Got a windfall? Investing it all at once usually beats spreading it out, but averaging in reduces regret. See the math.
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Because markets rise more often than they fall, investing a lump sum immediately keeps your money in the market longer and usually ends higher than dollar-cost averaging the same amount over months. Averaging in trades some expected return for lower risk of buying right before a drop. This uses a steady average return; real results depend on the path. Illustrative.