Leverage is a notion whose meaning has evolved as a result of financial innovation during recent decades. Traditionally, leverage related to the relative proportions of debt and equity funding a venture. The higher the proportion of debt, the more leverage. A leveraged venture entailed more risk and potential reward for equity holders. Consider a stylized example. A corporation is established by ten investors. Each puts up USD 100 in equity. There is no debt. After one year, the corporation will be liquidated. At that time, if its net assets are worth USD 900, each equity investor will realize a –10% return. If assets are worth USD 1100, each investor will realize a 10% return. This is summarized in Exhibit 1.
Now consider the same corporation, but financed differently. The same ten investors each put up USD 100, but only five of them hold equity. The other five hold debt. Debt holders are guaranteed to receive USD 105. At the end of the year, if the corporation's assets are worth USD 900, there will be USD 375 left over after paying debt holders. Each equity investor will realize a –25% return. If, on the other hand, the corporation's assets are worth 1100 at year end, there will be USD 575 left over after paying debt holders. Each equity investor will realize a 15% return.
As the examples illustrate, debt financing magnifies the risk as well as the possible reward for equity holders. Traditionally, the word "leverage" referred to the use of debt financing. In recent decades, that meaning has shifted to encompass any technique that similarly magnifies risk and reward for an investor. Consider a call option. It offers a leveraged alternative to taking an outright position in an underlier. Let's compare the risk-reward characteristics of an outright position vs. a call option position. Suppose shares of XYZ corporation are trading at USD 100 and currently pay no dividends. An investor pays USD1000 to buy 10 shares. She holds the position for three months. If, at the end of that period, XYZ is trading at USD 92, the investor will realize a –8% return. If it is trading at USD 108, the return will be 8%. See Exhibit 3.
Now suppose, instead of taking an outright position in XYZ stock, the investor purchases 3-month call options struck at the money. These are trading at USD 5, so the investor spends USD 1000 to buy 200 options. If, at the end of three months, XYZ is trading at USD 92, the options will expire worthless. The investor's return will be –100%. If the stock is trading at USD 110, her return will be 60%. See Exhibit 4.
Today, similar opportunities for leverage abound. Essentially all derivatives—including futures, forwards, swaps, vanilla options and exotics—provide leveraged. They offer indirect interest in an underlier for an initial investment that is less than the value of that underlier. With some derivatives, such as forwards or swaps, no initial investment is required. Securities lending and repurchase agreements can be used to leverage a portfolio. In essence, they represent secured borrowing. Short selling offers leverage—proceeds of a short sale are not a loan, but they can be invested just the same. Even traditional debt-base leverage has evolved, with junk bonds emerging in the 1970s as a legitimate asset class in their own right. The widespread proliferation of leverage during the latter half of the 20th century is perhaps the primary motivation for modern financial risk management.
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