Standard Mean-variance Analysis Research Articles

Volatility Transmission in U.K. Housing: A Multivariate GARCH Approach

Executive Summary. Despite its importance for gauging the probability of large losses and portfolio management, there has not been an investigation of how GARCH conditional volatility is transmitte...

Clustering in U.K. home price volatility

In the wake of the 2007–09 global financial crisis, there has been heightened interest in correctly gauging the probability of large losses on assets, particularly house prices. If an asset exhibits GARCH effects in its returns, there is a much higher probability of large losses during volatile periods than standard mean-variance analysis indicates. While there has been much research on regional home prices in the United Kingdom, the focus has been on the conditional mean and convergence rather than on the possibility of GARCH effects and volatility clustering. The findings of this study reveal that the majority of U.K. regions indeed exhibit GARCH effects, and these GARCH effects have heterogeneous impacts on returns across regions. The existence of these GARCH effects in the majority of the U.K. regions has many important implications, ranging from proper portfolio management to government policy.

Optimal forest management under financial risk aversion with discounted Markov decision process models

The common assumption of risk neutrality in forest decision making is generally inadequate because the stakeholders tend to be averse to fluctuations in the return criteria. In Markov decision processes (MDPs) of forest management, risk aversion and standard mean-variance analysis can be readily dealt with if the criteria are undiscounted expected values. However, with discounted criteria such as the fundamental net present value of financial returns, the classic mean-variance optimization is numerically intractable. In lieu of this, this paper (i) presents a linear-programming method to calculate the variance of discounted criteria conditional on any specific policy and (ii) adopts, as an alternative to the variance measure of risk, the “discount normalized variance” (DNV), an economically meaningful criterion consistent with income-smoothing behavior. The DNV is then used in procedures analogous to mean-variance analysis and certainty-equivalent optimization tractable by quadratic programming. The methods are applied to the management of uneven-aged, mixed-species forests in the southern United States. The results document the trade-off between the expected net present value and risk of financial returns, as well as the consequences for selected ecological criteria.

Portfolio selection in a two-regime world

Abstract Standard mean-variance analysis is based on the assumption of normal return distributions. However, a growing body of literature suggests that the market oscillates between two different regimes – one with low volatility and the other with high volatility. In such a case, even if the return distributions are normal in both regimes, the overall distribution is not – it is a mixture of normals. Mean-variance analysis is inappropriate in this framework, and one must either assume a specific utility function or, alternatively, employ the more general and distribution-free Second degree Stochastic Dominance (SSD) criterion. This paper develops the SSD rule for the case of mixed normals: the SSDMN rule. This rule is a generalization the mean-variance rule. The cost of ignoring regimes and assuming normality when the distributions are actually mixed normal can be quite substantial – it is typically equivalent to an annual rate of return of 2–3 percent.

Risk Parity and Beyond - From Asset Allocation to Risk Allocation Decisions

While it is often argued that allocation decisions can be best expressed in terms of exposure to rewarded risk factors, as opposed to somewhat arbitrary asset class decompositions, the practical implications of this paradigm shift for the optimal design of the policy portfolio still remain largely unexplored. This paper aims at analyzing whether the use of uncorrelated underlying risk factors, as opposed to correlated asset returns, can lead to a more efficient framework for measuring and managing portfolio diversification. Following Meucci (2009), we use the entropy of the factor exposure distribution as the number of uncorrelated bets (also known as the effective number of bets, or ENB in short), implicitly embedded within a given asset allocation decision. We present a set of formal results regarding the existence and unicity of portfolios designed to achieve the maximum effective number of bets. We also provide empirical evidence that incorporating constraints, or target levels, on a portfolio effective number of bets generates an improvement in out-of-sample risk-adjusted performance with respect to standard mean-variance analysis.

The performance of model based option trading strategies

This paper analyzes returns to trading strategies in options markets that exploit information given by a theoretical asset pricing model. We examine trading strategies in which a positive portfolio weight is assigned to assets which market prices exceed the price of a theoretical asset pricing model. We investigate portfolio rules which mimic standard mean-variance analysis is used to construct optimal model based portfolio weights. In essence, these portfolio rules allow estimation risk, as well as price risk to be approximately hedged. An empirical exercise shows that the portfolio rules give out-of-sample Sharpe ratios exceeding unity for S&P 500 options. Portfolio returns have no discernible correlation with systematic risk factors, which is troubling for traditional risk based asset pricing explanations.

Retirement Investor Risk Tolerance in Tranquil and Crisis Periods: Experimental Survey Evidence

We conduct a choice experiment to investigate the impact of the financial crisis of 2008 on retirement saver investment choice and risk aversion. Analysis of estimated individual risk parameters shows a small increase in mean risk aversion between the relatively tranquil period of early 2007 and the crisis conditions of late 2008. Investment preferences of survey respondents, estimated using the scale-adjusted version of a latent class choice model, also change during the crisis. We identify age and income as important determinants of preference classes in both surveys and age is also identified as a key determinant of variability (scale). Young and low income individuals make choices that are more consistent with standard mean-variance analysis, but older and higher income individuals react positively to both higher returns and increasing risk in returns. Overall we find a mild moderating of retirement investor risk tolerance in 2008.

