Tag: volatility

Volatility and Returns

Indian mid-caps, represented by the NIFTY MIDCAP 100 TR index, has out-performed its large-cap peer, the NIFTY 50 TR index.

It has done so with higher volatility. Here is the rolling 200-week standard deviation of weekly returns of the two indices:
standard deviation of weekly returns

MIDCAP volatility has been persistently higher than NIFTY volatility in the past:
ratio of standard deviations

A portfolio of bonds and mid-caps should exhibit lower volatility than an all-equity portfolio. Here are the standard-deviation ratios for different allocations to bonds:
standard deviation ratios of different bond allocations
B05, for example, represents a portfolio of 5% short-term bonds and 95% MIDCAP index. As allocation to bonds increases, portfolio volatility decreases.

We see from the chart above that a 75% MIDCAP + 25% BOND portfolio has almost never seen volatility greater than an all NIFTY portfolio. So, what are we giving up in returns to reduce volatility? About 2% in returns:

75% MIDCAP + 25% BOND returns


  1. On an annualized basis, the allocation portfolio gives up about 2% in returns compared to all MIDCAP portfolio and is on par with NIFTY’s.
  2. After taxes and transaction costs, expect the allocation portfolio to under-perform buy-and-hold NIFTY.
  3. No pain. No gain.

Code and charts are on github.

Is the Low Volatility Regime Breaking?

NIFTY 50 volatility the last couple of years have been extremely low by historical standards. If you look at the rolling median of weekly returns over 50 weeks (about a year), you can see how the range has narrowed:
median weekly returns
The standard deviation, a popular measure of volatility, has come down as well:
standard deviation of weekly returns

As the charts illustrate, the markets have been moving in tight ranges. And narratives have been built around it:

  1. Global central banks (US, Europe, Japan) have been flooding the markets with liquidity, essentially writing a put on the market.
  2. Markets have become less riskier thanks to increased regulations after the 2008 global financial crisis.
  3. Investors have a new-found enthusiasm for “SIP it and forget it.” This, plus the NPS bid, has cushioned the NIFTY 50.
  4. Increased liquidity in the derivatives market has allowed investors to buy volatility, thereby reducing the need to decrease risk by offloading equities in the cash market.
  5. The majority government at the center has provided policy certainty and political scams have not paralyzed decision making.

Narratives can change overnight. And if the last few months have taught us anything, the market drives the narrative. Also, new investors have only seen a low volatility environment and think it to be “normal.” So any reversion to the old volatility regime would be a rude awakening. Are we really in a new world or is volatility about to revert to its longer-term mean?

Code and additional charts on github.
Also read our Volatility Collection.

Stock and Bond Correlations and Volatility

Stocks and Bonds are not correlated. They are not negatively correlated. And neither are they positively correlated. One doesn’t “zig” when the other “zags.” This is exactly why portfolio allocations start with stocks and bonds – the diversification math works on uncorrelated asset classes. When you combine the two assets together you get lower portfolio volatility.

Here are some charts that show how the two asset classes differ:

S&P 500 and 3-month t-bills



Nifty 50 and 0-5 year TRI



Country Equity Index Volatility

Previously, we saw how different country indices performed relative to their deepest drawdowns. Peak drawdowns only tell half the story. Here, we look at historical volatility. To keep things simple, we will define volatility as the standard deviation of daily returns. i.e., close-to-close volatility.

The country-ticker key can be found here.

2004 through 2018



Bar plot:
Heat map:


  1. The year 2017 was uniformly a low-volatility year. So were 2005 and 2014.
  2. Some countries, Greece (NQGRT) for example, have been extremely volatile. Some, Malaysia (NQMYT) for example, have been surprisingly less.
  3. India (NQINT) has been middle of the pack.

Code and charts on github.

Source: NASDAQOMX data from Quandl.

VIX and Equity Index Returns, Part II

Please read Part I for the introduction.

Holding-period back-test

In Part I, we ran a quick back-test that would go long the equity index if the VIX was in a certain quintile and saw how the 5th quintile produced the lowest draw-down returns. The index was held only for a day. However, our box-plot of VIX quintile vs. subsequent n-day returns begs us to look at alternate holding periods as well. What would the returns be if we held onto the index beyond a day?

Here is how long-only S&P 500 returns when VIX is in the 5th quintile, across different holding periods looks like:
S&P 500 returns

The problem with this strategy is that when there is a steep fall in the index, the VIX keeps going higher and will be in the 5th quintile for an extended period of time. Have a look at the 2008-2009 segment in this chart:
VIX quintiles over S&P 500

What happens if we used the change in VIX to time the equity index?

VIX returns deciles

If we bucket VIX returns (percentage change over previous close over n-days, 1000 trailing observations) into deciles and observe the next 5, 10, 15 and 20-day returns of the underlying index over them:
S&P 500 returns over changes in VIX

There is no determinable pattern here. Perhaps the VIX and the index are co-incident with none holding the power of prediction over the other.

Interested readers can browse the github repo for corresponding Nikkei 225 and NIFTY 50 charts.