37 lines
2.2 KiB
Plaintext
37 lines
2.2 KiB
Plaintext
290 • The Intelligent Option Investor
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preceding equation, we can see that the left side of the equation is levered
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(because it contains only options, and options are levered instruments),
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and the right side is unlevered. Obviously, then, the two cannot be exactly
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the same.
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We can fix this problem by delevering the left side of the preceding
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equation. Any time we sell a put option, we have to place cash in a mar -
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gin account with our broker. Recall that a short put that is fully margined
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is an unlevered instrument, so margining the short put should delever
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the entire option position. Let’s add a margin account to the left side and
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put $K in it:
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C
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K − PK + K = S
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This equation simply says that if you sell a put struck at K and put $K
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worth of margin behind it while buying a call option, you’ll have the same
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risk, return, and leverage profile as if you bought a stock—just as in our
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big-picture diagram.
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But this is not quite right if one is dealing with small differences.
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First, let’s say that you talk your broker into funding the margin ac-
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count using a risk-free bond fund that will pay some fixed amount of
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interest over the next year. To fund the margin account, you tell your
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broker you will buy enough of the bond account that one year from
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now, when the put expires, the margin account’s value will be exactly
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the same as the strike price. In this way, even by placing an amount less
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than the strike price in your margin account originally, you will be able
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to fulfill the commitment to buy the stock at the strike price if the put
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expires in the money (ITM). The amount that will be placed in margin
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originally will be the strike price less the amount of interest you will
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receive from the risk-free bond. In mathematical terms, the preceding
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equation becomes
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C
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K − PK + (K – Int) = S
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Now all is right with the world. For a non-dividend-paying stock, this fully
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expresses the technical definition of put-call parity.
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However, because we are talking about dividend arbitrage, we have to
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think about how to adjust our equation to include dividends. We know that
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a call option on a dividend-paying stock is worth less because the dividend |