Portfolio allocation and the investment horizon: a multiscaling approach

A new approach is proposed for analysing portfolio allocation over various time scales. This new approach is based on wavelet analysis, which decomposes a given time series on a scale-by-scale basis. Empirical results indicate that, as the investment horizon lengthens, a greater weighting should be allocated to stocks. An explanation for this result is that the mean-reverting property of stock returns causes investors to perceive that stocks are less risky than bonds and T-bills at longer time scales compared with shorter time scales. When we include the effect of risk aversion, it is found that the higher the risk aversion, the less the Sharpe ratio, indicating that a more conservative investor prefers a smoother consumption stream.     

Historical simulation approach to the estimation of stochastic discount factor models

We propose an approach to the estimation of the parameters of stochastic discount factor (SDF) models which is based on the idea that the next period joint distribution of the variables in a SDF and asset returns can be well approximated by their joint historical distribution. The estimates of the SDF parameters may therefore be found as the values of the parameters at which the mean of the historical distribution of the product of the SDF with an asset return equals one. Each time period, the estimates are updated using the most recent periods of data and hence can change over time. This method can be viewed as an alternative to the approaches that specify a particular functional form relating the SDF parameters to proxies for the state of the world.     

Multivariate asset price dynamics with stochastic covariation

A Markov chain with an expanding non-uniform grid matching risk-neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with pre-specified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from option data. For Markov chains, dynamically consistent sequences of bid and ask prices are developed by applying the theory of nonlinear expectations with drivers given by concave distortions applied to the one-step-ahead risk. The procedures are illustrated by generating dynamically consistent bid ask sequences for a variety of structured products, such as locally capped and floored cliquets, rolling calls and puts and hedged and unhedged variance swap contracts. Two-sided nonlinear barrier pricing of straddles is also accomplished. All methods are illustrated on the surface of JPM on October 15, 2009.     

Financial factors and firm growth: evidence from financial data on Taiwanese firms

We investigate the possible predictability of firm growth in Taiwan using cross-sectional data of financial factors for the years 1997 and 2003 via principal component analysis. Our results reveal that the 18 financial variables (sales growth rate, total assets, total sales, return on assets, return on equity, gross margin, operating cost minus depreciation divided by sales plus other trading income, acid test ratio, debt–equity ratio, time interest earned, average receivables per average daily sales, inventory, average payables per average daily sales, working capital, working capital as a fraction of total assets, long-term liabilities as a fraction of total assets, and sales as a fraction of net worth of the firm) that we employ bunch together into five different financial ratios for the years 1997 and 2003 that are stable between these years. These financial factors are short-term liquidity, return on investment, long-term liquidity, firm size and capital turnover. Regressing these ratio groups (extracted principal components) on firm growth, we find return on investment in the year 1997 was positively and significantly related to firm growth, while long-term solvency was negatively related to firm growth. In addition, smaller firms tended to grow faster. By 2003, larger firms grew faster than smaller ones and short-term liquidity was positively and significantly related to firm growth, while return on investment was no longer a significant determining factor. Our findings suggest that firms that finance internally or do not rely too heavily on indebtedness may end up growing slower during boom periods but they are the ones that survive and outperform after the bust.     

Systematic risk and timescales

Abstract

In this paper we propose a new approach to estimating the systematic risk (the beta of an asset) in a capital asset pricing model (CAPM). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. At each scale, the wavelet variance of the market return and the wavelet covariance between the market return and a portfolio are calculated to obtain an estimate of the portfolio's beta. The empirical results show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model are more relevant in the medium long run as compared to short time horizons.     

Pricing credit default swaps with bilateral value adjustments

The aim of this work is to examine the influence of mutual fund flows on market timing models, thus providing unbiased timing coefficients. However, as this control is motivated by the existing relationship between mutual fund flows and market returns, we first analyse this relationship, considering previous and concurrent market returns. However, unlike existing studies, we do not consider future returns, since investors do not observe them when making investment decisions. Thus, we feel it is more appropriate to consider expected market returns. We construct the expected market returns by running an AR model and considering the available public information about the macro-economy. The relationship is analysed under different conditions, considering a variety of different mutual fund flow measures, and considering (or not) the sensitivity of mutual fund flows to positive and negative market returns. We also propose different controls for the traditional timing models, and we further analyse the reverse-causality problem. The study demonstrates, for a sample of equity mutual funds registered for sale in the USA, that the poor market timing performance found in this and other prior studies can be completely attributed to the perverse effect of the fund managers’ liquidity service.     

MaxVaR for non-normal and heteroskedastic returns¶

In this work we propose Monte Carlo simulation models for dynamically computing MaxVaR for a financial return series. This dynamic MaxVaR takes into account the time-varying volatility as well as non-normality of returns or innovations. We apply this methodology to five stock market indices. To validate the proposed methods we compute the number of MaxVaR violations and compare them with the expected number. We also compute the MaxVaR-to-VaR ratio and find that, on average, dynamic MaxVaR exceeds dynamic VaR by 5–7% at the 1% significance level, and by 12–14% at the 5% significance level for the selected indices.     