Clustering in U.K. Home Price Volatility

In the wake of the 2007–09 global financial crisis, there has been heightened interest incorrectly gauging the probability of large losses on assets, particularly house prices. If anasset exhibits GARCH effects in its returns, there is a much higher probability of largelosses during volatile periods than standard mean-variance analysis indicates. While therehas been much research on regional home prices in the United Kingdom, the focus hasbeen on the conditional mean and convergence rather than on the possibility of GARCHeffects and volatility clustering. The findings of this study reveal that the majority of U.K.regions indeed exhibit GARCH effects, and these GARCH effects have heterogeneousimpacts on returns across regions. The existence of these GARCH effects in the majorityof the U.K. regions has many important implications, ranging from proper portfoliomanagement to government policy.

An Experimental Survey of Investment Decisions for Retirement Savings

We implement a choice experiment to investigate the extent to which retirement savers follow standard mean-variance analysis when choosing from a menu of investment options. We conduct this survey once during a period of …nancial tranquility (March 2007) and once during …nancial crisis (October 2008). We model choices using the scale-adjusted version of a latent class choice (…nite mixture) model. We identify income and age as important determinants of the preference classes, and underlying risk tolerance and age as key determi- nants of variability (scale). Estimated marginal eects of variations in net expected returns and risk on choice of investment option show classes populated by young and low income individuals as more likely to respond consistently with standard mean-variance analysis. However classes populated by older and higher income individuals react positively to both higher returns (lower fees) and increasing risk in returns where risk is presented as a widen- ing range of possible investment outcomes. Crisis-period results con…rm these conclusions, although we see some moderating of overall risk exposures compared with tranquil-period results.

Retirement Investor Risk Tolerance in Tranquil and Crisis Periods: Experimental Survey Evidence

We conduct a choice experiment to investigate the impact of the financial crisis of 2008 on retirement saver investment choice and risk aversion. Analysis of estimated individual risk parameters shows a small increase in mean risk aversion between the relatively tranquil period of early 2007 and the crisis conditions of late 2008. Investment preferences of survey respondents, estimated using the scale-adjusted version of a latent class choice model, also change during the crisis. We identify age and income as important determinants of preference classes in both surveys and age is also identified as a key determinant of variability (scale). Young and low income individuals make choices that are more consistent with standard mean-variance analysis but older and higher income individuals react positively to both higher returns and increasing risk in returns. Overall we find a mild moderating of retirement investor risk tolerance in 2008.

Volatility Transmission in U.K. Housing: A Multivariate GARCH Approach

Executive Summary. Despite its importance for gauging the probability of large losses and portfolio management, there has not been an investigation of how GARCH conditional volatility is transmitted between regions in the United Kingdom. This is an omission, as assets exhibiting GARCH have a much higher probability of large losses during high volatility periods than standard mean-variance analysis indicates. The findings indicate that there is a high conditional covariance between shocks of adjoining regions, and that the conditional covariance declines markedly as distance between regions increases. This suggests some scope for diversification benefits by holding a geographically varied set of housing assets.

Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.

Volatility Clustering in U.S. Home Prices

Generalized autoregressive conditional heteroscedasticity (GARCH) effects imply the probability of large losses is greater than standard mean-variance analysis suggests. Accurately capturing GARCH for housing markets is vital for portfolio management. Previous investigations of GARCH in housing have focused on narrow regions or aggregated effects of GARCH across markets, imposing one nationwide effect. This paper tests fifty state housing markets for GARCH, and develops individual GARCH models for those states, allowing for different effects in each. Results indicate there are GARCH effects in over half the states, and the signs and magnitudes vary widely, highlighting the importance of estimating separate GARCH models for each market.

Static Mean-Variance Analysis with Uncertain Time Horizon

We generalize Markowitz analysis to the situations involving an uncertain exit time. Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. Although efficient frontiers in the generalized and the standard Markowitz case may coincide under certain conditions, we demonstrate that, by means of an example, in general that is not true. In particular, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa. As a result, an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions. Numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean-variance analysis when time horizon is uncertain.

Weak Interest Rate Parity and Currency Portfolio Diversification

This paper presents a dynamic model of optimal currency returns with a hidden Markov regime switching process. We postulate a weak form of interest rate parity that the hedged risk premiums on currency investments are identical within each regime across all currencies. Both the in-sample and the out-of-sample data during January 2002 - March 2005 strongly support this hypothesis. Observing past asset returns, investors infer the prevailing regime of the economy and determine the most likely future direction to facilitate portfolio decisions. Using standard mean variance analysis, we find that an optimal portfolio resembles the Federal Exchange Rate Index which characterizes the strength of the U.S. dollar against world major currencies. The similarity provides a strong implication that our three-regime switching modelis appropriate for modeling the hedged returns in excess of the U.S. risk free interest rate. To investigate the impact of the equity market performance on changes of exchange rates, we include the S&P500 index return as an exogenous factor for parameter estimation.

Do Hedge Funds Belong in Taxable Portfolios?

The authors examine the suitability of hedge funds in taxable investment portfolios. They apply standard mean-variance analysis to taxable portfolios that include hedge funds as an asset class. They first review the performance characteristics of hedge fund portfolios and then describe the problems faced by taxable investors and the tax structures available for holding assets. Third, they specifically add hedge funds to portfolios of traditional assets. Lastly, the authors provide general guidelines on the appropriate allocation to hedge funds for taxable investors. They conclude that hedge funds significantly improve portfolio efficiency for taxable investors and find that sizeable allocations are appropriate, even for conservative portfolios, though they concede that their results also show that more aggressive taxable investors should commit much less to broad hedge fund portfolios than nontaxable investors.