Mar

12

As the S&P approaches its all time high, slowly but steadily, one ponders the implications as it appears to be pre-ordained with the slow but consistent rise occurring.

It is well known that the markets' volatility are auto-correlated when the jump in prices occur quickly. But if the large change in price is slow but steady such as we've seen last few weeks, does volatility increase? Does this signal reverse trends are more likely than normal? Of course this needs to be defined better, yet, I wonder if someone knows the answer(s) from previous studies?

Rocky Humbert writes: 

Russ: There are multiple answers to your question.

1. Firstly, you have to differentiate between the VIX (which is based on a "market" estimate of future volatility using live options prices) versus the actual realized volatility. It is theoretically possible — in fact, quite likely — that the VIX can diverge from actual market volatility for long periods of time. Right now, the VIX is about 11.5% and the November 2013 VIX future is 18.90. So right there, you see the market has priced in a higher VIX. Assuming that this market is efficiently arbitraged, it means that 8 month options are much more expensive than 1 month options. There is some path dependency here, but in a nut shell, it means the answer to your question is no, eh yes. (That is, Mr. Market believes the answer to your question is yes in the longer term, but no in the shorter term.)

2. Secondly, the definition of volatility is simply the standard deviation of returns. As a silly example, imagine if the S&P went up by 5% EVERY SINGLE DAY. In this absurd example, the VIX is extremely low (even though the market is going bonkers), since it's a monotonically increasing value and the change in returns every day is 0. (That is, so long as the velocity of the market is constant, there is NO volatility.) In this silly example, I would expect the spot vix to collapse (due to arbitrage) but the long term vix futures would explode. (It's important to not forget how the VIX is calculated.) Similarly, if the S&P were declining by 5% EVERY SINGLE DAY, the VIX would also collapse. Again, a stupid example. But the math doesn't lie. Of course, the historical behavior of markets is that things don't move in a straight line. But for any given period of time, markets can and do move in a straight line.

So to answer your question precisely, "if a large change in price is slow but steady does volatility increase?" one must note how the calculation is made– and one must further appreciate that monotonically increasing or decreasing markets are the very definition of low volatility. The short answer therefore is "NO".

All of this begs for (and rationalizes) why as someone who sees very little value in the S&P, I am still making some nice returns by owning short dated call options (and I periodically roll up my strike prices.) This strategy will work until it doesn't. But it's already worked long enough to justify the simplistic assumptions underlying it — which is that I neither want to be the greater fool nor the lesser fool. Just a profitable old fool who plays the hand that I'm dealt. Not the hand which I wish I was dealt. Nor the hand that will be dealt tomorrow.This period will undoubtedly end with fireworks and tears. But when and from where? That NO ONE knows. Keep things stupid and simple….


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