The Deceptive Math of Financial Leverage

In physics a lever is a tool for obtaining a large torque (rotational motion) with a relatively small force. Anytime you use a screwdriver, a lug wrench, a jack, a crowbar, or a doorknob, you are using a lever. In each of these circumstances the rotations achieved would be nearly impossible without the lever.

By analogy, the leverage principle in finance is intended to magnify rates of return on invested money so that relatively small amounts of money can grow much faster than the actual rate of return on the investment. But in finance the tool used to obtain leverage is debt. Borrowing against an asset to fund an investment is financial leverage.

For example, a homebuyer who takes out a mortgage is leveraging the asset—the home—to increase the rate of return on the money used for the down payment. Suppose a buyer puts $10,000 down on a $100,000 house and finances the remaining $90,000 using the house as collateral. If the value of the house rises 50% to $150,000, the homebuyer now has $60,000 of equity in the house. The $10,000 investment has multiplied 6-fold even though the asset only increased 50% in value. Had the buyer paid $100,000 cash for the house a 50% return on investment is all that would have been achieved.

Investors in the stock market can also use leverage. An investor with a normal brokerage account is allowed to borrow up to 50% of the value of stocks owned to purchase more stocks. That means $10,000 can be used to purchase up to $20,000 worth of stocks. This is called buying on margin. If the stocks double in value to $40,000 the investor now has $30,000 in equity—a tripling of the initial $10,000 investment.

Leverage seems like a kind of financial magic. For many investment banks and hedge funds it was magic because these institutions were not bound by the normal rules that limit ordinary investors and homeowners. Stockowners cannot borrow more than 50% of the value of their stocks; homeowners cannot borrow more than the value of their homes. But, in the unregulated dream world of investment banking and hedge funds, there was no limit on the amount the managers could borrow against their assets. For example, by the time Lehman Brothers went bankrupt it was leveraged more than 30 to 1. It owed $30 for $1 in assets it held. Imagine a homeowner borrowing $3 million against a $100,000 home. That might sound crazy, but that’s effectively what Lehman Brothers did.

The motivation for investment banks and hedge funds to leverage their assets to such absurd levels is that it allows them to report fantastic rates of return for modest investment gains. Suppose a $3 million cash investment returns just 5% in a year so that the value is $3.15 million. That does not sound all that impressive. But, suppose the fund managers had only $100,000 in equity in that $3 million investment. The total equity after the 5% gain is now $250,000. The fund managers can now report a “return on equity” of 150%. That is an eye-catching number to report to investors, prospective customers and stockholders. The managers can reward themselves with bonuses for the their remarkable results. At the same time the appreciation of the actual investment was nothing out of the ordinary. It is a beautiful example of a two-headed quarter—using numbers to have it both ways.

But leverage has a dark side. Not only does it magnify gains it also magnifies losses. In the example above, if the $3 million investment loses just 3.3% of its value, the $100,000 of equity is completely wiped out. In markets with normal volatility, a 3.3% downward move is not unusual for a solid investment. The problem is that many of the investments were in mortgages, which are also a leveraged investment. Many of the subprime mortgages being called assets, were for homeowners who had no equity in their houses. Leverage was piled upon leverage. No wonder the banks have no idea what the mortgage securities they hold are worth. Homeowners with no equity have every incentive to walk away when prices fall. After all, when a homeowner invests nothing, there is nothing to lose.

In the same manner, the executives and fund managers had nothing to lose by taking on such absurd levels of debt. They pocketed huge salaries and bonuses for their financial “genius.” And it was an ingenious scheme—taking home the profits and billing the taxpayers and stockholders for the losses.


Joseph Ganem is a physicist and author of the award-winning The Two Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy