An application of hidden Markov models to asset allocation problems

Filtering and parameter estimation techniques from hidden Markov Models are applied to a discrete time asset allocation problem. For the commonly used mean-variance utility explicit optimal strategies are obtained.     

Stabilizing non-fundamental asset price movements under discretion and limited information

Inflation, output and interest rate stabilization are all potential central bank objectives. We explore whether monetary policy should respond to asset price fluctuations when they are driven by irrational expectational shocks to the future returns to capital. In our model, an optimistic shock to future returns generates both an increase in equity prices and physical investment. The increased investment is inefficient and, thus, a central bank optimally responds to this expectations shocks. This induces a trade-off between stabilizing nominal prices and non-fundamental asset price movements. We compare the optimal policy under different assumptions: full versus limited information and commitment versus discretion. If the central bank has limited information about whether an asset price movement has a fundamental or non-fundamental origin, then the central bank responds less aggressively to the non-fundamental exuberance shocks than under full information. Without commitment, a central bank responds more aggressively to non-fundamental exuberance shocks.     

Habit-based asset pricing with limited participation consumption

We calibrate and estimate a consumption-based asset pricing model with habit formation using limited participation consumption data. Based on survey data of a representative sample of American households, we distinguish between assetholder and non-assetholder consumption, as well as the standard aggregate consumption series commonly used in the CCAPM literature. We show that assetholder consumption outperforms non-assetholder and aggregate consumption data in explaining bond returns, bond yields, and the volatility of bond yields. We further show that the high volatility of assetholder consumption enables the model to explain the equity premium puzzle and the risk-free rate puzzle simultaneously for a reasonable value of relative risk aversion.     

Optimal tax-timing and asset allocation when tax rebates on capital losses are limited

This article studies the portfolio problem with realization-based capital gain taxation when limited amounts of losses qualify for tax rebate payments, as is the case under current US tax law. When the tax rate applicable to realized losses exceeds that on realized capital gains, it can be optimal to realize capital gains immediately and pay capital gain taxes to regain the option to use potential future losses against a higher tax rate. This incentive adds an entirely new and as yet unstudied dimension to the portfolio problem. It causes risk averse investors to hold more equity and attain higher welfare levels than is the case when trading under a tax system that seeks to collect the same amount of taxes, but does not allow for tax rebate payments. This is because the benefit to these investors from having their losses subsidized is greater than the suffering from having profits taxed at a higher rate.     

Technical analysis: An asset allocation perspective on the use of moving averages

In this paper, we analyze the usefulness of technical analysis, specifically the widely employed moving average trading rule from an asset allocation perspective. We show that, when stock returns are predictable, technical analysis adds value to commonly used allocation rules that invest fixed proportions of wealth in stocks. When uncertainty exists about predictability, which is likely in practice, the fixed allocation rules combined with technical analysis can outperform the prior-dependent optimal learning rule when the prior is not too informative. Moreover, the technical trading rules are robust to model specification, and they tend to substantially outperform the model-based optimal trading strategies when the model governing the stock price is uncertain.     

Beyond Sharpe ratio: Optimal asset allocation using different performance ratios

As the assumption of normality in return distributions is relaxed, classic Sharpe ratio and its descendants become questionable tools for constructing optimal portfolios. In order to overcome the problem, asymmetrical parameter-dependent performance ratios have been recently proposed in the literature. The aim of this note is to develop an integrated decision aid system for asset allocation based on a toolkit of eleven performance ratios. A multi-period portfolio optimization up covering a fixed horizon is set up: at first, bootstrapping of asset return distributions is assessed to recover all ratios calculations; at second, optimal rebalanced-weights are achieved; at third, optimal final wealth is simulated for each ratios. Eventually, we make a robustness test on the best performance ratios. Empirical simulations confirm the weakness in forecasting of Sharpe ratio, whereas asymmetrical parameter-dependent ratios, such as the Generalized Rachev, Sortino–Satchell and Farinelli–Tibiletti ratios show satisfactorily robustness.     

Momentum investing and the asset allocation decision

This study examines the active asset allocation decisions of Australian multisector fund managers to determine whether active fund managers engage in momentum strategies. We find evidence supporting the existence of momentum investing in active asset allocation strategies. This evidence exists in the Australian Equities, Australian Fixed Interest and Listed Property asset classes. Interestingly, balanced funds adopt contrarian strategies in the International Equities asset class. We also examine whether there is any association between a fund's market timing skill and the execution of momentum strategies. Our results show that fund managers with no market timing skill are momentum investors.     

Economic value of analyst recommendations in Australia: an application of the Black–Litterman asset allocation model

This study empirically examines the investment value of security analyst recommendations on constituent stocks of the S&P/ASX 50 index. We find that stocks with favourable (unfavourable) recommendations on average outperformed (underperformed) the benchmark index. An investment strategy using the Black–Litterman asset allocation model that incorporates consensus analyst recommendations, in conjunction with daily rebalancing, outperforms the market in terms of return and risk‐adjusted performance measures. The investment strategy involves high levels of trading, and no significant abnormal returns are achieved after transaction costs. Less frequent rebalancing, under most situations, causes a decrease in both performance and turnover. Filtering of dated recommendations causes an increase in turnover, while having mixed effects on investment returns.     

Access to information and international portfolio allocation

We examine whether foreign equity holdings of portfolio investors depend on the level of information accessibility between the investors’ home and host countries. Using a comprehensive data set, alternative measures of information accessibility and robust analytical techniques, we show that differences in access to cross-country information significantly influence investors’ portfolio allocation decisions. Furthermore, the results suggest that for a given level of access to information, investors prefer to invest more in countries with a higher quality of legal/macro-institutions. Finally, the findings also confirm that the implications of information accessibility are more pronounced when markets are turbulent.     

Dynamic asset allocation with stochastic income and interest rates

We solve for optimal portfolios when interest rates and labor income are stochastic with the expected income growth being affine in the short-term interest rate in order to encompass business cycle variations in wages. Our calibration based on the Panel Study of Income Dynamics (PSID) data supports this relation with substantial variation across individuals in the slope of this affine function. The slope is crucial for the valuation and riskiness of human capital and for the optimal stock/bond/cash allocation both in an unconstrained complete market and in an incomplete market with liquidity and short-sales constraints.     

Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model

Within a VAR based intertemporal asset allocation model we explore the effects on return predictability and optimal asset allocation of adjusting VAR parameter estimates for small-sample bias. We apply a simple and easy-to-use analytical bias formula instead of bootstrap or Monte Carlo bias-adjustment. Regarding return predictability we show that bias-adjustment in the multivariate setup can yield very different results than in the univariate case. Furthermore, bias-correcting the VAR parameters has both quantitatively and qualitatively important effects on the optimal portfolio choice. For intermediate values of risk-aversion, the intertemporal hedging demand for bonds and stocks is heavily affected by the bias-correction. Utility calculations also show large effects of bias-adjustment, both in-sample and out-of-sample.     

Timing and diversification: A state-dependent asset allocation approach

Abstract

The influence of changing economic environment leads the distribution of stock market returns to be time-varying. A conditionally optimal investment hence requires a dynamic adjustment of asset allocation. In this context, this paper examines the improvement in portfolio performance by simulating portfolio strategies that are conditioned on the Markov regime switching behaviour of stock market returns. Including a memory effect eliminates the empirical shortcoming of discrete state models, namely that they produce a standard and an extreme state in stock returns. So far, this has prevented the regimes from being used as a valuable conditioning variable. Based on a discrete state indicator variable, is presented evidence of considerable performance improvement relative to the static model due to optimal shifting between aggressive and well diversified portfolio structures.     

Disagreement and asset prices

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns, return volatility, and trading volume in the mortgage-backed security market. We find that increased disagreement is associated with higher expected returns, higher return volatility, and larger trading volume. These results imply that there is a positive risk premium for disagreement in asset prices. We also show that volatility in and of itself does not lead to higher trading volume. Instead, only when disagreement arises in the market is higher uncertainty associated with more trading. Finally, we are able to distinguish empirically between two competing hypotheses regarding how information in markets gets incorporated into asset prices. We find that sophisticated investors appear to update their beliefs through a rational expectations mechanism when disagreement arises.     

