Investment Theory and Risk Management, + Website

Adjusting for Leverage

Leverage is insidious. Suppose I have $100 of my own equity to invest and I supplement that amount with $900 in borrowed funds. That's 9:1 leverage. Colloquially, this is sometimes referred to as nine turns of leverage. I now have $1,000 in working capital. If my investment earns 10 percent, then my dollar return is $100. That's a 100 percent return on my equity. That's the power of leverage. Now, imagine, instead, that my investment lost 50 percent. I now default on my loan but my equity loss is limited to my original $100. Of course, I am abstracting away a few details but the example illustrates how leverage permits me to enjoy all the upside while limiting my downside exposure. Before the credit crisis, U.S. investment banks were leveraged at around 30:1, meaning that every dollar in equity invested was accompanied by 30 dollars of borrowed funds. The historical average was closer to 15:1. By way of contrast, Long-Term Capital Management, at the time of their default, was leveraged about 90:1!

First, some definitions: Leverage is the fraction ω of total working capital that is debt financed:

This implies that D = ωE/(1 – ω), where D and E are debt and equity, respectively. The leveraged return, , is the growth rate of working capital, net of financing costs, ...