Non-linear Twists in Stock & Bond Correlation

Stocks and bonds are negatively correlated. Translation: they must move against each other most of the time. Because intuitively, stocks bear higher risk than bonds so investors go to stocks when they want to take more risks and flee to bonds when they feel a storm is coming. Plus the numbers tell the same story, too – correlation coefficient between SPY and TLT from 2002 to 2015 is -0.42, year-over-year correlation on daily returns are:


However, this effect was very week from 2004 to 2006. This makes sense because in a credit expansion like that, it was hard for any asset class to go down (except for cash, of course).

But this observation reveals that the conventional stock & bond correlation might be conditional or even deceptive. One might ask, is this stock & bond relationship significantly different in bull and bear markets? Does it also depend on market returns? Or does it just depend on market directions?

To keep it simple, I will stick to SPY and TLT daily returns. If I split my data into bull (2002-2007 & 2012-2015) and bear (2008-2011) periods, and divide each of them into two groups (market goes up & market goes down), then dice each group by quantiles of market returns, I will get:

corr_bull bear_corr

The graphs show that these two assets tend to dramatically move against each other when the market is going extremely up or down. Also this effect seems more pronounced when a bull market is having an up day or a bear market is having a down day. But there’s nothing significantly different between the bear and bull groups.

Next I can try not to split the data into bear & bull, instead I’ll just divide it by market direction, then quantile of performance.


This graph clearly shows that stocks & bonds mostly only move against each other when the market is having a extremely up or down day, either in a bull or bear market. Of course, one could argue that this is a self-fulfilling prophecy because big correlation coef’s feed on big inputs (large market movements), but in the chart the correlation coef’s do not change proportionally through quantiles, which confirms a non-linear relationship.


4 thoughts on “Non-linear Twists in Stock & Bond Correlation

  1. I don’t want to muddy up your blog with my limited knowledge 🙂 but, at 56 and 50 years of age and 29 years of having 401’s we have taken 2 big hits to our 401’s that we have never really recovered from. By splitting or investments into the bond market and mutual funds I know that we weathered a couple of stock market storms. On the other hand, we would have done better in stocks in recent years BUT this complete false stimulation of the dollar and keeping prime at nothing leaves me under the bed. It’s a shame that savers are being punished by politics.

    • Hi Susan I agree that diversification works. There’s strong evidence that suggests aggressive diversification is one of the best investment strategies in the long run. But sadly I don’t have enough expertise to comment on monetary policy yet.

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