In Search of Low (or Negative) Correlation Between Asset Returns 14 comments
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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 they’ve 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 I’m speaking from personal experience and this is not the first time it’s 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 I’m 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-à-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, I’ve 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.
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This article has 14 comments:
The "Trend" is the index itself, or in the case of commodities, the actual futures price. I just had to differentiate betwen the index and its daily (or monthly) returns.
Something I'm studying next is going a little bit against conventional theory with regard to minimizing volatility and maximizing return. The basis of the idea is to find very volatile asset classes such as emerging markets, commodities and small/micro cap stocks. All of these will be ETFs to eliminate the fear of total loss. Based on my preliminary studies, while many of these asset classes over the last few years have been performing well (with positive correlation), some clearly outperform others in various timeframes. The increased volatility helps to better identify rebalancing points.
For example, the beginning of 2006 was a bit rough for small cap stocks and the U.S. indices in general. Meanwhile, commodities were still charging ahead. The deviation reverted to mean as commodities flattened and stocks began running up around June. The deviation between these two asset classes was fairly clear and a rebalance would've worked wonderfully. I've found a few of these deviations over time in other asset classes. So here we have no big crash, but a great opportunity to rebalance. Choosing higher volatility is a way to hopefully get a larger deviation (prompting a rebalance) and better returns over time (ex: a portfolio of small caps will generally outperform the blue chips over time).
With regard to when all assets crash, I've come to accept that this is just inevitable and really represents a buying opportunity across all asset classes. All asset classes bombed with the exception of bonds. If one was 50/50 (bonds, stocks, let's say), you would've dramatically underperformed and 50% of your portfolio would've still taken a hit. I don't see the benefit of being in "less risky" asset classes.
I don't think this idea is going to help anyone's ulcer or someone who can't accept a big hit in the short term, but may be a better way to help the "buy low/sell high" side of the efficient portfolio theory.
Thank you for the article.
Your article mirrors many of the themes in my articles on Seeking Alpha. There are, however, a few important issues that I would like to raise. First, correlations between prices (as I understand your trend) are not a good basis for planning. There are a range of econometric / statistical reasons for this. Things with serial correlation in time (like prices) will often exhibit spurious (i.e. accidental, transient) correlations between them (like correlations between stock prices). Looking at returns removes this issue. The other important thing is that in order to plan, you need forward-looking estimates of portfolio risk and return. Your article seems to imply that investors can use historical data to get to a good asset allocation. They can't. Bernstein (in The Intelligent Asset allocator) deomonstrates the incredibly bad results you will end up with if you do asset allocation using a Mean-Variance Optimization and historical data. My point is that the problem is harder than you seem to suggest--you need a FORWARD view: you can't do asset allocation just b looking in the rearview.
In other words, I agree 100% that correlations are an important input to portfolio planning. I also agree and have pointed out a number of times that foreign indices provide much less protection than people think because the correlations can be quite high (as you show).
Thank you for all comments. Firstly, I wanted to make the article accessible and intuitive rather than a scientific treatise, I'm aware that every serious econometrician or statistician who is involved with portfolio theory will strictly look at asset returns and not even bother with the actual prices. I wanted to put these up to show the logic behind that and show the differences between the two.
Secondly, I'm aware that market concerns itself with forward-looking information, however the supposedly "forward-looking data" you put in your black box models are called "begging the question" in philosophy. That is, by the very action of putting in your "forward-looking data", you're already making predictions about the future so all these "black box" models are nothing more than glorified astrology to me. In other words, it is another version of Descartes' famous proof of the existence of God, but the assumptions he makes to come to that conclusion already presuppose what he's trying to prove, and hence the famous "Cartesian Circle" in philosophical terms.
My article does not imply that future will resemble the past, I've already stated that in the end if you read the article thoroughly.
I'm saying that a simple understanding of how correlation works will lead people to make more intelligent decisions about stock and etf ownership. And I'm showing historical data to support that idea, because I just don't think it is appropriate to show "forward-looking data" to support what I'm trying to prove, however I'm aware that's what the financial industry does.
Of course there are models that incorporate company growth and clearly stock market takes that into account as we see certain stocks that seem very expensive in terms of traditional valuation ratios but might not be that way.
One of the conclusions I was trying to arrive at with that article was that it is possible to incorporate these so called "high risk" companies in a framework of a more diversified portfolio and clearly some of my "high-flying bets" in technology have failed (such as Sigmatel, my all-time embarrassment, and no it did NOT have a high P/E when I bought it and I did NOT increase my position as the stock fell, one of my trading rules), however if all these volatile stocks are incorporated in a portfolio that has enough oil, energy, materials and defensive consumer goods companies and such, you'll be able to absorb those losses and it will be a lot easier to carry a stock that requires an iron stomach.
I have reservations about Monte Carlo analysis however if it’s done with the knowledge that the assumptions that go into the model may be wrong, or worse biased, I think it can be a very useful tool.
But I’ve seen things in financial practice that do resemble pseudo-science rather than being a framework of hypothesis testing – we cannot “prove” something, that wouldn’t be science, theories are good to the extent that they are open to falsification.
I’m very happy with all the reactions the article is getting. I should probably announce that I hold Google and Sigmatel at this moment, though Google has become a significantly larger part of my portfolio and Sigmatel is about to go to zero, literally. Probably time to rebalance. I’m saying these to make the point that a portfolio can be successful overall even if it includes a stock that is close to extinction.
For instance to determine possible returns for a bond portfolio, the analyst needs to define the set of interest rates, or some path, which is clearly influenced by the analyst's preconceptions about the functioning of the bond market as well as international liquidity flows or the Federal Reserve and things like that (which will probably mirror the recent past, hence my objection to "forward-looking data"). What you put into the model determines what you get out of it. Of course these are categorized as "model risk".
That's all I know...
My problem is that these days it seems almost impossible to find stocks that aren't correlated. I use www.assetcorrelation.c... and there don't seem to be any combinations of stocks that don't all move together in the bad times (which is exactly when you want to be diversified!)
On Oct 17 07:14 PM KevinT wrote:
> Hi all,
>
> My problem is that these days it seems almost impossible to find
> stocks that aren't correlated. I use www.assetcorrelation.com
> and there don't seem to be any combinations of stocks that don't
> all move together in the bad times (which is exactly when you want
> to be diversified!)
Just wondering, are there any ETF's which are truly negatively corelated to indexes like S&P, Nasdaq etc. (Maintaining some consistent ratio)
There are instruments (stocks) like Ultra-Short, Double Short, Triple Short, Direxion etc. However I find they are all trending down. This defeats the purpose entirely.
Pls comment.
Sam