Tag: correlation

The Shifting Sands of Auto-Correlation

Autocorrelation represents the degree of similarity between a given time series and a lagged version of itself over successive time intervals. Our previous post on using run length encoding discussed how you can inspect the streakiness of returns. ACF allows you to inspect the relationship between day-0 and day-n returns.

Let’s have a look at the ACF of NIFTY and BANKNIFTY returns. Here is a plot of the ACFs of both real returns and up/down returns in 2015.

Zoom into the up/down ACF of NIFTY, see how day-0 direction correlates strongly to day-1, day-2 and day-3? Combine this with what we got from running an rle and you might just have a trend-following strategy.

Before we run off to make our millions, lets see how other years faired. Enter 2021.

While NIFTY’s day-0 direction correlates strongly to day-1, it is the inverse of day-2’s and day-3’s. Did it become mean-reversion-y? One implication of this give-up is that a trend model tuned to work well with 2015 data is unlikely to repeat its performance in 2021.

However, ACFs from 2015 through 2021 have day-1 correlations as always positive. What if you just bet that an up day will be followed by another up day and vice versa?

MSCI Country Momentum Index Correlations

In MSCI Country Index Correlations, we looked at country index correlations through time. Here is a quick update that “flattens” out the rolling correlation of the momentum versions of these indices with the MSCI INDIA MOMENTUM Index.

Three-year Rolling Correlations

MSCI Country Momentum Index 3-year Rolling Correlations

Five-year Rolling Correlations

MSCI Country Momentum Index 5-year Rolling Correlations


Momentum is a lose proxy for sentiment and the tides of optimism floats all boats. All equity markets are correlated with each other – some strongly (HONG KONG) and some weakly (CANADA.)

The median correlations across both 3- and 5-year rolling periods are greater than +0.70 between INDIA MOMENTUM and EMERGING MARKETS MOMENTUM.

Cumulative Returns of INDIA and EM MOMENTUM (MSCI)

No market is an island. Sentiment is tail that wags the dog.

MSCI Country Index Correlations

All stocks are correlated to one-another. In times of crisis, these correlations explode higher. The same is true for country indices. For example, if you look at the rolling 5-year monthly return correlations between the MSCI INDIA index and other country indices, Jordan is the least correlated and Hong Kong is the most correlated.

Least Correlated:
least correlated with INDIA

Most Correlated:
mostcorrelated with INDIA

The annual return charts show the zig/zag nature of these markets:

So, does it make sense to construct a 50/50 portfolio between INDIA and JORDAN? In theory, the resulting portfolio should have lower draw-downs and lesser volatility than either taken alone.

In contrast, here is the 50/50 INDIA/HONG KONG portfolio:

A take-away from this is that diversification within the same asset class (in this case equities,) does not help with drawdowns. Nor does it necessarily lead to higher returns. It is way of protecting yourself from mistakes that are only apparent in hindsight. Just ask investors who were invested 100% in Jordan the last decade.

Code and charts on github.
Related: Stock and Bond Correlations and Volatility

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



Macro: NIFTY vs. INR/OIL Correlation, Part III

This is the last part of the study. Part I, Part II

The reason why a linear model between NIFTY and USDINR built in Part II failed could have been because:

  1. Weekly returns were not appropriate for the relationship. Perhaps INR affects NIFTY at a higher frequency.
  2. There is no linear relationship because a rising/falling INR. Changes are not uniformly good/bad.

One way to visualize it is to plot the NIFTY returns density at different USDINR return thresholds. If there is no obvious difference in the densities between NIFTY returns when USDINR is positive vs. when it is negative, one could conclude that there is no straight forward relationship between the two.

Here is the NIFTY weekly returns density when USDINR is going up (the rupee is depreciating):
density plot NIFTY vs. USDINR
Note the curve when USDINR weekly returns are greater than 0.5% vs. when are greater than 2%. There is a bearish bias.

And, NIFTY weekly returns density when USDINR is going down (the rupee is appreciating):
density plot NIFTY vs. USDINR

If you juxtapose the above densities, it is apparent that when the rupee is appreciating, the densities skew right, And when the rupee is depreciating, there is a left skew. These charts show that there is “a” relationship – just not what can be captured by a linear model.

Code and density plots for NIFTY vs. OIL can be found on github.