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
Take-away
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.
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.
Earlier this year, AQR had published a paper that showed momentum behavior also exists in equity factors (like value, quality, etc.) and not just in vanilla equities.
In this article, the authors document robust momentum behavior in a large collection of 65 widely-studied, characteristic-based equity factors around the globe. They show that, in general, individual factors can be reliably timed based on their own recent performance. A time series “factor momentum” portfolio that combines timing strategies of all factors earns an annual Sharpe ratio of 0.84. Factor momentum adds significant incremental performance to investment strategies that employ traditional momentum, industry momentum, value, and other commonly studied factors. Their results demonstrate that the momentum phenomenon is driven in large part by persistence in common return factors and not solely by persistence in idiosyncratic stock performance.
Factor Momentum Everywhere – Tarun Gupta, Bryan T. Kelly (AQR)
We put this idea to the test by constructing a long-only portfolio with five of the strongest factors – Momentum, Quality, Low-volatility, Value and Small-cap. The strategy was to go long whatever factor had the best returns over the last 12-months. We also looked at going long the best factor from the previous month. In both cases, the portfolio was re-balanced every month.
The strategy using a 12-month formation period was a disappointment. There was no discernible improvement over a buy-and-hold of the large-cap index.
India (12-month Formation) US (12-month Formation)
However, the one-month formation period widely out-performed the large-cap benchmark.
India (1-month Formation)US (1-month Formation)
Needless to say, shorter the look-back period, larger the number of trades. So we added another back-test that averaged factor returns over 6-through-12 months to check if there was an acceptable middle-ground. Turns out, there is.
India (6..12-month Formation) US (6..12-month Formation)
Forward Test
We setup US portfolios back in May this year when we first got to know about this paper. The 12-month and the 6…12-month formation period portfolios can be found here and here. They both seem to have out-performed SPY and MTUM so far.
We constructed the Factor Momentum 6-12 Theme for Indian equities that tracks the last strategy outlined above but given the lack of liquidity in factor ETFs, it trades the underlying stocks directly.
Investing in Factor Momentum
Indian investors can use brokers like TD Ameritrade or Interactive Brokers to invest in US stocks. The trades are posted on the slack channel mentioned on the pages linked above. You can execute the trades yourself by monitoring the messages on the channel.
If you are interested in executing this strategy on Indian equities, talk to us!
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
NIFTY ALPHA 50 TR vs NIFTY 50 TRNIFTY100 ALPHA 30 TR vs NIFTY 50 TRNIFTY ALPHA 50 TR vs NIFTY100 ALPHA 30 TR
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
Conclusion
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!
A wise man once said, the decision to go passive is a very active one.
At first, going passive meant buying and holding a broad-based index fund. But that was over 40 years ago. Since then, in the US, the market has evolved and the number of indices, index funds and ETFs have exploded. Think of a theme, strategy, asset class, market or geography, there is an ETF for that.
As of today, there are 2,319 ETFs in the US. And given the intense competition over the last decade, fees have been driven to single-digit basis-points in most cases. Given this fee pressure, US based issuers looked east and landed on Europe a couple of years ago. And there too, competition quickly reduced fees and expanded access.
The next big virgin market is India.
Given this back drop and the small but increasing interest in passive indexing, if a DIY investor wishes to just buy and hold a market-cap based index, which one should she buy?
The most practical choices boil down to NIFTY 50, NIFTY NEXT 50 (collectively forming the NIFTY 100) and the NIFTY 500 indices.
Given the fee differentials between the NIFTY 100 and NIFTY 500 based ETFs/funds, the big question to ask is: Is there any advantage of reaching below the 100 mark? Is 100 enough?
Market-caps follow a power-law. For NIFTY 100, 80% of the index is covered by the top 35 stocks and for NIFTY 500, the number is 82. So unless the rest of the stocks in the index deviate to an extreme degree in terms of total returns (change in price + dividends,) the top 35/80 stocks power most of the returns.
Cumulative ReturnsAnnual Returns
So, the answer is No. Unless NIFTY 500 based ETFs/funds achieve fee and liquidity parity with the NIFTY 100 based ones, investors are not missing out on anything by sticking with the mega-caps.
Check out the goodies on pluto. Questions? Slack me!
