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The Margin Inequality

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June 21, 2012 – Comments (0)

In this post, I mentioned the speculative nature of purchasing stock on margin. The risks associated with using margin are many and it may be the case that they cannot all be quantified. I would like to explore one risk associated with margin which can be given a rough model. I call it the Margin Inequality.

The question: What is the highest Debt/Equity ratio that one can take on while suffering a portfolio loss L but still maintaining a maitenance requirement M?

I'm going to assume that all of the assets in the portfolio are marginable assets. In the real world, some assets have restrictions placed on them making that assumption inapplicable.

Let D be debt, E be equity, M be the margin maitenance requirement (as set by regulation or brokerage firm) and  L be the loss suffered. Then the margin inequality is given by:

D/E < (1+ ML - L - M) / (M + L - ML)

This is the highest debt level that one can have while being capable of withstanding a portfolio loss L while still having a minimum margin maitenance of M. Here's an example:

Suppose that the margin maintenance M = 25% and we want to construct a portfolio that can withstand a 40% loss (think 2008) and not fall below the margin maintenance level. 

D/E < (1 + 25% x 40% - 40% - 25%) / (25% + 40% - 25% x 40%)

. . .

D/E < .818

While having a debt/equity ratio below that value won't guarantee that you won't get a margin call, the opposite is almost sure. If D/E > .818 and your portfolio takes a 40% dive, your broker will probably be liquidating assets at the worst possible time. 

And of course, the margin maintenance requirement varies from broker to broker so check the details of the margin policy at the broker you use. 

The safest bet, of course, is to not use margin at all but if you are, you should go about it intelligently, being aware of the risks involved. 

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