variance-analysis

# Variance Analysis

**Important**: This skill assists with variance analysis workflows but does not provide financial advice. All analyses should be reviewed by qualified financial professionals before use in reporting.

Techniques for decomposing variances, materiality thresholds, narrative generation, waterfall chart methodology, and budget vs actual vs forecast comparisons.

## Variance Decomposition Techniques

### Price / Volume Decomposition

The most fundamental variance decomposition. Used for revenue, cost of goods, and any metric that can be expressed as Price x Volume.

**Formula:**
```
Total Variance = Actual - Budget (or Prior)

Volume Effect  = (Actual Volume - Budget Volume) x Budget Price
Price Effect   = (Actual Price - Budget Price) x Actual Volume
Mix Effect     = Residual (interaction term), or allocated proportionally

Verification:  Volume Effect + Price Effect = Total Variance
               (when mix is embedded in the price/volume terms)
```

**Three-way decomposition (separating mix):**
```
Volume Effect = (Actual Volume - Budget Volume) x Budget Price x Budget Mix
Price Effect  = (Actual Price - Budget Price) x Budget Volume x Actual Mix
Mix Effect    = Budget Price x Budget Volume x (Actual Mix - Budget Mix)
```

**Example — Revenue variance:**
- Budget: 10,000 units at $50 = $500,000
- Actual: 11,000 units at $48 = $528,000
- Total variance: +$28,000 favorable
  - Volume effect: +1,000 units x $50 = +$50,000 (favorable — sold more units)
  - Price effect: -$2 x 11,000 units = -$22,000 (unfavorable — lower ASP)
  - Net: +$28,000

### Rate / Mix Decomposition

Used when analyzing blended rates across segments with different unit economics.

**Formula:**
```
Rate Effect = Sum of (Actual Volume_i x (Actual Rate_i - Budget Rate_i))
Mix Effect  = Sum of (Budget Rate_i x (Actual Volume_i - Expected Volume_i at Budget Mix))
```

**Example — Gross margin variance:**
- Product A: 60% margin, Product B: 40% margin
- Budget mix: 50% A, 50% B → Blen