For disciples of modern portfolio theory, there’s no question that the negative correlation between equities and Treasuries is important. The thinking goes that the historically negative correlation indicates the level of protection that bonds can provide in case a significant equity market sell-off occurs.
But according to a new commentary from PIMCO, the stock-bond correlation may not actually say much about what really matters to investors. “Intuitively, a negative correlation between equities and bonds … would suggest that bonds perform well when equities sell off,” said the analysts behind the note. “In fact, however, this is not true.”
The technical reality, they said, is based on what “correlation” is. Defining it as a measure of “the commonality in the deviation from trend for two series of returns,” the authors of the commentary explained that two series are positively correlated when they tend to be above or below their respective trends at the same time. Negatively correlated series, in contrast, tend to go on opposite sides of their mean values within a given time period.
“What the correlation does not measure, however, is the relative performance of the two time-series,” they said. They argued that one time-series can have a positive trend while another has a negative trend, and it would still be technically possible for the two to be negatively correlated, though it would likely be “counterintuitive” to how most people understand correlation.
As a historical example, they pointed to the cumulative returns over cash (represented by 90-day T-bills) of both Treasuries and US equities during the recession from December 1969 to November 1970. Over that timeframe, bonds returned 10.9% over cash, hence providing valuable diversification from equities that returned -7%.
“[T]he correlation between equities and bonds was positive, at 0.4, measured over the same period as the recession, using daily data,” the authors noted. They pointed out that bonds tended to be above their positive trend values at the same time equities were above their negative trend values.
To show that the seeming paradox wasn’t a one-time event, the PIMCO analysts showed the in-sample (daily) correlations between stocks and bonds, as well as the performance of each asset class, in the first half of every US recession since 1970. In five of those seven timeframes, they observed, relative returns were counterintuitive to what the sign of the correlation implied. Either a positive correlation emerged when asset-class returns were opposite to each other (i.e., negative equity returns and positive bond returns), or a negative correlation showed when both asset classes had positive returns.
“Bonds have historically hedged equity risk in recessions because returns have been positive, not necessarily because correlations have been negative,” the analysts concluded.
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