The Curious Case of Portfolio Selection: Analysis of Correlations and Diversification over Time

Abstract

This paper revisits the Modern Portfolio Theory (Markowitz, 1952) by investigating correlations between countries and for various bonds, stocks and real estate indices over time from an U.S. perspective. Analyzing the changes over time can provide information for investors on the question whether they should construct portfolios dynamically by taking possible changes into account. The goal of this thesis is to come to a generalized statement about (1) the degree of stability of correlations over time, (2) the pattern of correlations over time, (3) the movement of the efficient frontier over time and (4) the diversification benefits over time. First, stability of correlations is tested with the Jennrich-Test (Jennrich, 1970). Subsequently, the pattern of the correlations is examined with three methods: rolling-window, EWMA and the DCC(1,1)-GARCH(1,1) model. In addition, the impact over time of these correlations on the efficient frontier is analyzed in two ways. In one way, sub-period efficient frontiers are created in order to investigate the effect of possible unstable correlations in a dynamic setting. In the other way, several variants of the mean-variance spanning tests, as laid out by Kan & Zhou (2008), are computed in order to gain information about the significance of the movements of efficient frontiers and possible diversification gains over time. Results show that correlations of stocks and real estate seem to be stable over time, but have the tendency to increase during a crisis. However, the strong increase seems to stabilize over time. These findings confirm the fact that correlations tend to be higher during bear markets than in bull markets, implying stabilization on the long-term. In contrast, correlations of bonds are not stable over time and could be the result of country-differences in the dynamics of risk characteristics of bonds and monetary policy. Correlations of bonds did not substantially increase during the crisis. Correlations of bonds have in fact fallen for a short period of time during the recession, although they do show small upward shocks. This implies possible short-term demand shifting from high (sovereign debt) risk to low risk government bonds. With regard to the effects of correlations on the risk-return trade-off, it has been found that this trade-off resembles the pattern of the correlation coefficients. Only stocks and real estate have an increase in risk over time and a substantial upward shock in risk during a recession. In contrast, bonds appear to be relatively resistant to a possible increase in risk, especially during a recession. Adding a short-selling restriction does not change the main findings, but it did show that a short-selling restriction limits (potential) diversification gains. Finally, on the basis of various spanning tests, it can be indicated that spanning tests need to be corrected for normality, as the spanning tests under normality can lead to distorted results and conclusions due to the nature of financial data in this study and in general. Results of the asymptotic spanning tests show that (1) an investor benefits from diversification (over time), (2) these benefits have the tendency to decline during recessions and that (3) a relatively large portfolio could make diversification gains quite resistant during recessions.