Portfolio theory tells us that if you manage to combine assets whose returns show low correlation with each other, you may be able to minimize risk while maximizing returns. This means that it is possible to be a prudent investor even if ones portfolio includes riskier assets, as long as those riskier yet higher yielding investments are balanced with others in a well-diversified portfolio. Theoretically, buy and hold investors may minimize those down days if they invest in assets whose returns have low (or possibly negative) correlation with each other.

Of course the problem is whether the portfolios that claim to be well diversified are indeed that way, including mine. Lately we have witnessed that being diversified across different industries or international markets is not good enough to escape those big down days, when almost every stock, domestic or international, gets hit. During these times stock investors do not have anywhere to turn unless theyve already hedged their stock portfolios with other asset classes.

These other assets may include buying protection in the form of derivatives or being equally invested in bonds, however both come with costs. Assuming that our buy and hold investor is not in the business of timing the market, he or she will have to pay significant premiums for buying protection in the form of derivatives. Or the investor will have to let go of the higher long-term excepted returns of more volatile assets if he or she wishes to be equally invested in bonds.

Which brings us back to the basics of investing, that those seeking higher returns will have to bear higher risks. Yet it is not fun to be a portfolio manager during such times when even the most stoic stocks, the ones you think are least correlated with the stock market, start getting hit as soon as program trading and other portfolio insurance schemes kick in. Of course Im speaking from personal experience and this is not the first time its happened to me, however if I lose my cool and start reacting to the market in the name of tactical decision-making, I tend to make things worse.

Which is why Im writing this article for those buy and hold investors who would much rather sit out these down days or weeks and to give an idea of how to construct a portfolio that will take minimum damage while this ugly unwinding unfolds.

To that end I have calculated correlation matrices for a variety of sector ETFs of U.S. stocks that I thought would show less correlation with S&P 500 Index (our benchmark). I have calculated correlations two ways: correlations between index trends and correlations between daily returns of indices. I have done the same thing for certain international ETFs to see how their trends and returns correlated with those of S&P 500. While I tried to choose specific ETFs that I believed would correlate less, the availability of data was more important in my calculations. I wanted to have at least 6 years of daily data, which ruled out commodities and bond ETFs and Chinese shares.

The first thing that strikes the eye is that domestic index and ETF trends, no matter which industry they come from, are highly correlated, around 80-90 %. This is mainly because most stocks and indices followed the market since the beginning of 2001, the time frame of this correlation exercise. The only exception to that rule has been technology stocks, which during this time frame under-performed all other industry categories that are of more defensive nature, such as consumer goods, or industries that reflect an increase in demand for commodities and energy, such as materials or oil services.

But we knew that already. Correlation exercise is not meant to figure out which indices or sector categories under-performed or out-performed the market. It is rather a measure of how index or sector returns differ from each other. Correlations between daily or weekly returns are much more relevant when measuring the risk exposure of individual assets in a portfolio. If we can combine assets whose returns have low correlation with each other, we can reduce the overall dispersion of returns, the volatility of our portfolio.

The figure above shows correlations between daily returns of different sectors. These are much lower, ranging from 20-50 %. Financial and technology returns, on the other hand, are highly correlated (80-90 %) with S&P 500. This means well-diversified portfolios that include diverse sectors, specifically energy, consumer goods, oil services, precious metals, and real estate stocks are going to be a lot more robust than portfolios constructed solely from technology, internet, or financial stocks.

You might say you knew that already. But every time I talk to investors, it amazes me to learn how concentrated their portfolios are in a few stocks, perhaps in the same industry. Even if these stocks capture alpha and expect to outperform the market, such a portfolio strategy is simply wrong. Or the ETFs investors hold may be well correlated, which does not result in an optimal portfolio in terms of diversification.

We can construct a much better portfolio knowing a little bit about how correlation works. Such a portfolio may also absorb the daily volatilities of those high-risk, high-return stocks. But it is still not diversified enough when sharp market movements and increased volatility occur.

I doubted that being internationally invested would significantly reduce portfolio volatility because as companies and markets have become more global, country correlations have increased. As we have seen recently, practically every market has been hit with selling pressure because of seismic waves that appear to have originated in China.

Emerging market trends show fairly high correlations, similar to U.S. sector trends. Correlations between emerging market returns are significantly lower, but so are correlations between U.S. sector returns. While a carefully crafted international portfolio might increase diversification, the results are not as good as one would have hoped, as the figures above indicate.

Being invested in stocks may not be good enough for the risk-averse investor. Increased returns come with increased risk. Sharp drops in the markets may be barely visible in the long run for investors with long horizons, but volatility is very tangible for us today and now. However, hedging for this type of volatility may come at a price or being invested in bonds and other negatively correlated instruments may mean missing out a sharp rally in the stock market when the time comes.

Nevertheless, I was a bit disillusioned when none of the sector correlations in the stock market, domestic or international, returned anything close to negative. In my quest to find negative correlation, I had to look into the commodities futures that included trading in agricultural produce and livestock. I looked into correlations between monthly prices and returns of various commodity futures for the last 30 years, where nearby futures in the portfolio rolled over to the following months after the last trading day. Here are some of the results, including correlations with 30-year Treasury bond yields and S&P 500 Index, our benchmark:

As expected, trends are a lot more divergent when it comes to commodities futures, which are influenced mainly by the supply and demand pertaining to the specific product or commodity. 30-year T-bond also shows a very definite negative trend vis—vis our benchmark. However this also indicates that owners of such negatively trended instruments will lag behind during times when the stock market turns bullish.

The optimal would be an asset whose trend is positively correlated with S&P 500 index but whose returns are negatively correlated with S&P 500 returns. With such an asset we would ensure not to miss out on a stock market rally while minimizing our losses on down days, perhaps weeks or years.

In the following graph, Ive calculated correlations between returns of commodity futures above and it turns out that monthly returns for gold and crude oil futures are negatively correlated with S&P 500 returns, despite the trends being positively correlated with the index.

Since the negatively correlated returns above are closer to 0 rather than 1, we cannot be certain that a truly negative correlation exists. However it is true that on down days, liquidity will follow more defensive instruments such as treasury bonds or gold, as we have observed recently when bond prices increased and yields dipped.

While there is no guarantee that the future is going to resemble the past, there are certain fundamental and/or technical reasons why correlations of index trends and returns look the way they do. These numbers could shed light on certain market moves or at least verify what we already know. Portfolios that are constructed according to these principles will turn out to be a lot more robust than ordinary ones, as well as out-performing less carefully designed ones in the long run.