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.     

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。     

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.     

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     

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.     

Stock Market Mean Reversion and the Optimal Equity Allocation of a Long-Lived Investor

This paper solves numerically the intertemporalconsumption and portfolio choiceproblem of an infinitely-lived investor whofaces a time-varying equity premium.The solutions we obtain are very similarto the approximate analytical solutionsof Campbell and Viceira (1999), except atthe upper extreme of the state spacewhere both the numerical consumption andportfolio rules flatten out.We also consider a constrained version ofthe problem in which the investor facesborrowing and short-sales restrictions.These constraints bind when the equitypremium moves away from its mean in eitherdirection, and are particularly severe forrisk-tolerant investors. The constraints havesubstantial effects on optimalconsumption, but much more modest effects onoptimal portfolio choice in theregion of the state space where they are notbinding.     

Loan Portfolio Swaps and Optimal Lending

Theories on loan portfolio swap hedging are based on a portfolio-choice approach. This paper presents an alternative: a firm-theoretic model for bank behavior with loan portfolio swaps. Our paper derives the optimal loan rate and rate-taking loan amount of the banks portfolio, and relates them to the market loan rate, counterparty loan rate, swap default risk, capital-to-deposits ratio, and deposit insurance. We find that in the bilateral default risk approach, the comparative static results are generated by four factors: the banks risk magnitude about the equity market value, loan composition in the swap contract, the substitution effect in the loan portfolio, and the income effect from the swap transaction. The results imply that changes in the payoff asymmetry in the event of swap default and the banks regulatory parameters have a direct effect on the banks loan portfolio for lending and swap transactions.We would like to thank two anonymous referees for helpful comments and advice.     

The Valuation Accuracy of the Price-Earnings and Price-Book Benchmark Valuation Methods

This paper evaluates the valuation accuracy of the price-earnings (P/E), the price-book (P/B) and a combined price-earnings and price-book (P/E-P/B) benchmark valuation methods. Performance of the benchmark valuation methods relies on the definition of comparable firms. In this paper, comparable firms are selected based on industry membership, size and return on equity as well as combinations of industry membership with size and with return on equity. We find that within the P/E and P/B benchmark valuation methods, the best definition of the comparable firms are based on industry membership combined with return on equity. However, only the industry membership is necessary to define the comparable firms for the combined P/E-P/B method. In sum, the results suggest that, when firm's value is unknown, the combined P/E-P/B valuation approach selecting comparable firms based on industry membership performs the best among all the approaches evaluated in this paper.We also find that the P/E benchmark valuation method performs better than the P/B benchmark valuation method and the combined method outperforms either the P/E or the P/B method. These results imply that earnings are more important than book value as a single-number firm valuator over our sample years (from 1973 to 1992) and that both earnings and book values are value relevant, one does not substitute perfectly for the other.     

Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets

The paper presents an incomplete market pricingmethodology generating asset pricebounds conditional on the absence of attractiveinvestment opportunities in equilibrium.The paper extends and generalises the seminal article ofCochrane and Saá-Requejowho pioneered option pricing based on the absenceof arbitrage and high Sharpe Ratios. Ourcontribution is threefold:We base the equilibrium restrictions on an arbitrary utility function, obtaining theCochrane and Saá-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms ofGeneralised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide aconsistent ranking of investment opportunities even when asset returns are highlynon-normal. Last but not least, we demonstrate that for Itô processes theCochrane and Saá-Requejo price bounds are invariant to the choice of the utilityfunction, and that in the limit they tend to a unique price determined by theminimal martingale measure.     

Valuation of the Firm's Liabilities When Equity Holders Are Also Creditors

Abstract:  This paper presents a tractable structural model whereby controlling equity holders are also among the creditors of the firm. As the firm approaches distress, equity holders can drain the assets of the firm and expropriate other creditors by repaying their credit before bankruptcy. The right of the bankruptcy court to revoke such repayment protects arm's length creditors, reduces the cost of borrowing and induces equity holders to anticipate repayment of their credit. Equity holders decide repayment neither too early nor too late, so as to reduce the risk of repayment revocation by the bankruptcy court. Similar conclusions apply to the preferential repayment of bank loans personally guaranteed by equity holders. The analysis also suggests that callable bearer bonds may be more valuable to equity holders than to other creditors.     

Size and Value Anomalies under Regime Shifts

This paper finds strong evidence of time-variations in the jointdistribution of returns on a stock market portfolio and portfoliostracking size- and value effects. Mean returns, volatilitiesand correlations between these equity portfolios are found tobe driven by underlying regimes that introduce short-run markettiming opportunities for investors. The magnitude of the premiaon the size and value portfolios and their hedging propertiesare found to vary across regimes. Regimes are shown to havea large impact both on the optimal asset allocation—especiallyunder rebalancing—and on investors' utility. Regimes alsohave a considerable impact on hedging demands, which are positivewhen the investor starts from more favorable regimes and negativewhen starting from bad states. Recursive out-of-sample forecastingexperiments show that portfolio strategies based on models thataccount for regimes dominate single-state benchmarks.     

Taxation of Interest Income

Why is interest income taxed so much more heavily than other forms of capital income? This differential tax treatment has generated substantial tax arbitrage, resulting in lower tax revenue, efficiency costs, and apparently net gains to rich borrowers and net losses to poor lenders, together suggesting that this tax treatment makes no sense on welfare grounds. In examining this argument more formally, this paper reveals two omitted considerations that can help explain the existing tax treatment. First, the forecasted increase in the market interest rate results in a redistribution from rich borrowers to poor lenders. Yet this redistribution comes at no marginal efficiency cost, starting from a situation with no distortions to portfolio choice, so at the margin dominates further redistribution through the income tax. In addition, information about an individual's portfolio choice reveals information about her earnings ability, even controlling for observed labor income, if those who are more able tend to be less risk averse. By making use of this extra information about earnings ability, the tax system can be better tailored to redistribute from able to less able, for any given efficiency cost.     

The Aggregation and Valuation of Deferred Taxes

Review of Accounting Studies - This paper clarifies some of the conflicting arguments about the value relevance of deferred taxes. We address two questions. First, does accounting aggregation hold,...     

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.