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.

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences.We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and ?itkovi? (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk \(\hat{\lambda}\) and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with \(\hat{\lambda}\) and with the leverage being proportional to the investor’s confidence in her estimate.     

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.

Adaptive basket liquidation

We consider the infinite-horizon optimal basket portfolio liquidation problem for a von Neumann–Morgenstern investor in a multi-asset extension of the liquidity model of Almgren (Appl. Math. Finance 10:1–18, 2003) with cross-asset impact. Using a stochastic control approach, we establish a “separation theorem”: the sequence of portfolios held during an optimal liquidation depends only on the (co-)variance and (cross-asset) market impact of the assets, while the speed with which these portfolios are reached depends only on the utility function of the trader. We derive partial differential equations for both the sequence of portfolios reached during the execution and the trading speed.     

The sentiment premium and macroeconomic announcements

Limits to arbitrage imply that market-wide investor sentiment should be a priced factor in the US equity market. While previous studies (Baker and Wurgler in J Financ 61:1645–1680, 2006) focus on the factor loading on market-wide investor sentiment, we study its factor premium in the present paper. This is important, because both factor loadings and premiums are required to estimate expected returns on stocks, which are essential for capital budgeting, portfolio evaluation, investment, and risk analysis decisions. If overpricing is more prevalent than underpricing (Stambaugh et al. in J Financ Econ 104:288–302, 2012), the premium on market-wide investor sentiment should be negative. Furthermore, the sentiment premium should be particularly significant on days without macroeconomic announcements, because there is a lack of information about the state of the economy at such times. We test these hypotheses in this paper, and find supporting evidence. Our findings have important theoretical as well as practical implications.     

An Intertemporal CAPM Approach to Evaluate Mutual Fund Performance

Merton (1973) and Campbell (1993) have demonstrated that if an investor anticipates information shifts, he will adjust his portfolio choice today in an attempt to hedge these shifts. Exploiting these insights, we construct a new performance measure to evaluate fund managers' hedging ability. This new measure is different from two widely adopted performance evaluation measures: securities selectivity and market timing. Moreover, an econometric methodology is developed to simultaneously estimate the magnitudes of these three portfolio performance evaluation measures. The results show that mutual fund managers are on average with positive security selection and negative market timing ability. Furthermore, the mutual funds with investment style classified as Asset Allocation generally have positive hedging timing ability.     

Robust Portfolio Rules and Asset Pricing

I present a new approach to the dynamic portfolio and consumptionproblem of an investor who worries about model uncertainty (inaddition to market risk) and seeks robust decisions along thelines of Anderson, Hansen, and Sargent (2002). In accordancewith max-min expected utility, a robust investor insures againstsome endogenous worst case. I first show that robustness dramaticallydecreases the demand for equities and is observationally equivalentto recursive preferences when removing wealth effects. Unlikestandard recursive preferences, however, robustness leads toenvironment-specific "effective" risk aversion. As an extension,I present a closed-form solution for the portfolio problem ofa robust Duffie-Epstein-Zin investor. Finally, robustness increasesthe equilibrium equity premium and lowers the risk-free rate.Reasonable parameters generate a 4% to 6% equity premium.     

Return enhancement trading strategies for size based portfolios

Recent theoretical work suggests that definitions of market efficiency that allow for the possibility of time-varying risk-premia will generally lead to return sign predictability. Consistent with this theory, we show that a logit model based on the lagged value of the market risk premium is useful for successfully predicting the return sign for CRSP small decile portfolio returns, but not large ones. We additionally employ this model in market timing simulations of micro-cap mutual funds in which investment can actually be made. The results indicate that a market-timing strategy based on our return-sign forecasting model outperforms a buy-and-hold strategy for 13 of 14 micro-cap funds studied. On average, the buy-and-hold strategy produces an average compound return of 11.98% per annum versus an average of 16.60% for the market-timing strategy. Nevertheless, trading restrictions make the return-sign forecasting model more practical to employ by the micro-cap fund portfolio manager rather than the individual fund investor.

