The Master Formula
Average Price = $\frac{(P_1 \times Q_1) + (P_2 \times Q_2) + ... + (P_n \times Q_n)}{Q_1 + Q_2 + ... + Q_n}$
Where:
- P: Price of the purchase.
- Q: Quantity (Number of shares) bought.
Dimensional Analysis: Dollars per Share
The unit of the result is always Currency/Unit. It is vital to ensure that your commissions and slippage are added to the $(P \times Q)$ numerator to get your True Net Average. If you ignore fees, your break-even point in the calculator will be lower than your actual break-even in your brokerage account.
Variations: Averaging in Short Selling
When shorting, "Averaging Up" is the equivalent of "Averaging Down" in longs. If you short at $100$ and the stock goes to $110$, your average price increases, which is technically "better" for your break-even, but it means you are losing money on your initial position. The formula remains identical.
Shortcuts & General Rules of Thumb
- The 50/30/20 Rule: A popular institutional scaling method: 50% size at the start, 30% on first confirmation, 20% on the breakout.
- Mental Check: If you buy equal quantities at two prices, the average is the exact midpoint. If you buy double the quantity at the second price, the average will be 2/3rds of the way toward that second price.
- The "One Percent" Rule: Never let your total position size (after all averaging) exceed a weight where a 1% drop in the stock hits your total account stop-loss limit.
Edge Cases: Corporate Actions
- Stock Splits: If a stock splits 2-for-1, your average price is halved and your quantity is doubled. The total investment remains the same.
- Dividends: Many traders subtract the "Dividend Received" from their cost basis to calculate a "Net Adjusted Average."
- Gaps: If you have a limit order to average down at $90$, but the stock gaps to $85$, your average price will be lower than expected, but your initial position is in deeper trouble.
