In which financial markets do mutual fund theorems hold true?

The mutual fund theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. The main results are:

Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets

We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann–Morgenstern investor in the liquidity model of Almgren (Appl. Math. Finance 10:1–18, 2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the optimal strategy with respect to the various model parameters. In particular, we find that the optimal strategy is aggressive or passive in-the-money, respectively, if and only if the utility function displays increasing or decreasing risk aversion. Surprisingly, only few further monotonicity relations exist with respect to the other parameters. We point out in particular that the speed by which the remaining asset position is sold can be decreasing in the size of the position but increasing in the liquidity price impact.      

Is the decline in the value relevance of accounting driven by increased conservatism?

This paper examines the association between conservatism and the value relevance of accounting information over the 1975 through 2004 period. We measure conservatism using approaches developed in Penman and Zhang, The Accounting Review 77:237–264, (2002) and Beaver and Ryan, Journal of Accounting Research 38:127–148, (2000) and value relevance using (1) adjusted R ² from regressions of price on earnings and book values, (2) adjusted R ² from regressions of returns on earnings and changes in earnings, and (3) returns earned by perfect foresight of earnings and book values. We find no evidence that firms with increasing conservatism exhibit greater declines in value relevance. Rather, we observe most significant declines in value relevance for firms where conservatism has not increased. When we adjust financial statements for the effects of conservatism, we find that the value relevance of adjusted numbers is generally lower and trends in value relevance unaffected. Based on these results, it is implausible that increasing conservatism drives the decline in value relevance.     

The numeraire portfolio: a new perspective on financial theory

The numeraire portfolio, also called the optimal growth portfolio, allows simple derivations of the main results of financial theory. The prices of self financing portfolios, when the optimal growth portfolio is the numeraire, are martingales in the ‘true’ (historical) probability. Given the dynamics of the traded securities, the composition of the numeraire portfolio as well as its value are easily computable. Among its numerous properties, the numeraire portfolio is instantaneously mean variance efficient. This key feature allows a simple derivation of standard continuous time CAPM, CCAPM, APT and contingent claim pricing. Moreover, since the Radon-Nikodym derivatives of the usual martingale measures are very simple functions of the numeraire portfolio, the latter provides a convenient link between the standard Capital Market Theory a la Merton and the probabilistic approach a la Harrison-Kreps-Pliska.     

Optimal Time to Sell in Real Estate Portfolio Management

This paper examines the properties of optimal times to sell a diversified real estate portfolio. The portfolio value is supposed to be the sum of the discounted free cash flows and the discounted terminal value (the discounted selling price). According to Baroni et al. (Journal of Property Investment and Finance 25(6):603–625, 2007b), we assume that the terminal value corresponds to the real estate index. The optimization problem corresponds to the maximization of a quasi-linear utility function. We consider three cases. The first one assumes that the investor knows the probability distribution of the real estate index. However, at the initial time, he has to choose one deterministic optimal time to sell. The second one considers an investor who is perfectly informed about the market dynamics. Whatever the random event that generates the path, he knows the entire path from the beginning. Then, given the realization of the random variable, the path is deterministic for this investor. Therefore, at the initial time, he can determine the optimal time to sell for each path of the index. Finally, the last case is devoted to the analysis of the intertemporal optimization, based on the American option approach. We compute the optimal solution for each of these three cases and compare their properties. The comparison is also made with the buy-and-hold strategy.

A note on portfolio choice for sovereign wealth funds

The current vast account surpluses of commodity-rich nations, combined with record account deficits in developed markets (the United States, Britain) have created a new type of investor. Sovereign wealth funds (SWF) are instrumental in deciding how these surpluses will be invested. We need to better understand the investment problem for an SWF in order to project future investment flows. Extending Gintschel and Scherer (J. Asset Manag. 9(3):215–238, 2008), we apply the portfolio choice problem for a sovereign wealth fund in a Campbell and Viceira (Strategic Asset Allocation, 2002) strategic asset allocation framework. Changing the analysis from a one to a multi-period framework allows us to establish a three-fund separation. We split the optimal portfolio for an SWF into speculative demand as well as hedge demand against oil price shocks and shocks to the short-term risk-free rate. In addition, all terms now depend on the investor’s time horizon. We show that oil-rich countries should hold bonds and that the optimal investment policy for an SWF as a long-term investor is determined by long-run covariance matrices that differ from the correlation inputs that one-period (myopic) investors use.