Optimal consumption and asset allocation with unknown income growth

Recent empirical evidence supports the view that the income process has an individual-specific growth rate component [Baker, M., 1997. Growth-rate heterogeneity and the covariance structure of life-cycle earnings. Journal of Labor Economics 15, 338-375; Guvenen, F., 2007b. Learning your earning: Are labor income shocks really very persistent? American Economic Review 97, 687-712; Huggett, M., Ventura, G., Yaron, A., 2007. Sources of life-cycle inequality. Working paper, University of Pennsylvania]. Moreover, the individual-specific growth component may be stochastic. Motivated by these empirical observations, I study an individual's optimal consumption-saving and portfolio choice problem when he does not observe his income growth. As in standard income fluctuation problems, the individual cannot fully insure himself against income shocks. In addition to the standard income-risk-induced precautionary saving demand, the individual also has learning-induced precautionary saving demand, which is greater when belief is more uncertain. With constant unobserved income growth, changes in belief are not predictable. However, with stationary stochastic income growth, belief is no longer a martingale. Mean reversion of belief reduces hedging demand on average and in turn mitigates the impact of estimation risk on consumption-saving and portfolio decisions.     

Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of a widely employed class of integrated moving average (IMA) models. We obtain a closed-form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. These results are useful due to the close analogy between the integrated GARCH (1, 1) model for conditional volatility and the IMA (1, 1) model for squared returns, which share the same autocorrelation function. In this framework, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the aggregate parameter in the portfolio volatility equation from the estimated vector IMA (1, 1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying standard univariate methodologies, such as RiskMetrics.     

Predictability of currency carry trades and asset pricing implications

This paper studies the time series predictability of currency carry trades, constructed by selecting currencies to be bought or sold against the US dollar, based on forward discounts. Changes in a commodity index, currency volatility and, to a lesser extent, a measure of liquidity predict in-sample the payoffs of dynamically re-balanced carry trades, as evidenced by individual and joint p-values in monthly predictive regressions at horizons up to six months. Predictability is further supported through out-of-sample metrics, and a predictability-based decision rule produces sizable improvements in the Sharpe ratios and skewness profile of carry trade payoffs. Our evidence also indicates that predictability can be traced to the long legs of the carry trades and their currency components. We test the theoretical restrictions that an asset pricing model, with average currency returns and the mimicking portfolio for the innovations in currency volatility as risk factors, imposes on the coefficients in predictive regressions.     

On the microstructure of price determination and information aggregation with sequential and asymmetric information arrival in an experimental asset market

Summary. Experiments were conducted on an asset with the structure of an option. The information of any individual is limited, as if only the direction of movement of the option value known for a single period without information of the value from when movement was initiated. However, if all information of all insiders were pooled, the value of the option would be known with certainty. The results are the following: (1) Information becomes aggregated in the prices as if fully informative rational expectations operated; and (2) The mechanism through which information gets into the market is captured by a path dependent process that we term The Fundamental Coordination Principle of Information Transfer in Competitive Markets. The early contracts tend to be initiated by insiders who tender limit orders. The emergence of bubbles and mirages in the markets are coincident with failures and circumstances that prevent the operation of the Fundamental Principle.The financial support of the national science foundation and the Caltech Laboratory for Experimental Economics and Political Science are gratefully acknowledged. The authors have benefited from helpful comments of David Grether, Kerry Back, Ivana Komunjer and Pete Kyle.     

Estimation of continuous-time models with an application to equity volatility dynamics

The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-ordering of continuous-time stochastic volatility models, the absence or presence of nonlinearities in the drift function, and the desirability of pursuing more flexible diffusion function specifications.     

The economic value of range-based covariance between stock and bond returns with dynamic copulas

The covariance between stock and bond returns plays important roles in the setting up of asset allocation strategies and portfolio diversification. In the present study, we propose a multivariate range-based volatility model incorporating dynamic copulas into a range-based volatility model to describe the volatility and dependence structures of stock and bond returns. We then go on to assess the economic value of the covariance forecasts based on our proposed model under a mean-variance framework. The out-of-sample forecasting performance reveals that investors would be willing to pay between 39 and 2081 basis points per year to switch from a dynamic trading strategy under the return-based volatility model to a dynamic trading strategy under the range-based volatility model, with more risk-averse investors being willing to pay even higher switching fees. Furthermore, additional economic gains of between 33 and 1471 annualized basis points are achieved when taking the leverage effect into consideration.