Average cost per share when you dollar-cost average

Question

You invest \600 in a stock at \30 per share, then another \600 at \60 per share. Solve in your head. What is your average cost per share? Aim: under 10 seconds.

Accepted Answer

Average cost is total dollars over total shares. Equal dollars at each price means you buy more shares when the price is low, so the low price gets more weight, which is exactly the harmonic mean of the prices: \bar p = \frac{2 p1 p2}{p1 + p2} = \frac{2 	imes 30 	imes 60}{90} = \frac{3600}{90} = \40 	ext{ per share}. Check it directly: \600 at \30 buys 20 shares; \600 at \60 buys 10 shares. That is 30 shares for \1{,}200 total, or \1{,}200 / 30 = \40 per share. Not \45, because you bought twice as many shares at the cheap price. Takeaway. Fixed-dollar buying (dollar-cost averaging) gives a…

Average cost per share when you dollar-cost average

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