A Brief History and Analysis of Equity Market Correlations vs. My Analysis

by: Reggie Middleton

We performed an analysis of the correlation of the stock prices of the companies that we have covered over the last two years to the broader stock market. Based on the price movements in the selected stocks and S&P 500 over the last decade, we mapped the pattern seen in the degree of correlation that is exhibited when there are changes in the overall market direction owing to change in the “perceived” macro-situation.

For the purpose of our analysis, we divided the total period under consideration (December 31, 2000 till August 31, 2010) in to four sub-periods reflecting four different market sentiments:

  • Pre-crisis- Dec 31, 2000 -Dec 31, 2007 – Long-term
  • Financial crisis- Jan 01, 2008 to March 09, 2009
  • Rally – March 10, 2009 to April 30, 2010
  • Correction – May 01, 2010 to Present

Based on the daily prices of the stocks and S&P 500 in the aforesaid periods, we calculated the following metrics to analyze the degree of correlation as well the relative price movements:

  • Correlation coefficient
  • Beta
  • Annualized volatility
  • Ratio between stock volatility and S&P 500 volatility
  • Annualized return
  • Z-score – calculated by dividing annualized return by annualized volatility
  • Ratio between stock z-score and S&P 500 z-score

Based on the matrix obtained, we have the following key observations:

  • Correlation – The movements of the selected stock prices are becoming increasingly aligned to the broader market movements as reflected in the increase in the correlation coefficients of the daily returns of the selected stocks to the daily returns of S&P 500. The correlation during the financial crisis period (Jan 01, 2008 to March 09, 2009) and the subsequent rally (March 10, 2009 to April 30, 2010) was substantially larger than the correlation observed in the pre-crisis period. The correlation during the recent correction phase (May 01, 2010 to present) has been even larger. One can hazard a guess that the primary rationale behind this increased correlation is that the selected stock set which primarily contain REITs and the bank stocks are the ones which are most influenced by the turn of events in the mortgage market and the overall financial system which are the heart of the current economic slowdown).
  • Volatility – The volatility in the daily returns of the selected stocks spiked substantially during the financial crisis. Comparing the volatility seen in the selected stocks with volatility seen in the broader market, it is observed that the increase in volatility in these stocks was multi-fold when compared with increase in the volatility in the broader market. The same can be easily seen in the ratio of stock volatility and S&P 500 volatility. The increase was particularly large in banks (PNC, STI, WFC, GS, MS, JPM, BBVA) and insurance (HIG, REITs (GGP, MAC) and monoline insurers (NYSE:AGO).

The volatility moderated across the selected stock set in the subsequent rally phase, but on a relative basis (compared to the volatility in the overall market), the volatility in the stocks still remained at very high levels.

The volatility during the recent correction phase has further moderated but volatility of certain stocks including STI, HOT, FRO, BBVA, HIG, AGO, USG and GET remain at high levels

  • Beta – Beta, which measures the change in stock return per unit change in market return, is a function of correlation of the stock returns to market returns and the ratio of stock volatility to market volatility (Beta = Correlation coefficient X Ratio of stock volatility to market volatility). Thus, this systematic risk can increase either due to increase in correlation (stock being more aligned to the general market movements) or increase in the relative volatility of the stock against the volatility in the broader market (due to stock specific issues).

Comparing across the sub-periods, it is observed that the beta of the selected stocks was the highest during the rally phase showing that the relative stock movement was higher when the market was rising than when the markets were falling (during financial crisis and the recent correction phase). On bifurcating the increase in beta into the two components – increase in correlation and increase in ratio of stock volatility to market volatility, it is observed that although the correlation has been consistently increasing across most of the stocks, the change in the ratio of stock volatility to market volatility is behind the change in the beta during different sub-periods. Thus, it can be concluded that although the movements in the stocks are becoming increasingly aligned to the market movements, the change in the stock volatility vis-à-vis market volatility is dictating the relative stocks’ performance vis-à-vis the broader market under different market sentiments.

The relative volatility of the stock’s returns vis-à-vis broader market under a particular market sentiment is determined by the stock specific issues as well as the base effect (The base effect can be explained with help of a example. For example, a stock A was trading at $100 at the beginning of financial crisis and fell 60% during the financial crisis phase. The market index B was trading at 1000 at the beginning of financial crisis and fell 30% during the financial crisis phase.Thus, during the financial crisis, the computed beta for the stock during financial crisis phase will be 2.0 ( i.e 60%/30%). However, if the market recovers to the pre-financial crisis level, the stock will have to increase by 150% and the market by 43%, implying beta of 3.5). The base effect partly explains the high beta observed in the rally phase (March 10, 2009 to April 30, 2010) against the beta during the financial crisis phase (Jan 01, 2008 to March 09, 2009).

  • Returns – We calculated the annualized returns of the stocks during the four sub periods based on the closing price at the beginning and end of each period and have compared the same with the annualized return of the S&P 500. It is observed that ratio was higher for the rally phase (March 10, 2009 to April 30, 2010) than the ratio for the financial crisis phase (Jan 01, 2008 to March 09, 2009). The same can be largely a result of the base effect, explained earlier.

It is further observed that negative movement seen in the stocks in the recent correction phase (May 01, 2010 to present) is in most cases, multifold the decline in market decline. The same is again due to beta > 1 which reflects a relatively larger negative impact of the change in market sentiment on the selected stocks than the impact on market as a whole. The stocks with highest declines during the correction phase include USG, AGO, HIG, WFC, WFSL, FRO, PNC and STI.

  • Z-score – We calculated the z-score to analyze the return per unit of volatility to evaluate these stocks as a potential hedge under a given scenario. The ratio of the z-score of stocks to the z-score of S&P 500 reflects the relative performance vis-à-vis market. However, since these stocks are highly volatile, the z-score of these stocks in the downtrend (financial crisis phase) and uptrend (rally phase) are very low. However, during the recent correction phase, the decline per unit of volatility has been quite high in some stocks which are available in the subscriber PDF attachment here: File Icon Market Correlation Analysis (available to all paying subscribers, click here to subscribe)

We have also looked at the banks that we have covered by parsing the latest credit metrics from the company filings. Yes, I am still bearish on the bank shenanigans, bailout games and all. Our findings are interesting and I will be publishing them shortly.

Disclosure: Short banks, retail and tech stocks