Lump sum or a little each month

Invest all at once or spread it out? Replay every start date since 2005 and count which won.

Invest $12,000 in

S&P 500

Spread it over

Judge the result after

Interest on waiting cash2.00% a year

Money not yet invested sits in a savings account.

Lump sum won74%104 of 141 start dates

Average lead of lump sum+2.8%

Worst start for lump sum-29.2%May 2008

Best start for lump sum+29.7%Feb 2009

Lump sum's lead over spreading it out, by start month

Tap a bar to replay that start date below.

Lump sum ended ahead Spreading it out ended ahead

Starting in Oct 2007, over 10 years

All at once$24,598

Over 12 months$28,140

How big the gap usually is

Each start month, lump sum's lead (right) or shortfall (left).

Putting $12,000 into S&P 500 all at once beat spreading it over 12 months in 74% of start dates, because markets that rise more often than they fall reward money that gets in early. But the losses are what people remember: when lump sum lost, it trailed by 8.6% on average, and by 29.2% starting in May 2008, against an average win of 6.8%. Spreading it out gives up some expected return to buy protection from regret.

Try this

Tap the bars around late 2007. How far behind does a lump sum fall when it lands right before a crash?
Switch to long Treasuries (TLT), then to Bitcoin. Does the winner change with the asset's volatility and trend?
Raise the interest on waiting cash to 5%. How much of lump sum's edge does it take away?

The math

V_{\text{DCA}} = \sum_{k=0}^{N-1} \frac{A}{N}\,(1+c)^{k}\,\frac{P_{T}}{P_{k}}

$A$: the amount to invest
$N$: number of monthly instalments
$c$: monthly interest on cash still waiting
$P_k$: price when instalment k is invested
$V_{\text{lump}} = A\,P_T / P_0$: the lump sum, everything bought at the first price

Ask the Loop about this Next: Retirement and sequence risk