37 lines
2.5 KiB
Plaintext
37 lines
2.5 KiB
Plaintext
Understanding and Managing Leverage • 171
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upward movement in the stock will offset the money spent on time value,
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the amount spent on time value is never recoverable.
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The remaining $11.25 of the premium paid for a $20-strike call op-
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tion is intrinsic value . Buying intrinsic value means that we are exposing
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our own capital to the risk of an unrealized loss if the stock falls below
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$31.25. Lambda is directly related to the amount of capital we are exposing
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to an unrealized loss versus the size of the “loan” from the option, so be-
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cause we are risking $11.25 of our own capital and borrowing $20 with the
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option (a high capital-to-loan proportion), our investment leverage meas-
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ured by lambda is a relatively low 2.50.
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Now direct your attention to a far OTM call option—the one struck
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at $39. If we invest in the $39-strike option, we are again effectively
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taking out a $39 contingent loan to buy the shares. Again, we take the
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time-value portion of the option’s price—in this case the entire premi-
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um of $1.28—to be the prepaid interest (an implied annualized rate of
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6.3 percent) and note that we are exposing none of our own capital to
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the risk of an unrealized loss. Because we are subjecting none of our
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own capital in this investment and taking out a large loan, our invest-
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ment leverage soars to a very high value of 15.63. This implies that a
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1 percentage point move in the underlying stock will boost our invest-
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ment return by over 15 percent!
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Obviously, these calculations tell us that our investment returns are
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going to be much more volatile for small changes in the underlying’s price
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when buying far OTM options than when buying far ITM options. This is
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fine information for someone interested in more speculative strategies—if
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a speculator has the sense that a stock will rise quickly, he or she could,
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rather than buying the stock, buy OTM options, and if the stock went up
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fast enough and soon enough offset any drop of implied volatility and time
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decay, he or she would pocket a nice, highly levered profit.
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However, there are several factors that limit the usefulness of lambda.
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First, because delta is not a constant, the leverage factor does not stay put
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as the stock moves around. For someone who intends to hold a position for
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a longer time, then, lambda provides little information regarding how the
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position will perform over their investment horizon.
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In addition, reading the preceding descriptions of lambda, it is ob-
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vious that this measure deals exclusively with the percentage change in |