Equal-dollar staging versus lump-sum and residual scaling

Two cash-deployment paths

A staged-buying procedure was defined as splitting a fixed cash sum into equal monthly purchases rather than placing the entire sum on one date. In the terms used here, that schedule is dollar-cost averaging: deploying a fixed cash amount through equal scheduled purchases instead of placing the entire amount on one date.

A lump-sum purchase places the entire available cash amount on a single entry date and holds that position for the chosen window.

Regular paycheck contributions were treated as a setting where staged buying is used because a lump sum is not available.

How the overlapping window test was built

One comparison used a 12000 single purchase against twelve 1000 purchases on the first trading day of each month in a broad equity index, then sold all shares at the close of a twelve-month window.

Those twelve-month windows were overlapped by starting each new test one month later from February 1950 through January 2014. An overlapping window test repeats the same holding-period comparison on successive start dates so one start month does not dominate the sample.

Stock dividends and interest on cash waiting to be invested were excluded from the summed test results.

Residual-share size procedure

A residual-share procedure, presented as distinct from equal-dollar staging, sized an opening purchase so a later sale at a chosen rise could recover the cash outlay while still holding a target share count.

Shares to buy were calculated as retained shares plus retained shares times 100 divided by the expected percentage increase. With 100 retained shares and a 25 percent expected rise, that calculation required buying 500 shares and later selling 400 to recover the original outlay.

That later reduction is a scale-out position: reducing a defined share quantity after a defined price rise, including selling down to a residual holding once earlier sales can recover the cash outlay.

Fluctuation adds and cuts

A fluctuation rule added 50 percent more shares after a 25 percent decline and cut the position by 50 percent after a 25 percent rise, then checked whether selling down to 100 shares could bring remaining cost to zero.

Adding a defined extra share quantity after a defined price decline is a scale-in position. The holding grows while the market is moving against the existing position.

After remaining cost reaches zero

After a zero remaining cost was reached on a residual holding, recovered cash was directed to another name to spread exposure while lowering ownership cost. A zero-cost residual is a leftover share count whose original cash outlay has already been recovered by prior sales.