Forecasting financial market volatility: Sample frequency vis-à-vis forecast horizon

This paper explores the return volatility predictability inherent in high-frequency speculative returns. Our analysis focuses on a refinement of the more traditional volatility measures, the integrated volatility, which links the notion of volatility more directly to the return variance over the relevant horizon. In our empirical analysis of the foreign exchange market the integrated volatility is conveniently approximated by a cumulative sum of the squared intraday returns. Forecast horizons ranging from short intraday to 1-month intervals are investigated. We document that standard volatility models generally provide good forecasts of this economically relevant volatility measure. Moreover, the use of high-frequency returns significantly improves the longer run interdaily volatility forecasts, both in theory and practice. The results are thus directly relevant for general research methodology as well as industry applications.     

What is the impact of wealth shocks on asset allocation?

I test the assumption of constant relative risk aversion using U.S. macroeconomic data and analyse the role of wealth shocks in generating transitory changes in asset portfolio composition. I show that the risky asset share exhibits cyclical behavior and it is significantly (and positively) affected by unexpected variation in wealth. Therefore, the empirical evidence suggests that risk aversion is counter-cyclical. I also find that the portfolio share of housing wealth falls when the agent is faced with a positive wealth shock, i.e. housing is a hedge against unfavorable wealth fluctuations. Finally, considering a variety of wealth definitions, the results show that: (i) wealth effects are stronger for direct holdings of risky assets than for indirect holdings, which highlights that investors do not typically trade some assets such as pension or mutual funds; (ii) although significant, wealth effects on asset allocation are mainly temporary as agents quickly rebalance the asset portfolio composition (i.e. there is weak evidence of inertia or slow adjustment in asset allocation); and (iii) changes in expected returns partially explain the variation in risky asset allocation.     

Empirical analysis of the average asset correlation for real estate investment trusts

The credit risk capital requirements within the current Basel II Accord are based on the asymptotic single risk factor (ASRF) approach. The asset correlation parameter, defined as an obligor's sensitivity to the ASRF, is a key driver within this approach, and its average values for different types of obligors are to be set by regulators. Specifically, for commercial real estate (CRE) lending, the average asset correlations are to be determined using formulas for either income-producing real estate or high-volatility commercial real estate. In this paper, the value of this parameter was empirically examined using portfolios of U.S. publicly-traded real estate investment trusts (REITs) as a proxy for CRE lending more generally. CRE lending as a whole was found to have the same calibrated average asset correlation as corporate lending, providing support for the recent U.S. regulatory decision to treat these two lending categories similarly for regulatory capital purposes. However, the calibrated values for CRE categories, such as multi-family residential or office lending, varied in important ways. The comparison of calibrated and regulatory values of the average asset correlations for these categories suggests that the current regulatory formulas generate parameter values that may be too high in most cases.     

Wealth-driven competition in a speculative financial market: examples with maximizing agents

This paper demonstrates how both the quantitative and qualitative results of a general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk-aversion assumption can be applied to the special case of optimizing behaviour. The analysis of the asymptotic properties of the market is performed using a geometric approach that allows the visualization of all possible equilibria by means of a simple one-dimensional Equilibrium Market Curve. The case of linear (particularly, mean–variance) investment functions is thoroughly analysed. This analysis highlights the features that are specific to linear investment functions. As a consequence, some previous contributions of the agent-based literature are generalized.     

Dynamic asset–liability management in a Markov market with stochastic cash flows

This paper provides a general model to investigate an asset–liability management (ALM) problem in a Markov regime-switching market in a multi-period mean–variance (M–V) framework. Emphasis is placed on the stochastic cash flows in both wealth and liability dynamic processes, and the optimal investment and liquidity management strategies in achieving the M–V bi-objective of terminal surplus are evaluated. In this model, not only the asset returns and liability returns, but also the cash flows depend on the stochastic market states, which are assumed to follow a discrete-time Markov chain. Adopting the dynamic programming approach, the matrix theory and the Lagrange dual principle, we obtain closed-form expressions for the efficient investment strategy. Our proposed model is examined through empirical studies of a defined contribution pension fund. In-sample results show that, given the same risk level, an ALM investor (a) starting in a bear market can expect a higher return compared to beginning in a bull market and (b) has a lower expected return when there are major cash flow problems. The effects of the investment horizon and state-switching probability on the efficient frontier are also discussed. Out-of-sample analyses show the dynamic optimal liquidity management process. An ALM investor using our model can achieve his or her surplus objective in advance and with a minimum variance close to zero.     

