Annals of Finance最新文献

This paper studies optimal portfolio selection problems in the presence of stochastic volatility and stochastic interest rate under the mean-variance criterion. The financial market consists of a risk-free asset (cash), a zero-coupon bond (roll-over bond), and a risky asset (stock). Specifically, we assume that the interest rate follows the Vasicek model, and the risky asset’s return rate not only depends on a Cox-Ingersoll-Ross (CIR) process but also has stochastic covariance with the interest rate, which embraces the family of the state-of-the-art 4/2 stochastic volatility models as an exceptional case. By adopting a backward stochastic differential equation (BSDE) approach and solving two related BSDEs, we derive, in closed form, the static optimal (time-inconsistent) strategy and optimal value function. Given the time inconsistency of the mean-variance criterion, a dynamic formulation of the problem is further investigated and the explicit expression for the dynamic optimal (time-consistent) strategy is derived. In addition, analytical solutions to some special cases of our model are provided. Finally, the impact of the model parameters on the efficient frontier and the behavior of the static and dynamic optimal asset allocations is illustrated with numerical examples.

Principal components analysis (PCA) is a well-known statistical method used to analyze the covariance structure of a random vector and for dimension reduction. When applied to an N-dimensional random vector of asset returns, PCA produces a set of N principal components, linear functions of the asset return vector that are mutually uncorrelated and which have some important statistical properties. The purpose of this paper is to consider the properties of portfolios based on such principal components, know as PC portfolios, including the efficiency of PC portfolios, the use of PC portfolios to reduce the return variance of a given portfolio, and the properties of factor models with PC portfolios as factors.

Two price economy principles motivate measuring risk by the cost of acquiring the opposite of the centered or pure risk position at its upper price. Asymmetry in returns leads to differences in risk charges for short and long positions. Short risk charges dominate long ones when the upper tail dominates the comparable lower tail for charges based on distorted expectations. Positive mean return targets acquire long positions with negative mean return targets taking short positions. In each case the appropriate risk charge is minimized to construct two frontiers, one for the positive, and the other for negative, mean return targets. Multivariate return distributions reflect limit laws given by Q self-decomposable laws displaying decay rates in skewness and excess kurtosis slower than those for processes of independent and identically distributed returns. Frontiers at longer horizons display greater efficiency reflected by lower risk charges for comparable mean return targets. The short side frontiers also display greater risk charges than their long side counterparts. All efficient portfolios deliver asset pricing equations whereby required returns in excess of a reference rate are a market price of risk times a risk gradient evaluated at the efficient portfolio. Variations in frontiers and points on the frontier induce differences in reference rates, risk gradients, and the market prices of risk that can yet lead to comparable required returns.

In this paper, we focus on the farmer’s risk income when using commodity futures, when price and output processes are randomly correlated and represented by jump-diffusion models. We evaluate the expected utility of the farmer’s wealth and determine the optimal consumption rate and hedging position at each point in time given the harvest timing and state variables. We find a closed form for the optimal consumption and positioning rate in the case of an investor with CARA utility. This result (see Table 3.3) is a generalization of the result of Ho (J Financ 39:351–376, 1984), which considers the special case in which price and output are diffusion models.

This paper challenges the use of stocks in portfolio construction, instead we demonstrate that Asian derivatives, straddles, or baskets could be more convenient substitutes. Our results are obtained under the assumptions of the Black–Scholes–Merton setting, uncovering a hidden benefit of derivatives that complements their well-known gains for hedging, risk management, and to increase utility in market incompleteness. The new insights are also transferable to more advanced stochastic settings. The analysis relies on the infinite number of optimal choices of derivatives for a maximized expected utility theory agent; we propose risk exposure minimization as an additional optimization criterion inspired by regulations. Working with two assets, for simplicity, we demonstrate that only two derivatives are needed to maximize utility while minimizing risky exposure. In a comparison among one-asset options, e.g. American, European, Asian, Calls and Puts, we demonstrate that the deepest out-of-the-money Asian products available are the best choices to minimize exposure. We also explore optimal selections among straddles, which are better practical choice than out-of-the-money Calls and Puts due to liquidity and rebalancing needs. The optimality of multi-asset derivatives is also considered, establishing that a basket option could be a better choice than one-asset Asian call/put in many realistic situations.

