GARCH model

What it means

Stock returns do not fluctuate at a constant rate. Quiet trading days often cluster together, as do turbulent ones. A GARCH model describes this pattern by updating its estimate of volatility as new returns arrive. GARCH stands for generalized autoregressive conditional heteroskedasticity; “conditional” means the estimate depends on information available up to that point.

The commonly used GARCH(1,1) version estimates the variance of the next period’s return, not its direction or the stock’s next price. Its volatility estimate is the square root of that variance. If the input returns are daily, the resulting volatility is daily; a percentage return gives a percentage volatility estimate. Unlike a single standard deviation calculated across a fixed historical window, the estimate changes as the model processes each new return.

How it is calculated

A standard GARCH(1,1) update is h_t = ω + αε_(t−1)² + βh_(t−1).

• h_t is the estimated conditional variance of the return for period t, expressed in squared return units.
• ω (omega) is a nonnegative baseline variance term, in the same squared units.
• α (alpha) is the nonnegative weight on the previous period’s squared return shock.
• ε_(t−1) is the previous return minus its modeled expected return, in return units; squaring it removes its sign.
• β (beta) is the nonnegative weight on the previous period’s conditional variance, h_(t−1).

The estimated volatility is σ_t = √h_t. Alpha and beta are unitless; their values and omega are estimated from historical returns rather than chosen from the latest observation alone. A common specification requires α + β < 1 for a finite long-run variance. Larger values of α + β indicate that volatility shocks tend to persist longer within that specification. The model’s period must match the return series: daily inputs produce a one-day-ahead estimate unless the model is extended to another horizon.

Worked example

Hypothetical example: Suppose daily returns are measured as decimals, and an estimated model has ω = 0.000004, α = 0.10 and β = 0.80. The previous day’s estimated variance is h_(t−1) = 0.000100, equivalent to 1.00% daily volatility. Suppose its return shock is ε_(t−1) = −0.02, or −2%.

1. Square the shock: (−0.02)² = 0.0004.
2. Weight the shock: 0.10 × 0.0004 = 0.000040.
3. Weight the previous variance: 0.80 × 0.000100 = 0.000080.
4. Add the terms: h_t = 0.000004 + 0.000040 + 0.000080 = 0.000124.
5. Take the square root: σ_t = √0.000124 ≈ 0.01114, or about 1.11% daily volatility.

The estimate rose from 1.00% to about 1.11% after the unusually large shock. Because the formula squares the shock, a +2% shock would contribute the same amount in this basic model. The result is not a prediction that the next return will be +1.11% or −1.11%.

Why it matters before you trade

A changing volatility estimate provides context for position size, short-horizon risk measures and execution conditions. For example, a one-day value-at-risk calculation that assumes a volatility level can change when that input changes. Higher estimated volatility may also make a fixed price limit or an expected execution cost harder to interpret without considering current conditions.

GARCH captures persistence in past fluctuations, but it cannot reliably anticipate an unobserved earnings surprise, trading halt or other abrupt event. Its output depends on the return data, estimation period and model assumptions. It is a risk input, not a trading signal or a guarantee about the range of future returns.

How PreTrAIde uses it

PreTrAIde’s pre-trade analysis estimates daily volatility using a blend of Parkinson, close-to-close, Yang–Zhang and simplified GARCH(1,1) estimators. Daily volatility is one input to its quantitative risk analysis, which also includes a one-day 95% value-at-risk estimate and volatility scores. PreTrAIde analyzes a stock basket before an order is placed and returns decision-support verdicts and reasoning; it does not place orders. Its product facts do not specify the blend’s weights or the simplified GARCH estimator’s exact parameters.

Common mistakes

• Treating volatility as direction. The estimate describes the scale of fluctuations, not whether the next return will be positive or negative.
• Mixing units. A decimal shock of 0.02 is 2%; entering 2 instead changes its squared contribution by a factor of 10,000.
• Confusing variance with volatility. 0.000124 is variance in decimal-return units squared; its square root is about 1.11% volatility.
• Assuming one model fits every market condition. Sudden regime changes, thin trading and extreme moves can make an estimate less representative of what happens next.
• Calling a daily estimate annualized. Converting between horizons requires an explicit assumption; the daily GARCH output is not automatically an annual volatility figure.