Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced byan expected-utility maximizing investor who, over a given timehorizon, is constrained to hold an asset which cannot be replicatedby dynamic trading and which therefore does not have a uniqueno-arbitrage price. We first derive the private valuation whichthe investor assigns to the nontraded asset in order to determinehis optimal investment in the traded assets. We thereby showthat, as part of this portfolio, the investor hedges the privatevaluation process of the nontraded asset, rather than its marketprice process. We also study the price at which the investorwould be willing to sell the nontraded asset if he were subsequentlyprohibited from trading in it, as well as the amount the investorwould be willing to pay to remove the trading restriction. Allthree values are shown to depend in an intuitive manner on theinvestor’s risk aversion, the residual risk of the nontradedasset unhedged by the traded assets, the difference betweenthe constrained holding and optimal unconstrained holding ofthe asset and the length of the time horizon over which theasset cannot be traded. JEL Classification: G11     

Optimal life insurance with no-borrowing constraints: duality approach and example

We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT.     

Hedging American Options in Merton's Model: A Locally Risk Minimizing Approach

An interesting problem, related to American options in incomplete markets, is the possibility to select a preferable equivalent martingale measure in order to compute the prices. With this in mind, we consider a particular option that may be viewed as a finite collection of suitable European options and for which the minimal martingale measure permits the minimization of the local risk. Since this option is an approximation of the American put, the stability result presented, concerning the portfolio decomposition, also suggests an argument in favor of the minimal martingale measure in the American case.     

Minimal Entropy Martingale Measures of Jump Type Price Processes in Incomplete Assets Markets

We consider the incomplete assets market and assume that the market has no-arbitrage. Then there are many equivalent martingale measures associated with the market. Among them, a probability measure which minimizes the relative entropy with respect to the original probability measure P, has a special importance. Such a measure is called the minimal entropy martingale measure (MEMM). In a previous paper, we have proved the existence theorem of the MEMM for the price processes given in the form of the diffusion type stochastic differential equation. In this article we discuss the MEMM of the jump type price processes, or especially of the log Lévy processes, and we give the explicit form of MEMM.     

动态不完全市场中不流动资产的定价

流动性对资产收益有重大影响,流动性好坏与资产能否流动是不同层面的问题,前者属于完全市场,后者属于不完全市场,但经典的金融经济学主要研究完全市场上的资产定价和最优组合策略。本文基于中国的现实制度背景,考察流动性受限对资产定价的影响,构建了动态不完全市场中不流动资产的定价模型及最优组合策略;证明了不流动性资产从根本上影响了最优组合策略,不流动资产折价率受到流动约束的时间长短、不流动资产收益的波动率等诸多参数的显著影响。     

Optimal hedging of variance derivatives

We examine the optimal hedging of derivatives written on realised variance, focussing principally on variance swaps (VS) (but, en route, also considering skewness swaps), when the underlying stock price has discontinuous sample paths, i.e. jumps. In general, with jumps in the underlying, the market is incomplete and perfect hedging is not possible. We derive easily implementable formulae which give optimal (or nearly optimal) hedges for VS under very general dynamics for the underlying stock which allow for multiple jump processes and stochastic volatility. We illustrate how, for parameters which are realistic for options on the S&P 500 and Nikkei-225 stock indices, our methodology gives significantly better hedges than the standard log-contract replication approach of Neuberger and Dupire which assumes continuous sample paths. Our analysis seeks to emphasise practical implications for financial institutions trading variance derivatives.     

Pricing and Hedging of Contingent Claims in Term Structure Models with Exogenous Issuing of New Bonds

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain contingent claims. Therefore, we extend the HJM-model in such a way that it lives on an arbitrary time horizon and possesses term structures that cover a constant finite interval of times-to-maturity. We consider the pricing and hedging of contingent claims in this framework.     

Portfolio Effects and Valuation of Weather Derivatives

In a mean‐variance framework, the indifference pricing approach is adopted to value weather derivatives, taking account of portfolio effects. Our analysis shows how the magnitude of portfolio effects is related to the correlation between weather indexes and other risky assets, the correlation between weather indexes, and the payoff structures of the existing weather derivatives in an investor's asset portfolio. We also conduct some preliminary empirical analysis. This study contributes to the weather derivative pricing literature by incorporating both the hedgeable and unhedgeable parts of weather risks in illustrating the portfolio effects on the indifference prices of weather derivatives.     

Stock Market Valuation of Deferred Tax Assets: Evidence from Internet Firms

Abstract:   We use the provisions of SFAS No. 109 , Accounting for Income Taxes , to examine the extent to which stock prices of Internet firms were associated with expectations of future profitability before versus after the 'market correction' in early 2000. We find that the valuation of deferred tax assets of firms with business models reliant on the level of web site traffic was significantly greater after the market correction. In our view, this evidence is consistent with pre‐correction mispricing.     

The Relations between Minimal Martingale Measure and Minimal Entropy Martingale Measure

We consider incomplete markets, where each risky asset fluctuation is a continuous semimartingale, and study a subset of Equivalent Local Martingale Measures in which Minimal Martingale Measure minimizes relative entropy.We also discuss, as special cases, some models with the risky assetfluctuation represented as a solution of some stochastic differential equations.Finally, we mention that the predictable representation property is essentialin order that Minimal Martingale Measure coincides with Minimal Entropy Martingale Measure.     

