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# The Price Paid

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The put-call ratio measures the amount of puts trading relative to calls in any given period. Technicians use this tool as a sentiment indicator, gauging whether traders in options are more bearish because they are trading more puts than calls, or more bullish because they are trading more calls than puts. The technician considers this a contrary indicator, with the magnitude of traders either being too bullish or bearish determined by comparing the current level with historical levels and subsequent market moves.

A better indicator, or at least one that makes the put-call ratio more informative about sentiment, is the relative price of the options. In general, high option prices indicate nervousness and fear by investors who are willing to "overpay" (by historical standards) to acquire either protection (in the case of buying puts) or upside (in the case of buying calls). As a contrary indicator, when traders are willing to overpay for protection (puts), the market will often do the opposite of expectations and grind higher. This is a subjective answer, but there is a real mathematical reason that this occurs.

Without going into heavy math, basically an option is more expensive when the volatility of the stock is higher. This makes intuitive sense: A trader will pay more for an option if it is likely that the stock can move 30% in a month versus 10%. We can measure on a normalized basis how expensive an option is by backing out the volatility variable in the Black-Scholes pricing model that results in the market price; this is called "implied volatility." For example, when an option has an implied annualized volatility of 30%, the price of the option implies that the stock will move 30% up or down over one year's time. If that same option goes up in price, all things being equal (stock price, interest rates, time to expiration, and dividends), the implied volatility of the option has gone up simply because the buyer believes the stock will be more volatile.

So how do option prices affect how the market actually trades? Again, without going into a lot of math, a short option position is essentially a future liability. If the option expires in the money, the seller must fulfill an obligation of either buying a stock at higher than market prices (short put) or selling a stock at lower than market prices (short call). The magnitude of that liability is called the delta (the first derivative of price) and changes over the life of the option based predominantly on changes in the stock price. This change of the liability is called gamma (the second derivative of price) and is affected by the price of the option: The higher the price of the option, the higher the implied volatility of the option, the lower the gamma, and the lower the change in the liability for any given change in the stock price. This can be shown mathematically, but essentially the price of the option acts as a buffer to the obligation. The lower the changes in the obligation, the fewer times the arbitrageur who has sold the option has to re-hedge; the less re-hedging, the less volatility. So it is a full circle. The price traders pay for options actually affects the volatility: the higher the prices they pay, the lower the actual volatility.

If we combine this analysis with the put-call ratio we get more information. When the put-call ratio is high (more puts trading than calls) and the price of the options is high, this is a good indication that traders are buying puts and paying too much for them. Arbitrage sellers will have less gamma and not have to re-hedge as much. Also those traders who overpaid for puts will probably buy stock in declines to protect the value of their puts. All this mitigates actual volatility and may lead to a slow grind up. Compare this to a high put-call ratio when option prices are low and the situation becomes more ambiguous. Traders may be selling puts too cheaply and creating a high gamma situation for themselves; this affects the structural leverage of the system.

The greatest example of this situation is the 1987 crash and the role portfolio insurance played. Portfolio insurance was sold in great quantities to money managers; it was essentially a futures program that insulated the manager's portfolio in declines by selling futures against long stocks as the market declined. The program synthetically replicated buying an index put on the portfolio: At a certain point the manager would be short futures equal in notional value to the long stock portfolio, and therefore have no market risk. The problem was that this "synthetic option" program was sold too cheaply. It is analogous to an extremely high put-call ratio with extremely low option prices. When the market began to decline, there was 100 times too much re-hedging activity occurring for the liquidity of the market to handle. This caused the most infamous crash in history, one that occurred with an extremely high synthetic put-call ratio, but with very low option prices.
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