DERIVATIVES 'R US/V1N13/Call Options as Insurance and Margin
VOLUME 1, NUMBER 13/May 15-22, 1995
After a one week hiatus, DRU is back. However, there will be another one week hiatus so this issue covers May 15 and 22.
This week I'm going to dissect the call option transaction and show you some insights that don't appear obvious on the surface. Many of you are familiar with put-parity but for those who are not, suppose you buy the stock and a put and borrow funds equal to the present value of the exercise price, promising to pay back the exercise price at the option's expiration.
Suppose at expiration, the stock ends up above the exercise price. Then the put expires worthless and you end up holding the stock and paying the bank an amount of money equivalent to the exercise price. If the stock ends up below the exercise price, you exercise the put and end up selling your stock for the exercise price, which is then passed on to the bank to pay off your loan. This strategy is identical to holding a call.
If a call is equivalent to owning the stock, owning a put and borrowing the present value of the exercise price, then you can say that a call is a protective put plus a loan that helps pay for it. Another way to look at a call is to say that it is like an insurance policy (the put) and a long position in the stock combined with a loan from the bank. The long stock plus loan is, thus, like a margin transaction. Therefore, a call is like a margin transaction plus an insurance policy.
Viewed from that angle, a number of interesting insights are offered. For example, as you probably know, you can buy stock on margin but have to conform to the margin requirements, which are 50 % initial margin and maintenance margin of usually 25 to 30 %. The same effect can be accomplished without the hassle of the margin requirements by buying a call. This creates a margin transaction that is also downside insured. If you don't want the downside insurance, just sell a put. That will offset the implicit put that is part of the call. Thus, a long call and a short put is like a margin transaction, which is why it also makes a good substitute for a futures transaction, itself a "margin-like" transaction.
Notice how the call gets completely around the margin requirements. Take an out-of-the money call where the stock price is substantially below the exercise price. Not only will the transaction implicitly borrow more than 50 % of the purchase price of the stock, but it will also involve borrowing some of the insurance premium. For example, consider a one-year call with volatility of .35, stock price of $100, strike of $120 and risk-free rate of 5 %. The call would be worth $8.83 and the put would be worth $22.98. Your $8.83 call premium would represent the purchase of stock for $100, the purchase of a put for $22.98, and the borrowing of $114.15 with a promise to pay back $120 in one year. Thus, your $100 stock was purchased by borrowing all $100, meaning you had no equity whatsoever in the stock, and you had $14.15 of borrowing that was used to help pay the $22.98 price of the put.
Another interesting insight from this is that we always tend to say that volatility helps a call by giving it the advantage of upside moves without any downside penalty. In other words, if volatility increases, your upside potential is greater but your downside potential is the same because if the call ends up out- of-the-money, you don't care how far out of the money it ends up. I don't see much harm in this view but frankly, it's not correct. Remembering that the call is a margin transaction plus a put, let us look at the effects of volatility on each component. First take the insurance. Does volatility affect the price of a put? Of course. A put will be worth substantially more if the volatility is higher. The insurer will demand a greater premium to accommodate the greater risk. Thus, the holder of the call pays a higher price because the downside risk is greater. What about the margin transaction? Does volatility affect it? That's a tricky one.
Under the strict assumptions of the Black-Scholes world, volatility does not affect the stock price. We know, of course, that it really does but I'm not sure anybody knows exactly how. Intuition says increased volatility should drive a stock price down. However, we know that a call is worth more if volatility increases regardless of whether we agree that a call consists of a margin transaction plus insurance. Thus, if volatility affects the stock, the effect could not offset the effect on the implied put. Consequently, the positive effect of volatility on a call is coming from the downside, not from the upside. This clearly establishes that the traditional view of volatility gives credit where credit is not due for the upside effect of volatility and not enough credit for the downside effect. So let's set the record straight. A call is worth more when the volatility is higher because it contains a limit on the downside loss. The upside effect of volatility is, at best, neutral and, at worst, a negative.
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