Investment Horizon and Composition of Optimal Portofolio: International Evidence

Little attention has been paid in the literature to the impact of different investment horizons on the portfolio compositiondespite its importance to portfolio managers. One exception isthe study by Gunthorpe and Levy (1994) on the U.S. stock market.Our paper extends the same study to the stock markets of Japan,Hong Kong and Korea. Using 40 individual stocks in each market,our results support those of Gunthorpe and Levy (1994) in thatthe composition of an optimal portfolio depends heavily on theinvestment horizon. When the investment horizon lengthens, theproportion of defensive stocks becomes larger while that ofaggressive stocks becomes smaller.     

The Effect of Information Quality on Optimal Portfolio Choice

Three types of agents acting on different information sets are considered: fully informed agents, insiders, and outsiders. Differences in information quality are shown to affect the properties of their optimal portfolios. For an outsider, the share of wealth invested in the stock is decreasing in the variance of the stock. However, for an insider, the effect of an increasing stock variance on the optimal portfolio weight is ambiguous. In a calibration to U.S. data, the confidence intervals of the insider's demand for the stock converge, whereas the outsider's confidence intervals become wider.     

Risk sensitive asset management with transaction costs

This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska. Mansucript received: July 1998; final version received: January 1999     

The creation of wealth

The paper is concerned with the existence of a consumption sequence that implies wealth to grow at a given rate. It is shown that under reasonable assumptions such a sequence exists and can be determined by solving a fixed-point problem.     

居民最优消费与投资组合 ——基于不完全市场的分析

运用动态最优控制理论与随机金融分析方法,研究由劳动收入的特质风险与借贷约束导致的非完全市场对消费者最优投资和消费策略、波动及福利损失的影响,得到相应的动态最优投资和消费策略.研究发现:非完全市场会显著抑制消费者的消费动机和投资动机,并加剧消费波动和投资波动.此外,财务困境下非完全市场会对消费者造成高达40％ 的福利损失.     

Payout Policy Relevance and Accounting‐based Valuation

DeAngelo and DeAngelo (2006) (D&D) argue ‘payout policy is not irrelevant and investment is not the sole determinant of value, even in frictionless markets’. Consistent with this view, we argue that the concept of a perfect capital market in Miller and Modigliani (1961) (M&M) and Fama and Miller (1972) can be extended to allow for managerial moral hazard if managers are assumed not to participate in securities trading. An updated version of the M&M valuation model is presented and the possibility of managerial free cash flow (FCF) retention through operating expense manipulation and sub‐optimal investment policies is discussed. Our analysis supports D&D's argument that payout policy is relevant and indicates that value relevance of payout depends on the quality of earnings measurement and the optimality of investment policy. Following this, we develop a framework for analyzing valuation and informational roles of payout in accounting‐based valuation models and apply this framework to the Ohlson (1995) and Feltham and Ohlson (1996) models. This analysis shows how these models permit payout valuation relevance due to managerial FCF retention but not payout informational relevance. Finally, we consider how the Feltham and Ohlson (1996) model can be extended to incorporate time variation in expected profitability of capital investment caused by time variation in managerial FCF retention activities and show that this explicitly affects payout value relevance. We conclude that the development of models where payout plays an explicit valuation role due to issues of moral hazard is an important direction for future research.     

The Determinants of Investor Valuation of R&D Expenditure in the Software Industry

This paper examines the cross-sectional variability in the market valuation of R&D expenditures in the pre-packaged computer software industry. Consistent with some prior research, this paper argues that R&D spending is valued heterogeneously by the stock market, and derives hypotheses regarding the determinants of the cross-sectional heterogeneity in the market valuation of R&D. The empirical tests use an extensive database containing product level information of software firms between 1994 and 1998, along with accounting and stock price data of the same period. The test results, consistent with our hypotheses, show that R&D spending is more valuable for firms with larger market shares, higher percentage of technical employees, and those that have diversified into different product categories. The results also indicate that market valuation of R&D spending is a function of product life cycle.     

The Valuation of Contingent Claims under Portfolio Constraints: Reservation Buying and Selling Prices

With constrained portfolios contingent claims do not generally havea unique price that rules out arbitrage opportunities.Earlier studies have demonstratedthat when there are constraints on the hedge portfolio,a no-arbitrage price interval for any contingent claim exists.I consider the more realistic case where the constraints are imposed on the total portfolio of each investor and define reservation buying and selling prices for contingent claims. I derive propertiesof these prices, show how they can be computed numerically, and study two simple examples in which the reservation prices and the corresponding hedging strategies are compared to the Black–Scholes setting.     

Portfolio and welfare consequences of debt market dominance

The ability to issue debt that pays in units of the domestic good leads a country to accumulate a large and negative net foreign asset position while maintaining a positive position in equity. This debt market advantage also helps to explain the weak relationship between the real exchange rate and relative consumption. Our stylized model matches the key facts about the U.S. international portfolio, the U.S. real exchange rate, and explains nearly 50% of the observed variation in the valuation effects. We find that taxing bond market transactions increases the volatility of the exchange rate, capital flows and allocations. In contrast, taxing equity positions stabilizes the exchange rate and capital flows while having little impact on the allocation. Lastly, the paper describes a global solution method for portfolio problems under incomplete markets.