Learning risk preferences from investment portfolios using inverse optimization

The level of risk an investor can endure, known as risk-preference, is a subjective choice that is tightly related to psychology and behavioral science in decision making. This paper presents a novel approach of measuring risk preference from existing portfolios using inverse optimization on mean–variance portfolio allocation framework. Our approach allows the learner to continuously estimate real-time risk preferences using concurrent observed portfolios and market price data. We demonstrate our methods on robotic investment portfolios and real market data that consists of 20 years of asset pricing and 10 years of mutual fund portfolio holdings. Moreover, the quantified risk preference parameters are validated with two well-known risk measurements currently applied in the field. The proposed methods could lead to practical and fruitful innovations in automated/personalized portfolio management, such as Robo-advising, to augment financial advisors’ decision intelligence in a long-term investment horizon.     

Quadratic minimization with portfolio and intertemporal wealth constraints

We address a problem of stochastic optimal control motivated by portfolio optimization in mathematical finance, the goal of which is to minimize the expected value of a general quadratic loss function of the wealth at close of trade when there is a specified convex constraint on the portfolio, together with a specified almost-sure lower-bound on intertemporal wealth over the full trading interval. A precursor to the present work, by Heunis (Ann Financ 11:243–282, 2015), addressed the simpler problem of minimizing a general quadratic loss function with a convex portfolio constraint and a stipulated almost-sure lower-bound on the wealth only at close of trade. In the parlance of optimal control the problem that we shall address here exhibits the combination of a control constraint (i.e. the portfolio constraint) together with an almost-sure intertemporal state constraint (on the wealth over the full trading interval). Optimal control problems with this combination of constraints are well known to be quite challenging even in the deterministic case, and of course become still more so when one deals with these same constraints in a stochastic setting. We nevertheless find that an ingenious variational approach of Rockafellar (Conjugate duality and optimization, CBMS-NSF series no. 16, SIAM, 1974), which played a key role in the precursor work noted above, is fully equal to the challenges posed by this problem, and leads naturally to an appropriate vector space of dual variables, together with a dual functional on the space of dual variables, such that the dual problem of maximizing the dual functional is guaranteed to have a solution (or Lagrange multiplier) when the problem constraints satisfy a simple and natural Slater condition. We then establish necessary and sufficient conditions for the optimality of a candidate wealth process in terms of the Lagrange multiplier, and use these conditions to construct an optimal portfolio.     

Discussion of “Investor recognition and stock returns”

Lehavy and Sloan (2008, Review of Accounting Studies) note that prior studies find that earnings and cash flows explain only a small portion of the cross-sectional variation in stock return. This motivates them to investigate empirically the ability of a behavioral model of capital market equilibrium proposed by Merton (1987, Journal of Finance, 42, 483–510) to explain the remaining variation in stock returns. Their primary findings show that security value is, as predicted, increasing in investor recognition of the security and that investor recognition is incremental to and more important than cash flows in explaining the cross-sectional variation of stock returns. While the research question is intriguing and well motivated, a number of methodological limitations may limit the reliability of the findings/interpretations. In this paper, I first evaluate the motivation and potential contribution of the Lehavy and Sloan (2008) study. I then outline methodological limitations underlying the study and offer ways of overcoming them. In the final section, I state my conclusions.     

Optimal mean-reversion strategy in the presence of bid-ask spread and delays in capital allocations

A portfolio optimization problem for an investor who trades T-bills and a mean-reverting stock in the presence of proportional and convex transaction costs is considered. The proportional transaction cost represents a bid-ask spread, while the convex transaction cost is used to model delays in capital allocations. I utilize the historical bid-ask spread in US stock market and assume that the stock reverts on yearly basis, while an investor follows monthly changes in the stock price. It is found that proportional transaction cost has a relatively weak effect on the expected return and the Sharpe ratio of the investor's portfolio. Meantime, the presence of delays in capital allocations has a dramatic impact on the expected return and the Sharpe ratio of the investor's portfolio. I also find the robust optimal strategy in the presence of model uncertainty and show that the latter increases the effective risk aversion of the investor and makes her view the stock as more risky.     

Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration

Multiscale stochastic volatility models have been developed as an efficient way to capture the principal effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book by Fouque et al. (Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives, 2011) analyzes models in which the volatility of the underlying is driven by two diffusions – one fast mean-reverting and one slowly varying – and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data.     

Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations

We consider the portfolio optimization problem for the criterion of maximization of expected terminal log-utility. The underlying market model is a regime-switching diffusion model where the regime is determined by an unobservable factor process forming a finite state Markov process. The main novelty is due to the fact that prices are observed and the portfolio is rebalanced only at random times corresponding to a Cox process where the intensity is driven by the unobserved Markovian factor process as well. This leads to a more realistic modeling for many practical situations, like in markets with liquidity restrictions; on the other hand it considerably complicates the problem to the point that traditional methodologies cannot be directly applied. The approach presented here is specific to the log-utility. For power utilities a different approach is presented in the companion paper (Fujimoto et al. in Appl Math Optim 67(1):33–72, 2013).     

Tukey’s transformational ladder for portfolio management

Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted Standard and Poor (S&P 500) portfolio as well as the often overlooked disadvantages of the market capitalization weighted S&P 500’s portfolio (see Bloomfield et al. in J Financ Econ 5:201–218, 1977; DeMiguel et al. in Rev Financ Stud 22(5):1915–1953, 2009; Jacobs et al. in J Financ Mark 19:62–85, 2014; Treynor in Financ Anal J 61(5):65–69, 2005). However, portfolio allocation based on Tukey’s transformational ladder has, rather surprisingly, remained absent from the literature. In this work, we consider the S&P 500 portfolio over the 1958–2015 time horizon weighted by Tukey’s transformational ladder (Tukey in Exploratory data analysis, Addison-Wesley, Boston, 1977): \(1/x^2,\,\, 1/x,\,\, 1/\sqrt{x},\,\, \text {log}(x),\,\, \sqrt{x},\,\, x,\,\, \text {and} \,\, x^2\), where x is defined as the market capitalization weighted S&P 500 portfolio. Accounting for dividends and transaction fees, we find that the 1/\(x^2\) weighting strategy produces cumulative returns that significantly dominate all other portfolio returns, achieving a compound annual growth rate of 18% over the 1958–2015 horizon. Our story is furthered by a startling phenomenon: both the cumulative and annual returns of the \(1/x^2\) weighting strategy are superior to those of the 1 / x weighting strategy, which are in turn superior to those of the \(1/\sqrt{x}\) weighted portfolio, and so forth, ending with the \(x^2\) transformation, whose cumulative returns are the lowest of the seven transformations of Tukey’s transformational ladder. The order of cumulative returns precisely follows that of Tukey’s transformational ladder. To the best of our knowledge, we are the first to discover this phenomenon.     

Stocks,bonds and the investment horizon: a test of time diversification on the French market

Abstract

In this paper, we investigate the relative performance of stocks and bonds for various investment horizons on the French market. We use a new matched block bootstrap approach to take account of estimation risk. Furthermore, in the light of non-normality of returns, we use two different risk approaches as inputs in portfolio optimization: the traditional variance, and a downside risk measure, the semi-variance. Our results suggest that an investor should avoid bonds in the long run due to the time diversification effect.     

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.

Multiple Regimes and Volatility Transmission in Securitized Real Estate Markets

We examine the dynamics and transmission of conditional volatilities with multiple structural changes in return volatility using Bai and Perron (2003)’s methodology, across five major securitized real estate markets as well as employing a multivariate regime-dependent asymmetric dynamic covariance methodology (MRDADC) that allows the conditional matrix to be both time- and state-varying. Our results imply that a multiple-regime time varying asymmetric variance and covariance approach is important in modeling real estate securities valuation and selection and portfolio optimization, and is consistent with popular beliefs that market volatility changes over time. Our MRDADC models detect the presence of significant mean-volatility linkages across the five major securitized real estate markets under different volatility regimes and would have implications for global investor in terms of estimating a dynamic risk-minimizing hedge ratio in international portfolio management.