Stock-bond correlation : time variation, predictability & hedging

Abstract

The correlation between stock and bond markets is of critical importance. Pension funds, mutual funds, institutions and individuals all face an asset allocation decision on the amount of wealth to invest across stock and bond markets. Indeed asset allocation decisions have been shown to account for in excess of 70% of the performance of portfolios (Brinson et al. [1991]). Since it is now widely accepted that the correlation between stocks and bonds is subject to fluctuations over time, with the implication that these changes impact portfolio risk and thus investors' diversification benefits, this thesis looks at three distinct but related topics to do with time variation in stock-bond correlation: contemporaneous changes, predictability and hedging unexpected changes. The first topic is an empirical examination of the economic mechanisms underlying the contemporaneous time variation in stock-bond correlation. Based on a theoretical framework motivated by the Campbell and Shiller [1988] decomposition to express unexpected stock and bond returns into news components related to macroeconomic fundamentals, time-varying co-movement among these innovations can reveal the macroeconomic drivers of the time-variation in realised second moments of stock and bond returns. Using a novel dataset of macroeconomic analysts' forecasts, uncertainty in cash flow (corporate pro ts) and the real short-term interest rate is able to explain a relatively substantial part of the variation in stock volatility. Bond return volatility can be attributed to the uncertainty in inflation and the real short-term interest rate, while the interaction between several of the macroeconomic news components account for a portion of the variation in the covariance between stock and bond returns. Most notably the interaction between cash ow news and real short-term interest rate news is a driver of negative stock-bond correlation. The second topic is on time-series predictability of realised stock-bond correlation. This is investigated in the context of improving investors' ex-ante allocation of wealth between stock and bond markets using macroeconomic analysts' forecasts. In-sample such forecasts display some predictability of the volatility and correlation. Out-of-sample however, analysts' forecasts are not able to improve investors' ex-ante allocation. Based on the framework of the global minimum-variance portfolio, net of transaction costs, analyst forecast data does not provide any benefits above historical returns in forming a minimum-variance portfolio. Whilst there are benefits to using such forecasts during the 2008 financial crisis, this is overshadowed by the effectiveness of simply using the realised correlation estimate to form the minimum-variance portfolio. The third topic investigates stock-bond correlation risk and the importance of unexpected changes in correlation for the asset-liability management mandate of a pension fund. Focusing solely on the role of interest rate risk, liabilities can be thought of as long duration bonds. Since pension funds are typically net long stocks and net short bonds, changes in the correlation between these two asset classes will affect the funding ratio. Empirically this is shown for a stylised pension fund with contributions invested 60/40 across stocks and long-term bonds: The funding ratio decreases when adverse changes to stock-bond correlation occur. A stock-bond correlation swap to hedge against such a risk is therefore naturally motivated. By structuring a stock-bond correlation swap contract, a utility indifference pricing model with stochastic correlation in an incomplete market is developed. The model incorporates the role of pension fund preferences in fairly pricing the swap and leads to several intuitive findings: model-implied quotes of the correlation-swap strike fall within the range of quotes obtained from actual stock-bond correlation swaps; the higher the risk aversion and/or the more important the liabilities are, the higher the correlation swap strike the pension fund would be willing to pay in order to hedge stock-bond correlation risk.