Category: Investing Insight

Investing insight to make you a better investor.

VIX and Equity Index Returns, Part I

shyam November 12, 2018November 13, 2018

The VIX is a measure of implied volatility of the underlying index. For example, the CBOE Volatility Index is a measure of 30-day expected volatility derived from S&P 500 Index call and put option prices, India VIX similarly uses the NIFTY 50 call and put options prices to derive a measure of volatility. The question we will try to address in this series of posts is whether the VIX can be used to time entries and exits on the underlying index.

The VIX time-series

The VIX on S&P 500 has been around since the 90’s whereas India VIX started out around 2009. Moreover, the US enjoys a much wider and deeper market for volatility products than any other market in the world. VIX futures, VIX options, VIX of VIX, volatility ETFs and their inverse, all trade fairly well. Whereas in India, even though VIX futures have been listed for a while, it rarely trades. Trading activity of a derivative (VIX, in this case) invariably has an effect on the underlying (S&P 500, NIFTY 50…) So we expect the relationship between S&P 500 VIX and the S&P 500 index to be closer than that between India VIX and the NIFTY 50 index.

VIX quintiles

To begin, we will bucket the trailing 1000-day VIX closing prices into quintiles and observe the next 5, 10, 15 and 20-day returns of the underlying index over them.
S&P 500 VIX

And, more recently:

What is striking here, is that subsequent returns off the 5th quintile (when VIX is at its highest) is higher with smaller negative outliers than returns off the 1st quintile (when VIX is a its lowest.) This is counter-intuitive to the notion that “volatility begets volatility” so investors are better off staying away from the market when it is volatile.

India VIX and NIFTY 50 shows a similar pattern*:

*Smaller sample compared to the S&P 500 dataset.

A simple back-test

What happens to a long-only portfolio if it is long the index only when the VIX is within a particular quintile?
S&P 500/VIX

The strategy that is long when VIX is in the 5th quintile (L5) out-performs the other quintile strategies. Also, if you ignore the 2008 collapse, L5 has the shallowest of drawdowns.
NIFTY 50/VIX
Something similar happens with NIFTY 50 as well:

Implications

Cash-only investors can point to the superiority of buy&hold compared to these VIX-based strategies. However, the shallow drawdowns exhibited by the L5 strategy (long index when VIX is in the 5th quintile) is attractive to leveraged traders. For example, NIFTY 50 futures leverage is between 8x and 10x. So even if you play it safe and leverage only 5x, L5 returns would end up at ~100% compared to buy&hold’s 80% over the same period.

We will dig deeper in the next part of this series. Stay tuned!

Code and more charts are on github.

Categories Investing Insight Tags backtest, VIX, volatility

Volatility and VIX Charts

shyam November 9, 2018November 9, 2018

Our Volatility and VIX Collection had some charts that were more than two years old. This post updates some of those charts and will re-create them more often.

Volatility can be measured in a number of ways and its profile changes based on the look-back period. The parameters are selected based on what the volatility estimate is used for. Moreover, no two indices exhibit the same profile – traders need to be vary of transplanting trading strategies that work for one market into another.

Historical volatility density plots

20-day historical volatility density plots

20-day historical volatility plots

US S&P 500

Japanese Nikkei 225

Indian NIFTY 50

Implied volatility

Code and a lot more charts are on github.

Categories Investing Insight Tags VIX, volatility

USDINR and Dollar Indices, Part IV

shyam November 6, 2018

Please read Part I for the introduction, Part II for a study of the spread between USDINR and the dollar indices and Part III for a spread-trading back-test on daily returns.

Weekly vs. Daily

In our previous posts, we used daily returns to setup the analysis. However, analyzing daily series on currencies and commodities is problematic. They trade 24/7 in a global marketplace and “closing” prices for commodities and currencies are hard to pin down at a granular level across markets. One way to ameliorate this issue is to use a weekly or a monthly series instead.

Here are the plots of the spreads and p-values from the adf-tests applied to weekly returns:

The back-test results mirror that of the daily series, with bets on momentum carrying through on the USDINR and DTWEXM pairs:

This gives us more confidence in our back-tests. We end our series with the following caveats:

Trading the spread involves trading both legs (as discussed in Part III.)
One can only buy a currency by selling another. i.e., buying USDINR implies going long USD and short INR.
Using the above analysis, if a trade involves buying USDINR in one of the legs, it does not inform anything on relative valuation of USD or INR.

Code and charts on github.

Categories Investing Insight Tags quant, USDINR

USDINR and Dollar Indices, Part III

shyam November 6, 2018November 6, 2018

Please read Part I for the introduction and Part II for a study of the spread between USDINR and the dollar indices.

Trading the spread

In Part II, we defined spread = A – βB. When we say “trade the spread” we literally mean going long or short the spread as defined. To actually implement the trade, one would have to create two legs: one that is long USDINR (A) and the other that is short β times one of the dollar indices (B). Since the dollar indices are not something that can be actually traded, the following back-tests are purely a theoretical exercise.

Back-test

We consider three scenarios:

C1: if the spread diverges beyond 1-sigma, bet on mean-reversion.
C2: if the spread diverges beyond 1-sigma, bet on it getting bigger.
D1: if the spread is between the average and 1-sigma, bet on it blowing out.

The first one is pure convergence and the last one is pure divergence. The second one is sort of like momentum – if the spread is already beyond 1-sigma, bet on it further blowing out.

It appears the second scenario, the one that bets on momentum carrying through, is the most profitable. Also, the most profitable pair seems to be USDINR and DTWEXM (Trade Weighted U.S. Dollar Index: Major Currencies).

In the last part in this series, we will run through this analysis for a weekly time-series of these indices.

Code and charts are on github.

Categories Investing Insight Tags quant, USDINR

USDINR and Dollar Indices, Part II

shyam November 5, 2018November 6, 2018

Please read Part I for the introduction.

In Part I, we saw that if we force the intercept to be zero during linear regression between two series A and B, we end up with A = βB. In this post, we go one step further and define spread = A – βB

Pair trading

Readers of our posts on pair trading will immediately recognize the above relationships. The idea here is that if we assume USDINR to be dependent on DTWEXB, DTWEXM and DTWEXO indices, then we:

calculate the spread between USDINR and each of the indices in turn,
check if the spread is ‘stable’ by conducting an adf test on the residuals of the linear fit and checking if the p-value is less than a threshold,
if the p-values confirm stability, then we can go long/short the spread whenever it deviates from the mean.

Spreads

When we plot the spreads and p-values, we see that a 50-day period is probably the most suitable time-frame over which to calculate the spread. And, we also observe considerable mean-reversion suggesting that a trading model can be built over it.

In Part III, we will back-test a couple of trading models based on these spreads.

Code and charts are on github.

Categories Investing Insight Tags quant, USDINR