Financial correlation

Abstract: Value stocks have higher returns than growth stocks in markets around the world. For 1975-95, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.60% per year, and value stocks outperform growth stocks in 12 of 13 major markets. An international CAPM cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns.

Abstract: We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series. The central result of the present study, which focuses on the case of financial price fluctuations, is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S 500 (or other major markets). In particular, the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.

Abstract: We show that results from the theory of random matrices are potentially of great interest when trying to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate financial time series. We find a remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). Finally, we give a specific example to show how this idea can be sucessfully implemented for improving risk management.

Abstract: Stocks for the Long Run Jeremy J. Siegel McGraw Hill, 1998 Jeremy Siegel has written a book that could have a great effect on the reader's wealth while challenging conventional academic views. It is written at the popular level but references the underlying academic articles (i.e. it is footnoted). Siegel is a finance professor at the University of Pennsylvania's Wharton School, so he is well qualified to draw on the academic literature. The basic message of the book is that stocks have been a wonderful long run investment, and can be expected to continue to be so. The emphasis is on the long run, because there is no doubt that stocks can be exceedingly risky in the short run. As an illustration of stocks' short-run risk, consider October 19, 1987, when the stock market dropped by 22.6% in one day (see Miller 1999 for a review of a book focusing on this episode). Because of the short-run riskiness of stocks, one who is saving for an event in the near future (such as the next vacation), runs a considerable risk of losing money. However, most saving is done not for such short-run purposes but for long-run purposes such as retirement, or to leave money to descendants. Siegel makes a convincing case that stocks are much better for such long-run purposes than either bonds or money market instruments. Bank deposits usually earn even less than money market instruments, and hence are also dominated by stocks. The textbooks I use in teaching finance present evidence that stocks have, on average, outperformed bonds since 1926. Siegel carries this evidence back to 1802, presenting data on the returns from stocks and bonds from 1802 to 1997. Over this long period stocks have had an average return of 8.4%, composed of price increases averaging 3.0%, and dividends averaging 5.4%. In contrast, long-term US government bonds have averaged 4.7%, and short-term US governments, 4.3%. This superiority of stocks held true for major subdivisions of the period studied also. Economists talk about the equity risk premium, the differential between stocks and bonds, which is usually interpreted as the reward to bearing the risks of equity. This of course varies tremendously year to year. Siegel plots a thirty-year running average of the equity risk premium. It is striking that it is virtually always well above 0% (the exceptions appear to be around 1841 and 1861, which are well over a century ago). Thus, for someone investing for the long run, it appears stocks virtually always exceed bonds in return. The riskiness of having stocks underperform bonds turns out to depend very much on the holding period. A fascinating graph (showing data from 1802 to 1997) shows the maximum and minimum real (i.e., inflation adjusted) annualized returns for various holding periods (p. 27). For short holding periods, there is the expected result that one can lose more money on stocks than on either bonds or T-bills, frighteningly more. The worst one-year return on stocks is -30.6% (the best is 66.6%). Incidentally, bonds prove to have appreciable risk over short periods also, with the worse bond performance being -21.9%, and the worst Treasury bill performance -15.6%. The bond and Treasury bill losses occur when high inflation lowers their real purchasing power. Bonds have this risk. In addition, they can experience large losses when interest rates rise unexpectedly, reducing their risk. That stocks are riskier than bonds, and bonds riskier than treasury bills (and bank deposits and other money market instruments) is standard textbook material. It is usually explained by investors disliking risk and being willing to incur higher risk only if rewarded with greater returns. Thus, investors should be willing to hold stocks only if promised much higher returns than bonds. However, most investors (especially those with large sums of money) have longer horizons than one year. However, the equity risk premium appears to shrink with holding periods. …