Tag: volatility

Volatility and Equity Index Returns

The VIX is a poor proxy for volatility, and so is standard deviation and Sharpe Ratios that treat downside volatility the same as upside volatility. Long-only investors don’t mind a bit of volatility as long as the numbers go up. Its the drawdowns that are usually terrifying.

Does swapping symmetrical volatility measures with something that measures only downside volatility make sense?

Enter the Omega Ratio: bucket the ratio into quintiles, map each quintile to an exposure. Lower the ratio, lower the exposure (outline).

    We get lower drawdowns (almost cut in half) and higher Sharpe Ratios but with lower returns for the most part. This strategy makes most sense for the NIFTY 50 and not so much for NIFTY500 MOMENTUM 50.

    While NIFTY 50 drawdowns are low, is a 20% drop something that can be leveraged?

    We also ran a sensitivity test on DRAG to see how transaction cost assumptions impact the strategy. We found that it actually impacts the lookback that is selected from the training set.

    We expect transaction costs to range 25-50bps so the flipping around of lookbacks is worrisome.

    The tl;dr is that reducing volatility comes at a cost and you pay it both in terms of reduced returns and transaction costs.

    Code and charts on github.

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    Changepoints vs. Buy & Hold

    A changepoint is a point in time where the statistical properties of a sequence change. For financial return series this typically means the mean, variance, or distribution of returns shifts — a stock that was trending sideways suddenly becomes volatile, or a calm market enters a turbulent regime.

    Can we use changepoint detection to time exposure to the market and beat simple buy-and-hold, on a risk-adjusted basis, on India’s NIFTY indices?

    First, we calculated an aggregate score using different changepoint algorithms to classify the return-series. This was done with both a sliding window and an expanding window of data.

    Then, we tried the simplest use of the signal: be fully invested when STABLE, fully out when UNSTABLE. This binary approach underperformed buy-and-hold badly, on both return and Sharpe ratio, on every index.

    Throughout the process, we kept a 50-day SMA as the base case to beat. It is a simple totem to keep us honest about the complexity vs. efficacy trade-off.

    The problem with this binary approach is that volatility clusters – the worst days and the best days tend to occur together. However, changepoint is backward looking so you will end up catching the worst days and missing out on the best days.

    To fix this, we added a direction condition: only treat instability as a reason to exit if the market is also in a downtrend (price below its 50-day moving average). Otherwise, stay invested through volatile-but-rising periods. It removes the worst part of the filter – exiting during uptrends.

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    The next step was to remove the binary nature of the strategy: size the position by mapping it to model confidence [0,1] and sizing only when the market is in a downtrend (close < 50-day MA); in uptrends, stay fully invested regardless of volatility.

    metrics

    This is how we narrowed in on Direction-Gated Continuous Sizing.

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    Sadly, using this technique instead of a basic SMA only made sense with the NIFTY 50 index. In every other situation, SMA won.

    You can dig deeper here. Code and charts are on github.

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    VVIX for VIX

    Came across an intriguing post by Markku Kurtti: Employing volatility of volatility in long-term volatility forecasts (outcastbeta). The gist of it is that the volatility of volatility and average volatility is more predictable. So, predict them separately and then put them together to get a volatility forecast.

    Our previous attempts at forecasting VIX have led us the conclude that nothing beats locf. Just extending the last value of VIX forward has beaten all of the models we’ve looked at.

    What if, we applied the process outlined in Mr. Kurtti’s blog for VIX?

    Not looking so good if you forecast out for 20-days.

    A good forecasting model should be able to estimate large spikes and reversion to mean from them. If not the former, then at least the latter. So, if a model is good at the mean-reverting bit, then you can combine both locf and the model to get better predictions.

    For example, if you only consider the 1-day forecast, then obviously locf has the upper hand.

    However, as you try to predict farther away, you expect the model to nail the mean-reversion bit.

    That is not the case here.

    Once again, locf wins.

    Code and charts up on github.

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    CGMM for VIX

    Previously, we explored using Meta’s Prophet library to predict VIX. It turned out that simply extrapolating the last value of the index worked better (Prophet for VIX). In fact, locf (last one carried forward) works better than GARCH(1, 1) and most other approaches. Can the same be said about Conditional Gaussian Mixture Models?

    We used the cgmm python library to forecast 20-day forward VIX and compared its root-mean-squared errors (rmse) to those of locf‘s.

    locf is pretty hard to beat.

    Especially so when the VIX index itself is volatile.

    Code up on github.

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    The Smirk, Part II

    While the concept of volatility smirk is simple, the pattern itself is unstable. For example, different expiries have different shapes.

    And these shapes change across days as well.

    One way to keep track of these changes is by fitting a model through the implied volatilities. Here, we fit a parabola (y = ax2 + bx + c). a, the coefficient of strike_pct2, gives a measure of the narrowness/steepness of the smirk.

    By sampling the curve and tracking these coefficients, you can begin to form an opinion on what is “normal” vs. a trading opportunity.

    Code and charts on github.

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