Risk & Performance Metrics

Every metric in TradePilot explained — with formulas, descriptions, and live calculations using AAPL sample data.

Return

Mean: -0.0039%

Daily Returns

Percentage change in price from one period to the next. The fundamental building block of all other metrics.

R_t = (P_t - P_{t-1}) / P_{t-1}

Where P_t is the price at time t. Also called simple returns or arithmetic returns.

Why it matters: Returns normalize price movements across different price levels, enabling comparison between assets and time periods.

Return

-2.59%

Annualized Returns

Compound returns scaled to a one-year period for standardized comparison across different time horizons.

R_annual = (∏(1 + R_t))^(252/N) - 1

Where N is the number of periods and 252 is trading days per year. Uses geometric (compound) growth.

Why it matters: Enables apples-to-apples comparison of returns across different holding periods and investment strategies.

Risk

18.16%

Annualized Volatility

Standard deviation of returns, scaled to annual frequency. The most common measure of total risk.

σ_annual = std(R) × √252

Volatility scales with the square root of time (assuming i.i.d. returns).

Why it matters: Higher volatility means wider range of possible outcomes. Used in Sharpe ratio, option pricing, and risk budgeting.

Risk

11.39%

Semideviation

Standard deviation of only negative returns. Measures downside risk, ignoring upside volatility.

σ_down = std(R | R < 0)

Only considers returns below zero. Investors care more about downside risk than upside "risk".

Why it matters: Captures the asymmetric nature of risk preferences. Used in the Sortino ratio as a better denominator than total volatility.

Portfolio

-0.35

Sharpe Ratio

Excess return per unit of total risk. The gold standard for risk-adjusted performance measurement.

SR = (R_p - R_f) / σ_p

Where R_p = annualized portfolio return, R_f = risk-free rate, σ_p = annualized portfolio volatility.

Why it matters: A Sharpe > 1.0 is generally considered good, > 2.0 is very good. Enables comparison of strategies with different risk levels.

Portfolio

-0.56

Sortino Ratio

Excess return per unit of downside risk. A more nuanced alternative to the Sharpe ratio.

Sortino = (R_p - R_f) / σ_down

Uses semideviation (downside volatility) instead of total volatility in the denominator.

Why it matters: Penalizes only harmful volatility. An asset with high upside volatility and low downside will have a better Sortino than Sharpe.

Risk

1.85%

Historic VaR

The loss threshold at a given confidence level based on historical return distribution.

VaR_α = -Percentile(R, α)

At 5% level: "There is a 5% chance that daily losses will exceed this value." Non-parametric — uses actual return data.

Why it matters: Required by regulators for bank capital requirements. Provides a concrete dollar-loss estimate at a given confidence.

Risk

1.88%

Gaussian VaR

Parametric VaR assuming returns follow a normal distribution.

VaR = -(μ + z_α × σ)

Where z_α is the z-score for the confidence level (e.g., -1.645 for 5%). Assumes normality of returns.

Why it matters: Fast to compute and analytically tractable. But underestimates risk if returns have fat tails (which they usually do).

Risk

1.90%

Cornish-Fisher VaR

Modified VaR that adjusts for skewness and kurtosis in the return distribution.

z_cf = z + (z²-1)S/6 + (z³-3z)(K-3)/24 - (2z³-5z)S²/36

Adjusts the Gaussian z-score using observed skewness (S) and kurtosis (K). Then VaR = -(μ + z_cf × σ).

Why it matters: Better captures tail risk than Gaussian VaR when returns are skewed or have fat tails — which is common in financial data.

Risk

2.45%

Conditional VaR (CVaR)

Expected loss given that losses exceed VaR. Also called Expected Shortfall — answers "how bad is it when things go bad?"

CVaR = -E[R | R ≤ -VaR]

Average of all returns that fall below the VaR threshold. Always ≥ VaR.

Why it matters: VaR only tells you the threshold; CVaR tells you what to expect beyond it. Preferred by risk managers because it is coherent and sub-additive.

Risk

-16.80%

Maximum Drawdown

The largest peak-to-trough decline in portfolio value. Measures the worst-case loss from a historical high.

MDD = min((V_t - V_peak) / V_peak)

Where V_peak is the running maximum value up to time t. Expressed as a negative percentage.

Why it matters: The most intuitive risk metric — "what is the most I could have lost?" Critical for investor psychology and fund survival.

Distribution

-0.0565

Skewness

Measures asymmetry of the return distribution. Negative skew means more frequent large losses.

S = E[(R - μ)³] / σ³

Third standardized moment. S < 0 = left-skewed (fat left tail), S > 0 = right-skewed, S = 0 = symmetric.

Why it matters: Most equity returns are negatively skewed — crashes are more common than equivalent surges. Used in Cornish-Fisher VaR.

Distribution

2.8802

Kurtosis

Measures tail heaviness of the distribution. Higher kurtosis means more extreme events than a normal distribution.

K = E[(R - μ)⁴] / σ⁴

Fourth standardized moment. K = 3 for normal distribution (mesokurtic). K > 3 = fat tails (leptokurtic).

Why it matters: Financial returns typically have K >> 3, meaning extreme events (crashes, spikes) occur more often than normal distribution predicts.

Portfolio

-6.59%

Alpha

Excess return of the portfolio over the risk-free rate. Measures absolute value added by active management.

α = R_p - R_f

Simple excess return. In CAPM: α = R_p - [R_f + β(R_m - R_f)] but TradePilot uses the simpler definition.

Why it matters: Positive alpha means the strategy outperformed the risk-free benchmark. The holy grail of active management.

Return

$-6.39

Momentum

Price difference over a lookback window. Used both as a metric and a ranking/selection criterion.

M(i, t) = P(i, today) - P(i, today - t)

Simple price-level momentum over t periods. Not returns-based — uses raw price difference.

Why it matters: The backbone of momentum strategies. Positive momentum indicates upward trend; negative indicates downward pressure.