今天看到AQR的Cliff一篇评论，主要观点是VIX主要是和历史已实现波动率有关，并不能比历史已实现波动率告诉我们更多的关于未来的信息。
If anyone reading this has always meant “recent realized return volatility” when commenting on the VIX, and has never attached much importance to it beyond that, please stop reading as the below has little point for you. But if you think the VIX is much deeper than that, read on!
It has become quite commonplace to note that the VIX is very low and to worry about it. Indeed, the VIX really is very low right now (i.e., less than 1st percentile low). I tend to think this is less of a worry than most (not that there aren’t other nice things to worry about, and it’s hard to disentangle them all as they are often versions of the same thing). But this note isn’t about that. It’s about a much simpler, smaller, but still important, issue — that when people talk about the VIX they are almost entirely talking about recent realized volatility. But somehow, because the VIX is a current forward looking measure (really a type of price) people seem to attach more to it than that. To simply just say, “things have not been bouncing around a lot lately” doesn’t quite sound like a damning indictment of current complacency as much as just a fact. Yet the VIX and realized volatility are almost entirely the same thing.
If you regress the VIX on the realized volatility over the prior month, you get a 78% R-squared. If you extend the regression to also include a slightly longer measure of realized volatility (60-day volatility) the R-squared goes up a bit to 82% and the regression results look like this2:
VIX = 6.7 + 0.44 * 20-day Volatility + 0.37 * 60-day Volatility3
The observed values today (intra-day 7/27/2017 when I wrote this) are a VIX of 10.3, a realized 20-day volatility of 6.9, and a realized 60-day volatility of 7.3. Using the above model, the forecasted VIX today is 12.4. So indeed today’s VIX of 10.3 is a bit low vs. this model’s best guess. That 10.3 versus 12.4 is a -0.6 standard deviation event error in case you are wondering (meaning the VIX is not shockingly low at all versus the model’s forecast). So if people want to worry that the VIX is -0.6 more complacent than usual at these levels of realized volatility, go for it.
More importantly, it’s perfectly fine to comment on realized volatility being very low and to worry about that. But we shouldn’t think the VIX is telling us more than that.4 And, importantly, I do think when commentators discuss the VIX they often think it has more import and gravitas than it really does. The VIX tells us almost nothing beyond how much markets have been bouncing around lately. So, instead of saying “the VIX is shockingly low” why not say “markets have been shockingly calm lately”? If you agree the latter is what you're really saying, we are simpatico. If you believe that says the same thing about investor complacency, great.
而我上周提到的，隐含波动率和未来的已实现波动率关系不大，也就是说VIX并不能很好的预测未来，本质上和上述观点类似，我认为VIX是当期交易员对未来市场的判断，但他们这种判断到底准不准谁也不好说。但是看了上面这个评论，我应该很高的描述自己的观点。VIX并不能比历史已实现波动率提供更多关于未来的信息，期权交易员的观点并不比其他市场参与者更高明。
下面我也做点实证：R-squared 0.632054
Variable Coefficient Std. Error t-Statistic Prob.
C 0.091504 0.005421 16.87900 0.0000
C2C_20_RV 0.812672 0.034881 23.29855 0.0000
不过，正如前面说的，ivix不是平稳序列，也很难证明自己是有意义的。
隐含波动率和历史已实现波动率
今天看到AQR的Cliff一篇评论，主要观点是VIX主要是和历史已实现波动率有关，并不能比历史已实现波动率告诉我们更多的关于未来的信息。
而我上周提到的，隐含波动率和未来的已实现波动率关系不大，也就是说VIX并不能很好的预测未来，本质上和上述观点类似，我认为VIX是当期交易员对未来市场的判断，但他们这种判断到底准不准谁也不好说。但是看了上面这个评论，我应该很高的描述自己的观点。VIX并不能比历史已实现波动率提供更多关于未来的信息，期权交易员的观点并不比其他市场参与者更高明。
下面我也做点实证：R-squared 0.632054
Variable Coefficient Std. Error t-Statistic Prob.
C 0.091504 0.005421 16.87900 0.0000
C2C_20_RV 0.812672 0.034881 23.29855 0.0000
不过，正如前面说的，ivix不是平稳序列，也很难证明自己是有意义的。