Simple Vol Estimators
Given the conditional volatility varies significantly over time it is very useful to generate a VIX proxy for cases where one does not have VIX prices. This includes the past, countries that do not have VIX indices, and even when trying to guess the VIX end-of-day. This latter problem is subtle but important because historical closing VIX prices are taken from the 4:15 ET in the US while the market closes at 4:00, and so using VIX prices for daily strategies can generate a subtle bias when used in daily trading strategies.
VIX
|
Var(VIX)
|
Actual Vol
|
Actual Variance
|
|
1986-2003
|
20.91
|
4.96
|
17.67
|
3.12
|
2004-2019
|
18.20
|
4.05
|
17.99
|
3.24
|
VIX/ActVol
|
Var(VIX)/ActVar
|
|||
1986-2003
|
1.18
|
1.59
|
||
2004-2019
|
1.01
|
1.25
|
As a liquid market price, the VIX is a good benchmark for any equity volatility model. The most common academic way to estimate volatility is some variant of a Garch(1,1) model, which is like an ARMA model of variance:
The problem is that you need to estimate the parameters {w, α, β} using a maximum likelihood function, which is non-trivial in spreadsheets. Further, there is little intuition as to what these parameters should be. We know that α plus β should be less than 1, and that the unconditional variance is w/(1-α-β). That still leaves the model highly sensitive to slight deviations, in that if you misestimate them you often get absurd extrapolations.
Alas, this has two problems. First, there is a predictable bias in the EWMA because it ignores mean reversion in volatility. Garch models address this via the intercept term, but as mentioned it is tricky to estimate and creates non-intuitive and highly sensitive parameters. We can see this bias by sorting the data by VIX into deciles, and take the average EWMA, where the relative difference in the VIX and the EWMA increases the lower the EWMA. As this bias is fairly linear, we can correct for this via the function
VIX | EWMA | EWMA* | |
Low | 11.1 | 8.1 | 10.6 |
2 | 12.7 | 10.2 | 13.2 |
3 | 14.0 | 11.4 | 14.7 |
4 | 15.6 | 12.4 | 15.8 |
5 | 17.1 | 13.4 | 16.9 |
6 | 18.7 | 15.0 | 18.7 |
7 | 20.7 | 17.3 | 21.2 |
8 | 23.0 | 19.1 | 23.1 |
9 | 25.9 | 21.3 | 25.3 |
High | 40.3 | 39.5 | 39.7 |
There are a couple of good reasons for this. As recessions imply systematic economic problems, there’s always a chance that negative news is not just a disappointment, but reveals a flaw in your deepest assumptions (e.g., did you know you don’t need 20% down to buy a house anymore?). This does not happen in commodities because for many of these markets higher prices are correlated with bad news, such as oil shocks or inflation increases. Another problem is that many large-cap companies are built primarily of exponential growth assumptions. Companies like Tesla and Amazon need large sustained growth rates to justify their valuations, so any decline could mean an inflection point to normal growth, lowering their value by 90%. Again, this has no relevance for commodities.
VIX
|
EricVol
|
EWMA
|
|
Low
|
11.1
|
10.8
|
8.1
|
2
|
12.7
|
13.6
|
10.2
|
3
|
14.0
|
15.0
|
11.4
|
4
|
15.6
|
16.1
|
12.4
|
5
|
17.1
|
17.2
|
13.4
|
6
|
18.7
|
19.2
|
15.0
|
7
|
20.7
|
21.9
|
17.3
|
8
|
23.0
|
24.0
|
19.1
|
9
|
25.9
|
26.7
|
21.3
|
High
|
40.3
|
43.2
|
39.5
|
EWMA
|
EricVol
|
|
2008
|
29%
|
82%
|
Oct-08
|
-19%
|
84%
|
total
|
37%
|
75%
|
VIX
|
EWMA |
EricVol
|
|
day-ahead
|
33.0%
|
26.9%
|
34.3%
|
Month-ahead
|
61.1%
|
58.4%
|
61.8%
|
If we look at regressions that predict future variance given our estimates, we see EricVol is significantly better than a simple EWMA. While it does slightly better than the VIX, I doubt this generates significant profits trading, say, the VXX, though readers are free to try.
Source: http://falkenblog.blogspot.com/2020/02/simple-vol-estimators.html
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