Marketing Period Risk in a Portfolio Context: Theory and Empirical Estimates from the UK Commercial Real Estate Market

The role of selling (or marketing) period uncertainty in understanding risk associated with property investment is examined in this paper. Using an approach developed by Lin (2004), and Lin and Vandell (2001, 2005), combined with a statistical model of UK commercial property transactions, we show that the ex ante level of risk exposure for a commercial real estate investor is around one and a half times that obtained from historical statistics. The risk related to marketing time uncertainty can be reduced by constructing a portfolio. We find that at least ten properties are necessary to reduce this risk, assuming independence between marketing period risk and price risk. These findings have important implications for mixed-asset portfolio allocation decisions.      

Optimal portfolio selection and compression in an incomplete market

We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modelled as diffusions and the market is incomplete. We find an explicit solution for the case of limited diversification of the portfolio, i.e. for the portfolio compression problem. By this we mean that any admissible strategy may include no more than m different stocks concurrently, where m may be less than the total number n of available stocks.     

Power mapping with dynamical adjustment for improved portfolio optimization

For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.     

Portfolio performance and accounting measures of earnings: an alternative look at usefulness

Measures of economic performance, such as accounting earnings, working capital and cash flows, have been evaluated in tests of relative explanatory power of regressions of market returns on earnings, working capital and cash flows. We employ a different test. Using Basu’s (J Finance 663–682, 1977) investment trading strategy, we measure portfolio returns based on these three accounting measures of earnings. The objective is to ascertain whether investment performance also supports the findings of the explanatory power studies that accounting earnings is the premier measure of performance. The evidence does not support this conclusion. Our findings are at variance with prior conclusions that accounting earnings is more useful than cash flow. The Basu trading strategy is effective for all three measures. Excess market returns are observed for all three measures, even when controlled for risk and for low priced stocks. But accounting earnings portfolios do not dominate working capital or cash flow portfolios. In fact, the raw returns to cash flow portfolios are marginally (statistically) larger than accounting earnings portfolios. Economically, a dollar invested in a portfolio using accounting earnings to select the stock would have an accumulated value of 22.73 while the same dollar investment using cash flow instead of accounting earnings would accumulate a value of22.73 while the same dollar investment using cash flow instead of accounting earnings would accumulate a value of 33.94 over the same 16 years starting with the second quarter of 1988 and concluding at the end of the first quarter of 2004. Thus, our results have implications for the studies of explanatory power of different measures of earnings and their comparison in the US and other markets.     

Redistributive taxation and social insurance under adverse selection in the insurance market

This paper extends the analysis of optimal income taxation under uncertainty studied by Cremer and Pestieau (International Tax and Public Finance, 3, 281–295, 1996). We introduce asymmetric information in the insurance market whereby private insurance companies cannot identify the risk probability of the agents, and we examine its effect on public policy. We consider the separating equilibrium of Rothschild and Stiglitz (Quarterly Journal of Economics, 90, 629–649, 1976) and Riley (Econometrica, 47, 331–359, 1979) where the low risk agent is only partially insured. The presence of the distortion in the insurance market changes the affinity of labor, and in some cases, we show that the scope of redistribution and the resulting social welfare are higher under asymmetric information than under full information. We also show that the increase in social insurance affects the utility and labor incentive of the low risk type by relaxing the self-selection constraint in the insurance market. The policy implications of the redistributive taxation and social insurance are analytically and numerically examined.      

