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A Different Way to Examine Correlation

It pays to focus more on the 'bad' correlation.

Terry Tian, 09/19/2012

Correlation has become a buzzword for investors who are considering alternative strategies. Correlation measures how a fund's return moves in relation to an index benchmark; the lower the correlation, the more diversification benefits investors can get. Besides the standard way of calculating correlation, Morningstar offers a supplementary data point called bear correlation, which provides insights into a fund's correlation to a benchmark only in down months. Bear correlation and its sister data point--bull correlation--can be found in Morningstar Direct and Morningstar Office by searching in the "Edit Data" dialogue box.

Bear Correlation
Bear correlation calculates the annualized monthly correlation between an investment and a selected benchmark index in the months when the selected benchmark index delivers negative returns. For example, over the past 10 years (August 2002-July 2012), the S&P 500 TR Index posted 78 positive monthly returns and 42 negative monthly returns. Therefore, a fund's 10-year bear correlation with the S&P 500 is calculated using the 42 negative-return monthly observations. Correlation and bear correlation can also be calculated using weekly data.

A fund's bear correlation to the stock market (as represented by the S&P 500 index) can significantly differ from its overall correlation. A high bear-market correlation means that a fund will suffer at the same time as the broad market, lessening its diversification benefits. Of course, correlations are period-dependent and ever-changing. One can never know whether historical correlations will persist. A clear trend is emerging, however--correlations across the board are rising.

Changing Landscape of the Correlation World
Over the past decade, globalization and financial innovation (the proliferation of derivatives and exchange-traded products in particular) have fundamentally changed the investment world. While global markets are now much cheaper and easier to access, rising correlations, both within and across asset classes, appear to be the collateral damage. For example, the correlation between high-yield bonds (as represented by the Bank of America Merrill Lynch U.S. High Yield BB-B Constrained TR Index) and the S&P 500 Index rose from 0.05 in 2002 to 0.52 in 2011 (using weekly data).

Because correlations have risen over the last few years, we divided our study of the last 10 years (521 weeks) into two periods: Aug. 4, 2002, to July 28, 2007, which is largely a bull market (the S&P 500 Index delivered 151 positive weekly returns and 109 negative weekly returns during this period); and July 29, 2007, to July 28, 2012, which incorporates the financial crisis and a rapid equity market rebound (the S&P 500 Index posted 121 negative weekly returns and 140 positive ones during this period). We used weekly return observations in order to generate statistically meaningful results.

We then calculated the overall correlations and bear correlations over the two five-year periods between each of Morningstar's 59 U.S. open-end mutual fund category averages and the S&P 500 Index and plotted them on Chart 1. The overall correlation is represented on the y-axis, while the bear correlation appears on the x-axis. The 59 mutual fund categories include U.S. and international stocks, sector stocks, government and taxable bonds, and allocation funds (excluding alternative categories). 

The 45-degree line on Chart 1 demonstrates a one-to-one relationship between a category average's overall correlation to the S&P 500 and its bear correlation to the S&P 500. If an observation falls above the line, the category average exhibited a lower bear correlation to the index than its overall correlation. Conversely, observations below the line resulted from a higher correlation to the S&P 500 index in bear markets. 

Terry Tian is an alternative investments analyst at Morningstar.
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