Borrowing to Finance Public Investment? The ‘Golden Rule of Public Finance’ Reconsidered in an Endogenous Growth Setting*

In this paper, we look for long‐run and short‐run effects of fiscal deficits on economic growth and welfare in a standard endogenous growth model. We show that, under very general hypotheses, the ‘golden rule of public finance’, which allows a government to run public‐investment‐oriented fiscal deficits, leads to a lower balanced‐growth path in the long run, and eventually in the short run, compared with balanced‐budget rules. Welfare effects are more difficult to assess, and depend on the form of the utility function. Our model shows that debt rules such as the golden rule may improve (if the consumption elasticity of substitution is ‘low’) or weaken (if the consumption elasticity of substitution is ‘high’) intertemporal welfare. Consequently, a balanced‐budget rule does not necessarily dominate debt rules from the point of view of welfare, while it does from the point of view of long‐run economic growth.     

Extending the capital asset pricing model: the reward beta approach

This paper offers an alternative method for estimating expected returns. The proposed reward beta approach performs well empirically and is based on asset pricing theory. The empirical section compares this approach with the capital asset pricing model (CAPM) and the Fama–French three‐factor model. In out‐of‐sample testing, both the CAPM and the three‐factor model are rejected. In contrast, the reward beta approach easily passes the same test. In robustness checks, the reward beta approach consistently outperforms both the CAPM and the three‐factor model.     

Estimating default barriers from market information

Brockman and Turtle [J. Finan. Econ., 2003, 67, 511–529] develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To eliminate this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive, but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of the asset value and the asset volatility of Brockman and Turtle.     

On market price of risk in Asian capital markets around the Asian flu

This study investigates a contemporaneous relationship between realized market risk premia, and conditional variance and covariance in nine Asian markets and the US. The time period for this study is before, during, and after the Asian financial crisis. A contemporaneous state-dependent capital asset pricing model (CAPM) that allows for negative and positive market prices of variance and covariance risk is investigated. In the light of significant upstate and downstate reward to local and world variance risk for all markets and all periods, we conclude that a market return-generating process is a piecewise function of local and world variance over time. Furthermore, a cross-sectional analysis of upstate and downstate market prices of variance and covariance risk indicates that reward to risk is a mix of reward to local and world variance, depending on the ever-changing correlation with the world market. Our findings are consistent with the one-factor conditional international CAPM.     

Investment decisions with financial constraints. Evidence from Spanish firms

This paper analyses to what extent the rejection of the investment dynamics implied by the Euler equation model with quadratic and symmetric adjustment costs can be attributed to the fact that the investment behavior of some firms in some periods is financially constrained by the availability of internal funds. I use a hierarchy of finance model which assumes that internally generated finance for investment is available at a lower cost than external finance, and implies the existence of distinct financial regimes depending on the firm’s financial policy. I estimate the empirical investment equation derived from the model using GMM, taking into account the endogeneity of the selection and allowing for debt finance, imperfect competition and the existence of a possible measurement error in the user cost of capital. The empirical results suggest that the Euler equation model is not seriously misspecified for a sub-sample of firms pursuing a particular financial policy.     

A new computational tool for analysing dynamic hedging under transaction costs

This paper highlights a framework for analysing dynamic hedging strategies under transaction costs. First, self-financing portfolio dynamics under transaction costs are modelled as being portfolio affine. An algorithm for computing the moments of the hedging error on a lattice under portfolio affine dynamics is then presented. In a number of circumstances, this provides an efficient approach to analysing the performance of hedging strategies under transaction costs through moments. As an example, this approach is applied to the hedging of a European call option with a Black–Scholes delta hedge and Leland's adjustment for transaction costs. Results are presented that demonstrate the range of analysis possible within the presented framework.     

Capital market equilibrium with heterogeneous investors

As a two-parameter model that satisfies stochastic dominance, the mean-extended Gini model is used to build efficient portfolios. The model quantifies risk aversion heterogeneity in capital markets. In a simple Edgeworth box framework, we show how capital market equilibrium is achieved for risky assets. This approach provides a richer basis for analysing the pricing of risky assets under heterogeneous preferences. Our main results are: (1) identical investors, who use the same statistic to represent risk, hold identical portfolios of risky assets equal to the market portfolio; and (2) heterogeneous investors as expressed by the variance or the extended Gini hold different risky assets in portfolios, and therefore no one holds the market portfolio.     

Bankruptcy in long-term investments

Long-term portfolio management is an important issue in modern finance and practice. We have analysed various known continuous-time strategies in portfolio management, with a focus on bankruptcy probabilities under these strategies. We show that, for each strategy, there is a threshold in the target return rate. When the target return rate is set above this threshold, the application of the strategy for a long investment horizon leads to certain bankruptcy. For a target return rate lower than this threshold, bankruptcy never occurs. Bankruptcy probabilities under a finite investment horizon are also studied. An empirical study based on the Dow Jones Industrial Average Index confirms these results. By comparing the behaviour of these strategies in various parameter regions, we reveal connections among these seemingly different strategies.