Portfolio Simulator or go straight to the free tools.
Sources
López de Prado (2018), Advances in Financial Machine Learning · Harvey, Liu, Zhu (2016) · Sharpe (1966) · Sortino & van der Meer (1991) · C. Bacon, Practical Portfolio Performance Measurement · SPIVA reports (S&P).
Educational content, not advice or a recommendation. Past performance and backtests do not guarantee future results.