Momentum Investing: How many stocks is too many / too few?Momentum Investing: How many stocks is too many / too few?

In Short

• Diversification i.e. holding a varied portfolio of stocks is a key tenet of investment risk management
• However, diversification has its limits and only counters individual company risk (Gitanjali Gems, Jet Airways, DHLF) and not systematic risk (2008 financial crisis)
• Research says a portfolio of at least 30 stocks is needed to be adequately diversified
• We backtest the impact of holding portfolios ranging from small to large number of stocks on portfolio performance and drawdowns

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How many stocks make a diversified portfolio?

First, why diversify? Almost all research into portfolio theory and risk management dives into standard deviations, variances and covariances. None of that is intuitive to most of us.

Let me try with language you and I actually use.

In an ideal world, an active investor would pick their "best stock", and put all their money into it. Why would you add the complexity of handling multiple stocks when you could just buy your highest conviction idea.

Unless you have a working time machine, you will admit the flaw in this reasoning.

You will distribute your money across a few different stocks with the assumption that some of those will move up steadily over time, some will go the other way, the odd stock will take off like a rocket, and the odd stock will go to zero. Overall, you expect the net result to be positive, and hopefully by picking those stocks well, better than the market. Makes sense so far?

Now, what would it take for your effort of spreading money across multiple stocks to be a waste of time? i.e. for all the stocks in your portfolio to move together? This too is intuitive. If your portfolio held every steel stock there is, you might just have a coronary on days when there is a commodity sell-off. To minimize your chances of coronaries, you want to buy stocks that are less likely to move together.

You build a basket of stocks that, as a combination, absorb the shocks that individual stocks experience. Shocks that individual stocks experience? Think Gitanjali Gems, Jet Airways. DHFL. Yes Bank. If one of those was 100% of your portfolio, you're already bankrupt and unlikely to be reading this. If one of them was part of a basket of stocks, you lost some part of your portfolio. Painful, but not fatal.

Diversification ensures you live to worry another day.

But then Bear Sterns and Lehman go bankrupt triggering a recession worldwide, or US drone strikes kill an Iranian general and Iran launches nuclear weapons at the US. Everything falls. Doesn't matter how many stocks you hold. Your portfolio suffers. Unless of course, you also hold Gold, and have a bunch of money stuffed in your mattress. This is Systematic risk, that can not be diversified away by buying more of the same asset class. You have to live with it, or just stay in fixed deposits. Turns out even those aren't necessarily safe as PMC Bank depositors found out.

Diversification can not make all risk disappear.

Now you start to see the problem. When you diversify, less of your money sits in your best investments. So you make less on the upside because you chose to protect yourself from only some of the downside.

There has been extensive research into how many stocks is the right amount of diversification. In the most frequently cited paper on the subject, the author Meir Statman says

"no less than 30 stocks are needed for a well-diversified portfolio"

This is the theory of diversification. But...

Stocks fall together more than they rise together

This chart needs some explanation. Stay with me for a minute. The y-axis is the number of trading days. x-axis is the percentage of universe of Indian stocks from Jan 2005 to Jan 2020.

Look at the center of the chart, the unshaded section where the market spends the majority of its time. Of the 3,700 odd trading days in this sample, on about 400 days, the market was split 50-50 i.e. 50 % of stocks were up, while 50% of stocks were down. (Hover over the red and green lines to see the values)

If the relationship between stock prices held in all conditions, the red and green lines would almost overlap. Or more realistically, they would randomly be above and below each other. But there is a pattern.

Move your cursor over the extreme right of the chart. On 9 days in history 100% of stocks moved up. While 100% stocks moved down on 17 trading days. Almost double the instances.

If you now follow the lines to the left, the number of days on which a "high" percentage of stocks moved down is consistently higher than the number of days on which a "high" percentage of stocks moved up.

As you keep moving left, the relationship reverses. i.e. A higher number of days saw a select few stocks advance than a select few stocks decline.

TLDR: When markets fall, stocks fall together. When they rise, only some rise together

The number of stocks a momentum strategy should hold

Now we need to decide how many stocks our momentum strategy should hold.

Our possibly controversial starting hypothesis: Since diversification is powerless against broad market declines (systematic risk), a strategy that rebalances monthly should hold the minimum number of stocks required to offer reasonable protection against individual stock risks (unsystematic risk) while looking to maximize gains from the strongest momentum stocks.

Remember momentum as a strategy buys stocks that are in strong uptrends. And since stocks within sectors tend to be highly correlated, there are high chances of stocks within the same sector will rank high on our momentum list.

So we go back and look at the data, and ask "What if".

Number of stocks matter

What if we picked portfolios with 5-10-15 and so on until 50 stocks at a time and rebalanced each month from 2007 to 2019?

The chart shows significant difference in final outcomes depending on the number of stocks. The 5 and 10 stock portfolios do the worst (hence the case for diversification). The 20, 25 and 30 stock do the best. The 35 to 50 stock portfolios are in the middle suggesting there is such a thing as too much diversification.

We can't just yet conclude that 20 stock portfolios are the best strategy.

Chart shows maximum drawdowns from peak value for each of the portfolios. The 20 / 25 / 30 stock portfolios suffer the least while the 5 and 10 stock portfolios never quite recover from the carnage.  Again the higher stock portfolios are in the middle.

Table shows the summary of portfolio outcomes:

Before we conclude a portfolio of 20 to 30 stocks is optimal, we'll run another test. This time incrementing the number of stocks by 1 and observing the outcome.

The Ulcer Index is a metric devised in 1987 by Peter Marin and Byron Mcann to measure downside volatility of investment strategies.

Simply put, it measures the decline from the highest point in a period of 14 days. Lower the Ulcer Index, more likely you will not have sleepless nights on account of your investment.

Going back to our initial hypothesis of picking the minimal number of stocks for ease of managing and also to be able to increase allocation to the top momentum stocks, a portfolio of 20 to 25 stocks looks like its best placed to deliver optimal returns in a momentum strategy. We currently hold 20 stocks in our Capitalmind Premium and the PMS portfolios (with minor differences between the two).

This is an on-going series of posts unpacking the momentum investing strategy. You can find the first one on testing whether momentum works in India here: Does Momentum Investing work in India?

The performance of our Premium Momentum portfolio for the Calendar Year 2019 is summarised here: Momentum Portfolio for Jan 2020 [premium subscribers]

In further posts, we will look into lookback periods, stop-losses, and other potential criteria that may or may not improve a basic momentum strategy.

Please note that backtested results are hypothetical and do not represent actual results. An investor applying this strategy would incur transaction costs and taxes on short-term gains which are not reflected in the backtest results. On the plus side, the backtests do not include dividends or their reinvestment. Our own momentum strategy at Capitalmind Wealth while built on the same principle varies in some ways from the above implementation and undergoes periodic reviews to use the most relevant factors.

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In the Capitalmind PMS, we manage a Momentum Portfolio. We also offer a Momentum Portfolio to our Premium subscribers. The CM Premium Momentum Portfolio is also accessible on smallcase.

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