Weighted Average: Ask What the Weight Was
A weighted average multiplies each value by an importance factor before averaging, so larger contributions count for more. It underlies average entry price, volume-weighted average price, diluted share counts and the cost of capital, and choosing the weight is the only real decision in it.
How it works
A weighted average multiplies before it averages. One hundred shares at 10 and nine hundred at 20 give a weighted average of 19, because the second purchase is nine times the size of the first.
The simple average of the same two prices is 15. Four units of difference, from identical inputs, purely because one method counted the sizes and the other did not.
Choosing the weight is the only real decision. Size, time, volume and market capitalization are all defensible weights for different questions, and they produce different answers to the same one.
Where traders meet it
A scaled entry has a weighted average cost. Three equal thirds at 100, 104 and 110 give 105 — and if the thirds were not equal, the answer moves toward whichever tranche was largest.
Averaging down improves the number and worsens the position. Buying again at 80 after buying at 100 lowers the average to 90, which looks like progress on a screen.
Meanwhile the exposure doubled. The average price fell ten percent and the amount at risk rose a hundred percent, and only one of those two numbers is displayed prominently. That asymmetry is why averaging down feels better than it is.
VWAP is this calculation applied to a session. Every trade weighted by its size, giving the average price at which the day’s volume actually changed hands.
In practice: where else it appears
Earnings per share uses a time-weighted share count. Shares issued in month four count for three quarters of the year, which is why the denominator rarely matches the year-end figure.
Inventory is frequently valued this way. Weighted average cost is one of the permitted methods, and it produces a different cost of goods sold — and therefore a different profit — from first-in-first-out.
The cost of capital is a weighted average too. Debt and equity each carry a rate, weighted by how much of each the company uses — which is the discount rate a valuation model needs.
Every average destroys information. An average entry of 90 could come from two purchases at 80 and 110 or twenty purchases between 88 and 92, and those are completely different positions.
So the question to ask of any average is what was weighted. An index weighted by market capitalization and one weighted equally describe the same companies and behave completely differently.
One case deserves separating because the two averages answer genuinely different questions: an index. A market-capitalization-weighted index tells you what the market as a whole did, because it reflects how much money is actually invested in each company. An equally weighted version tells you what the average company did, which is a different and equally legitimate question.
The two diverge most when a few very large constituents move. A handful of enormous companies rising while most fall produces a rising capitalization-weighted index and a falling equal-weighted one — both correct, describing the same day. When the two disagree sharply, the disagreement is the story, and it is a reading nobody gets from either number alone.
The same logic applies to a portfolio. Return weighted by position size says what your money did; return weighted equally says what your selections did. A large gap between them says your sizing, rather than your picking, is doing most of the work — in either direction, and that is worth knowing before changing how you choose what to buy.
What a weighted average is not
It is not a simple average. The two disagree whenever sizes differ.
It is not neutral. The weight is a choice that changes the answer.
It is not a complete description. The spread is gone.
And it is not always the right average. Sometimes equal weighting is.
How this connects
Scaling in is the planned version of the tranche example above. The sizes are decided in advance, and pyramiding is the variant that adds only as price moves in favor, lifting the average cost rather than lowering it.
The average cost also feeds cost basis for tax, so the method a broker uses to match a sale against earlier purchases changes the reported gain.
Moving averages differ only in their weights. A simple moving average weights every bar equally, a weighted moving average leans linearly toward recent bars, an exponential moving average decays geometrically, and a volume weighted moving average uses traded size.
VWAP has extensions built on the same weighting. Anchored VWAP starts the calculation at a chosen event instead of the session open, and VWAP bands add deviations around the line.
Index construction is the everyday case. The Nasdaq Composite weights by market capitalization, while the Dow Jones weights by share price, which is why a high-priced member moves it more than a larger company.
Portfolio beta is a weighted average too, each holding’s beta counted by its share of the money invested.
And dollar cost averaging is where the weight works for you. Fixed contributions buy more units when prices are low, so the average cost per unit ends below the simple average of the prices paid.
When it fails as a summary
A weighted average is dominated by its largest component. Nine hundred of one thing and one hundred of another produces a figure that is essentially a description of the nine hundred, and the smaller contribution is invisible.
A second failure is a moving average entry price used as a performance measure. It improves whenever you add at a lower price, so it rewards exactly the behavior that increases risk.
A third is comparing weighted figures computed on different weights. Two index returns weighted differently are not comparable, however similar the constituents.
A fourth is a time-weighted share count read as a share count. The year-end figure is what you own a fraction of; the weighted one is only for the earnings calculation.
And a fifth is trusting an average without the range. The spread behind it is what tells you whether the average describes anything.
The original data
Of the 24,971 trading and investing videos in this site’s corpus, “valuation” returns 8 at a median of 160,764 views, “financial statements” 2 at a median of 536,039, and “cash flow” 15 at a median of 67,134 across 14 channels. Every figure counts each video a single time.
The figures in the diagrams on this page are illustrative. The 15 against 19 from the same two prices is the whole idea in one comparison, and the 100-to-900 split is deliberately extreme to make the effect visible — real weightings are usually less lopsided and work in exactly the same way.
The habit worth keeping is to record the range alongside the average, in a position and in a set of accounts. Highest paid, lowest paid, and the weighted average between them takes one extra line and preserves the information the average removes — which is the difference between knowing your cost and knowing your position.
Related
VWAP is the intraday version used as a reference level. Position sizing is where the weight in a scaled entry gets decided. And financial statements is where the accounting versions appear.
I check whether my average entry price is flattering me. It improves when you add to a losing position, which is the one circumstance where a better average price means a worse situation.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.