Taken From Goldman Sachs Research Note

A Significant “Daily Reversion” Pattern is Now Apparent in US Equity Returns

Peter Berezin

January 26, 2009 

When the Short-term Trend is Not Your Friend 
It is often argued that equity markets are ‘trendy’. Indeed, over the past century, daily returns on the S&P have had a slight positive correlation. That is, the market has tended to do better if the previous day’s return was positive. However, this correlation in daily returns has shown a notable pro-cyclical bias. It is has tended to be positive during bull markets and negative during bear markets.

This has been particularly apparent over the past year. Since the start of 2008, the S&P has declined by 43%. Yet, if one only held the market on days following a down day, one would have earned a cumulative return of 36% (ignoring transaction costs and interest earned on days when one is out of the market). In contrast, if one only held the market on days following an up day, the cumulative return would have been -58%.

In terms of daily (close to close) returns, the average return since the start of 2008 following down days has been 0.28% while the average return following up days has been -0.62%, a daily difference of 91 bps.

Since October, this pattern has become even more pronounced. The average daily return following down days has been 0.24% compared to -1.06% following up days, a difference of 129 bps.

Interestingly, despite the stabilization in equity markets over the past two months, the anomaly has only increased. Since December 1^st, the average return following down days has been 1.15% compared to -1.24% following up days.

Other US indices such as the NASDAQ Composite have shown a similar pattern. Outside the US, however, the pattern is less discernable. It is fairly pronounced for the FTSE but does not appear to show up for either the DAX or the Nikkei.

Nevertheless, even though the pattern is less noticeable in non-US indices, it still seems to significantly affect non-US stocks traded in the US. For example, the difference in daily returns depending on whether the previous day’s return was positive or negative is even greater for the MSCI EM ETF than for the S&P. Indeed, the MSCI Japan ETF shows a large differential in returns – 91 bps – even though the Nikkei itself shows no such pattern.

What’s Going On?
How can one explain this? Part of the explanation seems to be quite straightforward. As mentioned above, the correlation in daily returns has tended to be negative in bear markets and positive in bull markets. As such, what we saw in 2008 was a return to what we saw in 2002-03. Intuitively, it appears that investors overreact to large swings in stock prices during bear markets, with the result that good days are followed by bad, and vice versa. In this respect, tracking the evolution of this correlation in daily returns is important from a market timing perspective, because it has historically helped to confirm a bottom in equity markets.

However, the magnitude of the negative correlation in daily returns that we are seeing now seems to be much greater than in past bear markets (indeed, it is even greater than during the Great Depression). This suggests other technical factors are at work. What they are is not clear, but they most likely have to do with the changing microstructure of US equity markets. This may have to do with shifts in leverage, positioning, or the behavior of index tracking ETFs – especially of the leveraged variety.