Academic

My post yesterday argued that the New York Times erred in endorsing the use of the VIX index as a measure of the level of fear in the market.  Professor Sjostrom?s comment to yesterday?s post raised an interesting question: doesn?t the relationship exhibited between an increased demand for S&P put options (one way to execute the portfolio insurance strategy described in earlier posts) and an increase in the VIX index provide evidence that the VIX index and fear are closely linked?

To provide an adequate answer to Professor Sjostrom?s question, it is helpful to address each of the six claims which Sjostrom uses as evidence to arrive at the conclusion that an increase in the VIX index is indicative of an increase in fear:

Claim 1: An increase in the demand for insurance is indicative of an increase in the level of fear.
I agree. Insurance is a way to moderate expected payouts.  Someone who is more fearful wants to reduce the variance of possible outcomes, and insurance would be a logical product to purchase. So, yes, an increase in the demand for insurance is indicative of an increase in the level of fear.

Claim 2:  An increase in the demand for insurance will increase the price of insurance.   
I am not convinced that this, as a general rule, is true.  One could imagine a situation in which the purchase of insurance is only for the purpose of risk sharing.  If insurance is only purchased to reduce risk, then the cost of insurance might decrease with an increase in the number of people seeking insurance. Alternatively, there are other circumstances in which an increase in the demand for insurance would raise prices.  Thus, an increase in the demand for insurance can either increase or decrease insurance costs, depending on the factors driving the demand for insurance. 

Claim 3: Purchasing S&P puts to limit one?s downside risk is comparable to the purchase of insurance.
The purchase of S&P puts that Sjostrom proposes creates what I described in earlier posts as portfolio insurance.  However, the term ?portfolio insurance? is misleading.  Portfolio insurance is essentially an asset allocation strategy, and can only loosely be compared to the act of buying insurance.  Portfolio insurance shifts assets from equities to cash, depending on movements in the price of equities within some predetermined range.  A secondary effect of purchasing portfolio insurance is that your asset value will not fall below a certain level, but this limit on losses is only a secondary effect.  If the primary goal is to insure that the value of your portfolio does not fall below a preset amount, then the more sound approach would be to move some funds out of equities and into cash before market trading starts.

There is also a second sense in which a choice to purchase S&P puts is not a form of insurance.  An investor always has the choice to either purchase S&P puts or to replicate the equivalent strategy in the open market.  Therefore, the choice to purchase S&P puts rather than replicate a put strategy in the open market (assuming low transactions costs) is comparable to betting on the volatility implicit in the S&P puts? price.  One purchases the put rather than replicate the put strategy, because of a belief that the volatility implicit in the put price is below the volatility that will actually occur.  I?ll put this observation aside, and make the following friendly amendment to Sjostrom?s question.  We can assume that when Sjostrom refers to those who purchase S&P puts he is referring both to those who purchase S&P puts and to those who choose to execute a portfolio insurance trading strategy.

Claim 4: An increase in purchases of S&P puts is indicative of an increase in the level of fear.
Above, I described how adopting a portfolio insurance strategy is only indirectly related to the purchase of insurance.  In fact, it is hard to conceive of a logical reason for anyone, much less an institutional investor, to purchase portfolio insurance. As noted above, if an investor wishes to insure his portfolio, then the investor should alter the percent of their holding invested in risky assets, rather than adopt a strategy in which they are exposed to risk under some conditions, but not other conditions.  (This is why I argued in a previous blog, Regulatory Rule #3, that the decision to purchase of portfolio insurance is an unsophisticated decision.)  Given this observation, there must be something other than fear which explains the choice to purchase S&P puts in Sjostrom?s example.

Claim 5:  An increase in the demand for S&P puts will increase the price of these puts.
Perhaps, but this is not obvious.  New information generated by an increased demand for put options will affect the pricing of those put options only to the extent that it changes expectations about future volatility.  If no other information is generated by the increased demand for put options, then it is unlikely that the price would increase.  Conversely, if a relationship does exist between an increased demand for S&P put options and an increase in the price of the S&P put options, the resulting increase in the S&P put option prices reveals information about volatility, not fear.

Claim 6:  An increase in the price of S&P puts will increase the VIX index.
I think Sjostrom is correct here.

I agree with Sjostrom. An increase in the price of S&P puts is correlated with an increase in the VIX index. However, such an increase in the price of S&P puts is more likely the result of expectations that volatility will increase than increased demand for S&P puts, and the odd preferences that could lead someone to purchase S&P puts as a form of portfolio insurance do not match our common sense notion of fear.  I would like to thank Sjostrom for providing the opportunity for this interesting and valuable discussion, and look forward to continuing the dialogue.