# Maximum leverage when avoiding forced liquidation

Posted On: 2015-10-20

Leverage can sometimes do more harm than good - when your leveraged account is in drawdown, the effective margin quickly increases as your net equity decreases. At the point you reach the maximum leverage your broker allow, you will either get a margin call or be forced to liquidate some positions. If liquidation is the only option for you it makes it even harder to recover when the market bounces, and you've effectively locked in a loss. There are however precautions you can take to avoid this situation.

We recently published an article describing the formula to find the optimal leverage when the objective was to maximize the instantaneous growth rate. Such formula is very beneficial when a momentum effect exists in the market, but it can do more harm than good in a mean reversion market since volatility drag now has an even larger effect on your account.

Volatility drag refers to the loss caused by geometric returns. Consider an investment of \$10,000 which first yields 10% loss and then a 10% gain. Most people will say we're now breakeven, but after the first loss the equity has dropped to 10,000*0.9=\$9,000, and the gain only brings it up to 9,000*1.1=\$9,900 so you're still \$100 short. The gain needs to be 11.1% to bring you back to breakeven.

If you now use leverage, and keep the level of leverage constant as your account suffers from a drawdown (which the Kelly Criterion used in the previous article does), then this effect will be even more severe. For example, if you use 30% leverage, the initial position is \$13,000 and after a 10% loss the value of this position goes down to \$11,700. Your net equity that initially was \$10,000 is now down to \$8,700 and to maintain 30% leverage you need to decrease your position with \$390. A gain of 10% increases the position to \$12,441 which is 4.3% less than the initial position (compared with 1% less in the no-leverage example).

It can therefore be interesting to know how large of a drawdown you can survive without being forced to liquidate any position, and especially what initial leverage this would equal. The following formula shows what your initial leverage must be less than, given a set maximum leverage and known drawdown:

Eq. 1.1

where LI is the initial leverage, LMAX is the maximum leverage allowed and DD is the maximum drawdown expected. All values are in percentage form.

The formula can modified to find the maximum drawdown you can survive without being forced to liquidate:

Eq. 1.2

Example - Let's assume your broker offer you a maximum leverage of 100%, and you expect that a maximum drawdown of 40% is possible, but not more. Plugging the numbers into the formula suggests that you shall have an initial leverage of no more than 42.9%. If your worst case scenario of a 40% drawdown were to occur your leverage would then be geared up to 100%.

There is one limitation to this simple formula however, and it's that it doesn't consider the cost of leverage. This would require the addition of a time dimension, and an estimate of the specific time frame when the drawdown is expected to occur, which is why it's left out.

Please note that this is NOT advice for how much leverage to use, since if your maximum drawdown expectations are incorrect and your broker offers high leverage the effect of forced liquidation on your capital will be severe. This formula is just to help you understand how your choice of initial leverage will be affected by broker margins and drawdowns.