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The Volatility Chain


Thanks John!


Note: Our goal in Minyanville is to remove intimidation from the financial markets and encourage an interactive dialogue among the Minyanship. We share this next discussion with that very intent.

Risk can be thought of in two basics constructs: systematic risk and unsystematic risk. (Warning: the picture that I am going to paint is overly simplistic. There are many cross-currents and changes in systematic risk can affect unsystematic risk and vice-versa. But the theory in general will serve you to understand what is going on.)

Systematic risk affects all stocks (or any financial asset) in varying degrees. Variables that affect systematic risk are things like interest rates, oil prices, or geo-political events.

Unsystematic risk is everything else and normally can be defined as company or industry specific risks. Variables might include management, accounting issues, mergers, and any other factor that would affect the cash flows of a company or industry and not that of the market in general.

You can see the overlap right away. Enron management's malfeasance affected stocks in general by branding all management as malevolent (perhaps an overreaction, perhaps not). Regardless, an increase in the risk of one company affected the "perceived" risk in many; a change in unsystematic risk changed systematic risk. Risk is not a zero sum game.

An increase in systematic risk is mostly observed in index option prices and this is measured by VIX. An increase in unsystematic risk is mostly observed in individual option prices. But an increase in either will affect the option prices to some varying extent in both markets and will manifest itself in a combination of primarily two ways.

Let's just say that the explosion in North Korea was a nuclear device (a stretch no?). In this case, systematic risk (or at least its perception) certainly would increase. So the risk in all stocks would go up; the big question (especially for me) is how would it be manifest?

Would the option prices of Johnson & Johnson (JNJ:NYSE) go up? A stock holder in JNJ may say no: the cash flows of the company which makes all kinds of health care products from stents to q-tips would not be affected with an increase in the probability of nuclear proliferation. She would not be inclined to go out and buy puts on the company itself (which would indicate an increase in unsystematic risk).

But she may be inclined to go out and buy index puts to protect her overall portfolio. When she goes out and buys the index put and does not buy the JNJ put she is implying that systematic risk has increased while unsystematic risk (at least in JNJ) has not.

Thus the spread between index option prices and JNJ option prices widens a little bit. The purchase of index puts sets off a chain of events. First, the market makers who sell her the index put must hedge the delta by selling SP500 futures. The sale causes the spread between futures prices and individual equity prices to widen. If it becomes wide enough, index arbitrage traders step in and buy the futures and sell the individual stocks; this causes JNJ, which is part of the index to drop a little. JNJ starts to go down not because the portfolio manager is worried about the company, but merely because the stock is a small part of a whole. Notice that the correlation between the SP500 and JNJ thus increases a little. And this is the main point: an increase in systematic risk tends to increase the correlation between stocks.

And this is the first way index option prices and the VIX increases: it is not due to an increase in unsystematic risk, it is not due to an increase in the implied volatilities of the options of the underlying stocks, it is due to an increase in the correlation between stocks.

But there is a second and more obvious way the VIX and index option prices can increase (although this is a less frequent way). Let's say that there is a perceived increase in the unsystematic risk of JNJ. The portfolio manager then buys a JNJ put. If this happens to enough different stocks all at the same time, option arbitrage funds like mine might step in and buy the index options and sell individual options. This scenario is rare but makes the chain complete.

So the VIX can increase (index option prices) due to an increase in systematic risk and a consequential increase in the correlation between stocks (eventually option arbitragers will step in and thus bid up JNJ options as well when the spread becomes wide enough). Or the VIX can increase due to an increase in the unsystematic risk of enough stocks without an increase in the correlation between stocks. In reality it is a combination of both.

It matters much as to the method of the rise when we label the VIX cheap or rich. The process of weighting systematic versus unsystematic risk is constant and accomplished through "arbitrage" between stock and option prices. It is only when it reaches extremes is it significant in conveying market sentiment.

When implied correlations are high, systematic risk is in general over-estimated and index option prices are high relative to individual option prices. The implied correlations in 1998 neared .9 (the maximum is 1). This was an extreme.

But when we see the implied correlations dip to .30 as they are now, we can begin to say that the VIX is now in cheap territory: systematic risk may be under-estimated.

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