Probably the reason why banks have been reluctant to pass on rate-cuts is because the yield curve has been flat as a pancake. The difference between short-term and long-term rates are near their historical lows.
Category: Investing Insight
Investing insight to make you a better investor.
GARCH(1,1)
GARCH(1,1) is a common approach for modeling volatility. They were developed by Robert Engle to deal with the problem of auto-correlated residuals (which occurs when you have volatility clustering, for example) in time-series regression.
What we did:
- Picked the best fit ARIMA(p,d,q) model for historical VIX over different look back periods
- Created a GARCH(1,1) model based on ARMA(p,q)
- Predicted t+1 VIX
500-day lookback
We found that modeling based on the previous 500-day VIX closing levels gave us the least prediction errors. The appendix has the charts for other lookback periods.
Prediction vs. Actual
Note how in some periods, the predicted value (red) is just the previous value.
Prediction error
Values less than zero implies that the model prediction overshoots the actual VIX level the next day.
Prediction vs. Actual Density Plot
The model bias towards higher estimation of VIX is made explicit here.
Next steps
We will integrate this model to our morning ‘Options Daily’ posts so that we get an idea of both the current state of VIX and the expected modeled behavior.
Caveats:
- The 500-day lookback is purely empirical. Maybe some other look-back period that we have not tested would have been ideal to model. We will never know.
- Only the known history can be modeled. The outputs should be used along with market determined proxies of expected volatility.
- There is always a probability distribution around a predicted value. We will publish this in our daily posts.
Appendix
VIX Model vs. Actual across various lookback periods. (pdf)
Volatility Forecasting I: GARCH Models, Rob Reider (pdf)
The iShares MSCI India ETF (INDA) tracks the MSCI India Total Return Index, representing about 85% of the Indian stock market. As a follow up to our earlier post on the historical volatility of the NIFTY 
, we thought we’ll compare the volatilities of INDA and SPY, the S&P 500 ETF.
10-day volatility:
50-day volatility:
As expected, a dollar denominated emerging market ETF is more volatile than the S&P. File this away in your brain attic.
Was 2014 an anomaly?
Here’s a density plot of NIFTY volatility across 10-, 20-, 30-, and 50-day periods:
And here’s how it was in 2004 (10-years ago):
For those of who argue that the introduction of the pre-open auction call in 2010 skews these results, here’s how 2011 looked like:
The unprecedented absence of a second “hump” in the volatility density plot for 2014 should give pause to investors looking for a repeat of 2014 anytime soon.
Reversion to higher volatility?
If you look at the 50-day volatility over different time-periods, you can observe how volatile volatility is:
This year’s observed volatility is closer to last-year’s than to its long-term mean. Here’s how 2015 has panned out so far:
We should expect higher volatility as the initial bull-run wears off and volatility reverts. This will have a ripple effect on pretty much every investment/trading strategy.
Appendix
Year-wise NIFTY volatility density plots (pdf)
Came across an interesting paper: Will My Risk Parity Strategy Outperform? Robert M. Anderson, Stephen W. Bianchi, CFA, and Lisa R. Goldberg. Even though they discuss risk parity, they make some pretty interesting points that relate to all investment strategies.
Today’s alpha is tomorrow’s beta
… the introduction of new securities can have an indirect effect; a strategy that was seemingly profitable in the past might have been less profitable if the new securities had been available and thus made the strategy accessible to a broader class of investors.
Before index ETFs, there was no cost-effective way of replicating an index. For example, NIFTYBEES was listed in 2002 and came with an expense ratio of 0.80% while retail brokerage charges were in the 0.5-1.0% range. Replicating the NIFTY index before NIFTYBEES came around was expensive. So any backtest before 2002 that that tries to argue the benefits of buying-and-holding an index ETF is likely bogus. Similarly, today’s active management strategies available to a select few hedge-fund investors are tomorrow’s “smart beta” ETFs that will be available to anybody with a demat account.
Leverage is an external source of risk
The notion that levering a low-risk portfolio might be worthwhile dates back to Black, Jensen, and Scholes (1972), who provided empirical evidence that the risk-adjusted returns of low-beta equities are higher than the CAPM would predict.
There are periods when banks pull their lines of credit based on macro factors that has nothing to do with your strategy. For example, during the 2008 financial crisis, your bank/broker would have pulled your credit lines forcing you to sell near the bottom and preventing you from buying the bounce. Any strategy that uses leverage – risk-parity, for example – should factor this risk.
Performance depends materially on the backtesting period
Even if we were reasonably confident that one strategy achieved higher expected returns than another without incurring extra risk, it would be entirely possible for the weaker strategy to outperform over periods of several decades, certainly beyond the investment horizon of most individuals…
Besides, most strategies have a rebalancing frequency – once a month, once a year, and so on. The specific day you choose to rebalance can have a material impact on your strategy. For example, rebalancing during options expiry, corporate events, etc… can meaningfully skew your risk/returns.
Borrowing and trading costs can negate outperformance
Value-weighted strategies require rebalancing only in response to a limited set of events. The risk parity and 60/40 strategies require additional rebalancing in response to price changes and thus have higher turnover rates. Leverage exacerbates turnover.
There is huge execution risk involved in strategies that requires shorting of shares. Given the regulations surrounding SLBS – lending/borrowing allowed only on those securities that are listed in F&O and that too only in increments of lot-sizes – the friction involved in shorting stocks are prohibitive.
Execution drift
There is likely going to be a big difference between model execution prices and actual execution prices. For example, when we rebalance our Themes, we use the latest available price in our database. These prices themselves could be stale by over 10 minutes. These changes then have to percolate down to investors who execute them in the market. From start to finish, there could be a price gap of over 20 minutes – a significant source of drift between the ideal P&L and actual P&L.
Conclusion
Investors should have a deployment checklist for their strategies that addresses the issues raised above. What we have found is that most strategies that look good on a simple backtest don’t look that great when costs, variable periods, drift and half-lives are factored in.