Robust portfolio estimation under skew-normal return processes

In this paper, we study issues related to the optimal portfolio estimators and the local asymptotic normality (LAN) of the return process under the assumption that the return process has an infinite moving average (MA) (∞) representation with skew-normal innovations. The paper consists of two parts. In the first part, we discuss the influence of the skewness parameter δ of the skew-normal distribution on the optimal portfolio estimators. Based on the asymptotic distribution of the portfolio estimator ? for a non-Gaussian dependent return process, we evaluate the influence of δ on the asymptotic variance V(δ) of ?. We also investigate the robustness of the estimators of a standard optimal portfolio via numerical computations. In the second part of the paper, we assume that the MA coefficients and the mean vector of the return process depend on a lower-dimensional set of parameters. Based on this assumption, we discuss the LAN property of the return's distribution when the innovations follow a skew-normal law. The influence of δ on the central sequence of LAN is evaluated both theoretically and numerically.     

The Optimal Log-Utility Asset Management under Incomplete Information

In this paper, we propose a theory for deriving the optimal portfolio that assures the log-utility investors of maximizing their expected utility. Restricting investors' information at defined levels, we propose the sample path-wise optimal portfolio (SPOP), which is consistent with the back-test framework used in actualinvestment. It is proven that, at any finite terminal time, this SPOP is asymptotically optimal among all the portfolios which are predictable under investors' incompleteinformation. The optimality is guaranteed by the continuous Bayesian updating formula. Finally, we discuss an algorithm for searching the SPOP, based on asset prices at discrete time intervals.     

Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279–300], Leland [J. Finance, 1980, 35, 581–594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9–37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.     

Continuous-time delegated portfolio management with homogeneous expectations: can an agency conflict be avoided?

In a continuous-time framework, the issue of how to delegate an investor’s portfolio decision to a portfolio manager is studied. First, we solve the first-best problem. For the second-best case, a specific quadratic contract is introduced resolving the agency conflict completely in the sense that the solutions to the first-best and second-best problems coincide. This contract can be implemented if the investor is able to observe the value of the growth optimal portfolio at her investment horizon. If the investment opportunity set is assumed to be constant, in equilibrium the value of the market portfolio is a sufficient statistic for the value of the growth optimal portfolio. Throughout the paper, we assume that the investor and the manager have homogeneous expectations about the investment opportunity set. This, however, does not necessarily mean that investor and manager are symmetrically informed about all prices.

Optimal portfolios under a correlation constraint

Under a correlation constraint the optimal constant/fixed-mix portfolio consists of the market portfolio, the riskless bond and the benchmark     

Optimal consumption and investment for markets with random coefficients

We consider an optimal investment and consumption problem for a Black–Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamic programming approach leads to an investigation of the Hamilton–Jacobi–Bellman (HJB) equation which is a highly nonlinear partial differential equation (PDE) of the second order. By using the Feynman–Kac representation, we prove uniqueness and smoothness of the solution. Moreover, we study the optimal convergence rate of iterative numerical schemes for both the value function and the optimal portfolio. We show that in this case, the optimal convergence rate is super-geometric, i.e., more rapid than any geometric one. We apply our results to a stochastic volatility financial market.     

Pricing growth-rate risk

We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S. We also consider a reference growth process G that may represent the growth in the payoff of a single asset or of the macroeconomy. Both S and G are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. We consider the pricing implications of parametrized family of growth processes G ^ε , with G ⁰=G, as ε is made small. This parametrization defines a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon, we trace a term structure of risk prices that shows how the valuation of risky cash flows depends on the investment horizon. Using methods of Hansen and Scheinkman (Econometrica 77:177–234, 2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily long.     

Relationship between Treasury bills and Eurodollars: Theoretical and Empirical Analyses

In this paper, we derive an equilibrium relationship between the yields on Eurodollar and Treasury bills based on equivalent martingale results derived by Harrison and Kreps (1979) and Harrison and Pliska (1981, 1983) as well as the corporate debt pricing model developed by Merton (1974). The derived equilibrium relationship incorporates the models used by Booth and Tse (1995) and Shrestha and Welch (2001) as special cases. The equilibrium relationship indicates that the conditional volatility of the yield on Eurodollars explains the variation in the TED spread. We empirically test the equilibrium relationship using a GARCH-M model and the concept of fractional cointegration. We use both the ex ante data implied by the respective futures contracts as well as the ex post spot data with daily, weekly and monthly frequencies. We find empirical support for the Equilibrium relationship.