Dollar Cost Averaging vs Lump Sum Calculator

How many monthly instalments the sum is broken into. One instalment is the lump sum itself. A window longer than the holding period is compressed to fit, because an instalment timed after the money comes out would never be invested, and the status line says when that has happened.

How long the money stays invested, counted from the first purchase rather than the last. Lengthening it grows both results and widens the gap between them in dollars, while shrinking it as a share, because the months spent out of the market are a fixed cost paid at the start.

How unsure you are about that return, as one standard deviation, quoted PER YEAR. It is as much a part of the answer as the return itself, which is why it is asked for rather than assumed. The grid runs the comparison across eleven returns spread around yours and reports how often each strategy wins; the deviation is scaled to your holding period by the square root of time, because the model applies one constant rate across the period and a long-run average is less uncertain than a single year. Fifteen percent is in the range of a diversified equity portfolio. Zero means you are certain, and the grid collapses onto your own figure.

The sum that is available now and would otherwise sit in cash. Both strategies start from exactly this money, which is the comparison: one puts it to work on day one and the other keeps part of it in cash for a while.

The return you assume the investment earns, every year, for the whole period. Held constant, and applied monthly as one twelfth of it. A negative figure is a real scenario here and is worth entering: it is the case in which feeding the money in comes out ahead, and the size of that lead is the protection the strategy is bought for.

The average price the instalments paid, with the day-one price set at one. It is the HARMONIC mean rather than the arithmetic one, because a fixed sum buys more units when the price is low, and that is the only real mechanism behind dollar-cost averaging. Above one means the plan bought into a rising market; below one means it bought the dip. It is worth exactly one over the ratio of the two results.

The values across the top of the grid: how many months the buying is spread over, stepped by a fifth of your own window, floored at one month and capped at the months held. Read a column to hold the window fixed. The middle entry is your own figure.

What the drip-feed would be AHEAD by if the market fell at the same rate you expect it to rise. It is the other half of the argument and the one the averages hide: set it against the gap above and you can see what the waiting buys as well as what it costs.

Reads OK, or explains why the inputs are not valid or why the answer deserves a second look.

The share of the returns in the band you allowed for in which investing it all at once comes out ahead. Read it as a shape rather than a forecast: it is the chance under YOUR assumption about how unsure the return is, and it says nothing about whether that assumption is right. It is read down your own column of the grid, so it is a statement about the market and never about the window you picked.

Machinery, and NOT an input. Excel substitutes each value from the row axis into this cell while it fills the grid; the rest of the time it mirrors Annual_Return. Change Annual_Return above, never this: the axis is derived from it, so editing the mirror moves the axis while the table walks and the grid comes out meaningless.

The body of the grid: the gap between the two strategies, recomputed for every combination of the two axes. One hundred and twenty-one cells, each one the whole comparison run again. It is a component of the table rather than a result on its own.

The values down the left of the grid: the annual return, spread five half-deviations either side of the one you expect after scaling to your holding period. Read a row to hold the return fixed and vary the window. The middle entry is your own figure.

Machinery, and NOT an input. The same for the column axis: Excel substitutes into it while filling the grid, and the rest of the time it mirrors Spread_Months.

Machinery. Excel requires the formula being tabulated to sit in the grid's top-left corner, where it means nothing to a reader, so it is formatted away. It holds Lump_Sum_Advantage.

How long the average dollar sits in cash before it is invested, which is half of one instalment less than the window. It is the quantity the whole shortfall is proportional to, so it is the single most useful number for judging a plan before running it.

The same gap as a share of the lump-sum result, which is the figure to compare across different sums and periods. It is roughly the return times the average months spent waiting, so it grows with both.

The gap in a lucky tenth. The distance between this and the unlucky tenth is the honest width of the answer, and on most inputs it is wide enough to be the finding.

The gap in an unlucky tenth of those returns, meaning the low end of the band. Below zero it is the drip-feed that is ahead, and how far below is the size of the protection you are buying. At a return comfortably clear of zero relative to your uncertainty, the whole band sits on the lump sum's side and this figure is positive.

The middle of the band. It sits below the single-point answer rather than on top of it, because the gap grows faster than the return does and the high returns pull the average up further than the low ones pull it down.

The two results differenced. Positive means investing it all at once came out ahead; negative means the drip-feed did, which happens whenever the return is negative. This is the figure the grid below recomputes for every pair of return and window.

What the whole sum is worth at the end if it is invested on day one. On any positive return this is the larger of the two results, always, and that is arithmetic rather than a finding.

How many monthly purchases the plan really makes: the window rounded to whole months, floored at one and capped at the months held. One means the plan is the lump sum under another name.

What the same sum is worth at the end if it is fed in over the window you chose. It is smaller on a rising market because the later instalments compound for fewer months, and larger on a falling one because they bought in cheaper.

The sum divided by the number of instalments actually made. It can differ from the sum divided by the window you typed, because a window longer than the holding period is compressed.