Tag: volatility

Volatility and Returns of Momentum Indices

The standard deviation over 200-days and future 20-day returns from 2010 through 2015 of NIFTY MIDCAP150 MOMENTUM 50 TR and NIFTY200 MOMENTUM 30 TR looks like this:

Can historical volatility, as measured by standard deviation, be used to enter and exit momentum strategies?

On a rolling basis, there doesn’t seem to be a strong correlation between historical volatility and future returns. Back-tests over this period might give you a config that might look like it works but it is probably a fluke.

Given that liquid ETFs for these indices are not available and we are stuck with index funds for the foreseeable future, we setup a back-test to calculate the 200-day std. dev. at the end of each month to decide whether to hold it for the next month. Needless to say, the results were pretty lackluster.

We chose the 2010-2015 period because it avoids the 2008 crash and the subsequent recovery. The back-tests look phenomenal when you include that data but we wanted to see how such a strategy would perform in “normal” markets before stress-testing it. We don’t want to be the generals always fighting the last war.

Code & charts: github


90 days of Minimum Volatility

We had discussed portfolios optimized for minimum volatility back in January (see: Low Volatility: Stock vs. Portfolio) and had setup Themes that track such strategies. Broadly, these fall into ETL (Expected Tail Loss) and Min-Var (Minimum Variance) optimized portfolios that either take in the entire universe of stocks or only those that have a high momentum score. So, we have Minimum Expected Tail Loss, Minimum Variance, Momentum (Min-ETL) and Momentum (Min-Variance).

We expect optimized portfolios of momentum stocks to perform better during market up-trends. During bears, we expect them to have lower drawdowns than the market. The Corona Virus Panic put these portfolios in through the wringer. Glad to report that they came out largely unscathed.

Minimum Volatility Portfolios vs. NIFTY 50

Our back-tests showed that optimized momentum portfolio would under-perform “raw” momentum during up-trends but should have lower drawdowns during down-trends.

Momentum: Optimized vs. raw

Optimized momentum portfolios saved the investor about 3-4% in drawdowns compared to the “raw” momentum portfolio. May not sound like much in this instance but think about the cumulative effect over multiple market corrections when you invest for the long-term.

Overall, optimized portfolios delivered what they promised.

WhatsApp us at +91-80-26650232 if you are interested in knowing more about these strategies.

Low Volatility: Stock vs. Portfolio

Lower the Risk, Higher the Returns?

Typically, investors expect higher returns from high risk investments compared to low risk ones. However, realized returns are the opposite of what they expect.

High Beta vs. Low Vol

This anomaly, where lower risk systematically results in higher returns, has spawned a number of “betting against beta” strategies. A common approach is to rank a universe of stocks by volatility and create a portfolio off the top-N. However, this approach could lead to a highly volatile portfolio if relative correlations are not considered.

1+1 = 0

Here are two stocks with their volatility plotted against time:

correlated low-vol stocks

If you create a portfolio off these two stocks, what happens to portfolio volatility?

A portfolio made off low-vol stocks can be high vol

In the worst case scenario, where all the volatilities are correlated, portfolio volatility can end up being a sum of all component volatility.

If low-vol stocks can create a high-vol portfolio, can high-vol stocks create a low-vol portfolio? Yes! It all depends on how the volatilities are correlated.

inversely correlated high-vol stocks

In the best case scenario, portfolio volatility can be a very low constant value if the components are inversely correlated.

a low-vol portfolio created off volatile components

It doesn’t matter if individual volatilities are high or low. What matters is the correlation of volatilities.

Portfolio Optimization

A simple ranking of stocks will not help in creating a low-vol portfolio. What we need is a holistic approach that considers the correlation of volatilities and optimizes the entire portfolio.

One way to go about this is to use gradient descent. Start with a random portfolio and go in the direction that minimizes variance (min-var) or expected tail loss (min-ETL)

min-var and min-ETL backtest

With a monthly rebalance, the chances of the portfolio getting trapped in a local-minima are low. And the backtest looks promising.

Investing in Low-Volatility Portfolios

Equity investors can map our Minimum Variance and Minimum ETL Themes to their portfolios to gain exposure to these low-vol strategies.

Reducing Crash Risk in the Nifty Alpha Indices

The NSE has a couple of strategy indices – the NIFTY Alpha 50 Index and the NIFTY100 Alpha 30 Index – based on historical CAPM alphas. The former selects 50 stocks from the largest 300 stocks whereas the latter selects 30 stocks from the NIFTY 100 index.

First, a look at a simple buy-and-hold strategy.

Buy-and-Hold Curves


The alpha indices have out-performed the plain-vanilla NIFTY 50. However, what jumps out off the page is the sheer depth and length of the drawdows that these indices have made.

Even though they give vastly better returns than the NIFTY 50 index, the lived experience would be too painful for most investors. Is there a way to reduce these drawdowns while retaining most of the out-performance?

In a 2012 paper, Momentum has its moments, Barroso and Santa-Clara outline a way in which historical volatility could be used to reduce momentum crashes.

Strategy Outline

The basic idea is that momentum risk is time-varying and sticky. And, periods of high risk are followed by low returns.

rolling 100-day sd
rolling 200-day sd

To test this theory out on the Alpha indices, we first split the time series into halves. The first to “train” and the second to “test.” We need a training set because we are not sure what the appropriate look-back for calculating risk should be (we check 100- and 200-days). The test set is a check of out-of-sample behavior of the strategy.

The theory laid out in the paper, that periods of high risk is followed by periods of low returns, is true. Subsequent returns when std. dev. is in the bottom deciles show large negative bias. Also, perhaps indicating a bit of mean-reversion, returns after std. dev. is in the 7-9th decile, have fat right tails.

NIFTY ALPHA 50 200-day cumulative returns by 200-day sd decile
NIFTY100 ALPHA 30 200-day cumulative returns by 200-day sd decile

Train In-Sample

The next question is the appropriate lookback and deciles for calculating the std. dev. Running this on the training set, we find:

training set: NIFTY ALPHA 50 – 200
training set: NIFTY100 ALPHA 30 – 200
training results

A strategy that goes long Alpha when std. dev. is in the 1-5 deciles side-steps severe drawdowns in the training set. Note, however, that it under-performed buy-and-hold during the melt-up of 2007.

Test Out-of-Sample

Applying a 200-day lookback on both the indices over the test set, we find that the strategy continues to side-step drawdowns but no longer out-performs buy-and-hold by a large margin.

test set: NIFTY ALPHA 50 – 200
test set: NIFTY100 ALPHA 30 – 200
test results


Using historical volatility (std. dev.) reduces drawdown risk in Alpha indices. But it comes at the cost of reduced overall returns over buy-and-hold over certain holding periods. However, given the magnitude of the dodge in 2008 and 2016, it is well worth the effort (and cost) if it helps keep the discipline.

Check out the code for this analysis on pluto. Questions? Slack me!

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.