This paper studies the general relationship between the gearing ratio of a Leveraged ETF and its corresponding expense ratio, viz., the investment management fees that are charged for the provision of this levered financial service. It must not be possible for an investor to combine two or more LETFs in such a way that his (continuously-rebalanced) LETF portfolio can match the gearing ratio of a given, professionally managed product and, at the same time, enjoy lower weighted-average expenses than the existing LETF. Given a finite set of LETFs that exist in the marketplace, I give necessary and sufficient conditions for these products to be undominated in the price-gearing plane. In an application of the duality theorem of linear programming, I prove a kind of two-fund theorem for LETFs: given a target gearing ratio for the investor, the cheapest way to achieve it is to combine (uniquely) the two nearest undominated LETF products that bracket it on the leverage axis. This also happens to be the implementation with the lowest annual turnover. For completeness, we supply a second proof of the Main Theorem on LETFs that is based on Carathéodory’s theorem in convex geometry. Thus, say, a triple-leveraged (“UltraPro”) exchange-traded product should never be mixed with cash, if the investor is able to trade in the underlying index. In terms of financial innovation, our two-fund theorem for LETFs implies that the introduction of new, undominated 2.5(times ) products would increase the welfare of all investors whose preferred gearing ratios lie between 2(times ) (“Ultra”) and 3(times ) (“UltraPro”). Similarly for a 1.5x product.

This paper develops a model for optimal portfolio allocation for an investor with quantile preferences, i.e., who maximizes the (tau )-quantile of the portfolio return, for (tau in (0,1)). Quantile preferences allow to study heterogeneity in individuals’ portfolio choice by varying the quantiles, and have a solid axiomatic foundation. Their associated risk attitude is captured entirely by a single dimensional parameter (the quantile (tau )), instead of the utility function. We formally establish the properties of the quantile model. The presence of a risk-free asset in the portfolio produces an all-or-nothing optimal response to the risk-free asset that depends on investors’ quantile preference. In addition, when both assets are risky, we derive conditions under which the optimal portfolio decision has an interior solution that guarantees diversification vis-à-vis fully investing in a single risky asset. We also derive conditions under which the optimal portfolio decision is characterized by two regions: full diversification for quantiles below the median and no diversification for upper quantiles. These results are illustrated in an exhaustive simulation study and an empirical application using a tactical portfolio of stocks, bonds and a risk-free asset. The results show heterogeneity in portfolio diversification across risk attitudes.

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical experiments in order to gauge the accuracy of our approximation.

We investigate whether and how strongly Basel 3 chief innovations jointly affected in different ways individual Eurozone banks’ stability (z-score) across six business models (BMs). We study this issue in the initial years when adaptation was most intense (2011–2014) and the Eurozone underwent a phase with sovereign crises abated by ECB policies easing financial conditions. In parallel, we run this exercise over 2000–2010 data, a time frame over which Basel 3 did not apply yet to see through the eyes of the regulator. Irrespective of BMs, we identify the leverage ratio as the most effective driver of banks’ stability. However, the impact on z-score of Basel 3 chief drivers does not seem to differ significantly on 2011–2014 vs. 2000–2010. Next, interactions with banks’ BMs suggest that Basel 3 innovations improve z-scores the most at traditionally focused banks (cooperative and savings banks), vis-à-vis diversified banks. Our results suggest Basel regulatory decisions were questionable. First, the front loading of the increased minimum capital requirements vs. the backloading of the leverage ratio phasing in may have lured banks from credit to financial assets. Second, our findings support the desirability of revising the current “one-size-fits-all” European prudential framework, which disregards BMs.

This paper studies the asset allocation problem for a retiree facing longevity risk and living standard risk. We introduce a risk capacity constraint to reduce the living standard risk in the retirement period. Whether the retiree focuses on intertemporal consumption or inheritance wealth, we demonstrate a unique number to measure the expected lump sum of the spending post-retirement. The optimal portfolio is nearly neutral to the stock market movement if the portfolio’s value is higher than this critical value; otherwise, the retiree actively invests in the stock market. As a comparison, we consider a dynamic leverage constraint and show that the corresponding optimal portfolio would lose significantly in stressed markets.