Keep constant leverage left of the equity peak

How leverage is defined

Leverage is position notional divided by trading equity, regardless of how much cash sits in the brokerage account versus a low-risk reserve. A 50000 position on 100000 of equity is 0.5, and a 100000 position on the same equity is 1.0. One S&P 500 futures contract at 450 with a 500 multiplier, backed by 100000 of equity, is 2.25 leverage, and a 1.0 percent price rise then changes equity by 2.25 percent.

Reset exposure to current equity

The applied-leverage setup uses a constant-leverage-rebalance. It resets exposure each day to a chosen multiple of current equity, not only at the start of a multi-day trade. After gains the position is scaled up. After losses, units are sold so exposure stays at the same multiple of the reduced equity.

How ending equity changed with leverage

The historical illustrations used daily S&P 500 futures from 1 January 1988 through 31 December 1993 and tracked an initial 100 of equity inside an account treated as large enough that unit-size rounding could be ignored.

On the always-long path, ending equity rose with leverage up to about 4.8 and then declined, with losses once leverage passed 9.

A 150-day moving-average-position-filter that was long only when price was above the average, otherwise flat, peaked near leverage 3.3 and turned negative past about 6.5.

A 200-day moving-average-position-filter peaked near leverage 5.2 and turned negative near 9.6. Worst-cumulative-drawdown was 14.4 percent at leverage 1 versus 64.4 percent at leverage 5.

Why deeper losses flatten the curve

Raising only the 13 October 1989 close from an 8.3 percent one-day loss to 12 percent or 20 percent, while leaving later prices unchanged, lowered peak ending equity and shifted the best leverage leftward, even though ending equity at leverage 1 stayed the same.

After a leveraged loss, selling units to restore the target multiple of reduced equity cuts participation in later recoveries, which is why deeper drawdowns flatten and left-shift the return-versus-leverage-profile.

Stay left of the historical peak

The practical checklist is to stay left of the historical peak, leave a buffer below that peak in case later drawdowns are worse, and reject any leverage whose historical equity path exceeded the trader's endurance.