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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.
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Case A |
Case B |
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Initial
equity investment |
1000 |
1000 |
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Investment per equity investor |
100 |
100 |
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Initial
debt investment |
0 |
0 |
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Investment per debt investor |
– |
– |
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Corporation's end-of-year asset value |
900 |
1100 |
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Cost of
paying off debt investors |
0 |
0 |
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Residual
value for equity investors |
900 |
1100 |
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Residual
value per equity investor |
90 |
110 |
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Return
realized by each equity investor |
–10% |
10% |
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Without any debt financing, equity
investors receive returns in proportion to the corporation's overall
performance. |
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.
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Case A |
Case B |
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Initial
equity investment |
500 |
500 |
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Investment per equity investor |
100 |
100 |
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Initial
debt investment |
500 |
500 |
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Investment per debt investor |
100 |
100 |
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Corporation's end-of-year asset value |
900 |
1100 |
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Cost of
paying off debt investors |
525 |
525 |
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Residual
value for equity investors |
375 |
575 |
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Residual
value per equity investor |
75 |
115 |
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Return
realized by each equity investor |
–25% |
15% |
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With debt financing, equity investors
receive returns out of proportion to the corporation's overall
performance. The returns are "leveraged." |
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.
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Case A |
Case B |
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Purchase
price per share |
100 |
100 |
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Number
of shares purchased |
10 |
10 |
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Total
investment |
1000 |
1000 |
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Stock
price after three months |
92 |
108 |
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Total value after three months |
920 |
1080 |
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Return |
–8% |
8% |
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Direct investment in a company's stock
offers returns directly proportional to the stock's performance. |
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.
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Case A |
Case B |
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Purchase
price per option |
5 |
5 |
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Number
of options purchased |
200 |
200 |
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Total
investment |
1000 |
1000 |
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Stock
price at expiration |
92 |
108 |
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Option
value at expiration |
0 |
8 |
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Total
value at expiration |
0 |
1600 |
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Return |
–100% |
60% |
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Call options are leverage. They magnify
risk and reward compared to a direct purchase of the underlier. |
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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