Portfolio Choice and Life Insurance: The CRRA Case

We solve a portfolio choice problem that includes life insurance and labor income under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equation using a similarity reduction technique that leads to an efficient numerical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family's risk aversion, consistent with practitioner guidance.     

Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

This paper examines the optimal consumption and portfolio-choiceproblem of long-horizon investors who have access to a risklessasset with constant return and a risky asset ("stocks") withconstant expected return and time-varying precision—thereciprocal of volatility. Markets are incomplete, and investorshave recursive preferences defined over intermediate consumption.The paper obtains a solution to this problem which is exactfor investors with unit elasticity of intertemporal substitutionof consumption and approximate otherwise. The optimal portfoliodemand for stocks includes an intertemporal hedging componentthat is negative when investors have coefficients of relativerisk aversion larger than one, and the instantaneous correlationbetween volatility and stock returns is negative, as typicallyestimated from stock return data. Our estimates of the jointprocess for stock returns and precision (or volatility) usingU.S. data confirm this finding. But we also find that stockreturn volatility does not appear to be variable and persistentenough to generate large intertemporal hedging demands.     

Financial and Demographic Risks of a Portfolio of Life Insurance Policies with Stochastic Interest Rates

Abstract

We refer to a recent paper by G. Parker (1997) in which the risk of a portfolio of life insurance policies (namely the risk related to the entire contractual life) is studied by separating the demographic component from the financial component. In our paper, after making a brief summary of Parker’s model, we propose two additional contributions: 1. We first give the problem a different formalization, thus allowing a portfolio risk analysis by management periods and a study of the risk due to the interactions among years;

2. We elaborate on a powerful and flexible algorithm for calculating the probability distribution of the sum of random variables that proves useful to solve not only the problems discussed in this paper concerning the risk analysis but also various other problems.

In the paper, we also show, for both contributions, some applications made under the same financial and demographic assumptions taken by Parker; we also compare our results with Parker’s results.     

Consumption and Portfolio Choice over the Life Cycle

This article solves a realistically calibrated life cycle modelof consumption and portfolio choice with non-tradable laborincome and borrowing constraints. Since labor income substitutesfor riskless asset holdings, the optimal share invested in equitiesis roughly decreasing over life. We compute a measure of theimportance of human capital for investment behavior. We findthat ignoring labor income generates large utility costs, whilethe cost of ignoring only its risk is an order of magnitudesmaller, except when we allow for a disastrous labor incomeshock. Moreover, we study the implications of introducing endogenousborrowing constraints in this incomplete-markets setting.     

Portfolio Insurance with Liquidity Risk

This paper studies a portfolio insurance problem with liquidity risk. We consider an investor who wants to maximize the expected growth rate of wealth in a low liquid market. The investor can trade assets only at random times and his wealth must not fall below a predetermined floor. We find the optimal expected growth rate and an optimal strategy. The optimal strategy is closely related with a traditional constant proportion portfolio insurance strategy. Also we show that the same strategy maximizes the growth rate almost surely. Further we study the floor effect on the growth rate.     

Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations

We derive a closed-form solution for the optimal portfolio ofa nonmyopic utility maximizer who has incomplete informationabout the alphas or abnormal returns of risky securities. Weshow that the hedging component induced by learning about theexpected return can be a substantial part of the demand. Usingour methodology, we perform an "ex ante" empirical exercise,which shows that the utility gains resulting from optimal allocationare substantial in general, especially for long horizons, andan "ex post" empirical exercise, which shows that analysts’recommendations are not very useful. (JEL C61, G11, G24)     

Household Life Cycle Protection: Life Insurance Holdings, Financial Vulnerability, and Portfolio Implications

Using the Survey of Consumer Finances, we examine the life cycle demand for different types of life insurance. Specifically, we test for the consumer's aversion to income volatility resulting from the death of a household's wage‐earner through the purchase of life insurance. We first develop a financial vulnerability index to control for the risk to the household. We then examine the life cycle demand for life insurance using several definitions of life insurance. We find, in contrast to previous research, that there is a relationship between financial vulnerability and the amount of term life or total life insurance purchased. In addition, we find older consumers use less life insurance to protect a certain level of financial vulnerability than younger consumers. Secondly, our study provides evidence that life insurance demand is jointly determined as part of a household's portfolio. Finally, we consider the impact of family members' nonmonetary contribution on the household's life cycle protection decision. Our results provide some evidence that households take into account the value of nonmonetary contribution in their insurance purchase.     

The Impact of Disability Insurance on a Portfolio of Life Insurances

The aim of this article is to study the impact of disability insurance on an insurer's risk situation for a portfolio that also consists of annuity and term life contracts. We provide a model framework using discrete time nonhomogeneous bivariate Markov renewal processes and in a simulation study focus on diversification benefits as well as potential natural hedging effects (risk-minimizing or risk-immunizing portfolio compositions) that may arise within the portfolio because of the different types of biometric risks. Our analyses emphasize that disability insurances are a less efficient tool to hedge shocks to mortality and that their high sensitivity toward shocks to disability risks cannot be easily counterbalanced by other life insurance products. However, the addition of disability insurance can still considerably lower the overall company risk.     

Time-Invariant Portfolio Insurance Strategies

This paper characterizes the complete class of time-invariant portfolio insurance strategies and derives the corresponding value functions that relate the wealth accumulated under the strategy to the value of the underlying insured portfolio. Time-invariant strategies are shown to correspond to the long-run policies for a broad class of portfolio insurance payoff functions.     

Insurance Portfolio Risk Retention

In this article, I introduce a statistic for managing a portfolio of insurance risks. This tool is based on changes in the risk profile when changes in a risk parameter, such as a deductible, coinsurance, or upper policy limit, are made. I refer to the new statistic as a risk measure relative marginal change and denote it as RM². By examining data from the Wisconsin Local Government Property Fund, I show how it can be used by an insurer to identify the “best” and “worst” risks in terms of opportunities for risk management. The RM² changes reflect the underlying dependence structure of risks; I use an elliptical copula framework to demonstrate the sensitivity of risk mitigation strategy to the dependence structure.     

Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities

We derive the optimal investment policy of a risk-averse investorin a market where there is a textbook arbitrage opportunity,but where liabilities must be secured by collateral. We findthat it is often optimal to underinvest in the arbitrage bytaking a smaller position than collateral constraints allow.Even when the optimal policy is followed, the arbitrage portfoliotypically experiences losses before the final convergence date.In fact, its initial performance may be indistinguishable fromthat of a conventional portfolio with a poor track record. Theseresults have important implications for the role of arbitrageursin financial markets.     

A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability

We present a simulation-based method for solving discrete-timeportfolio choice problems involving non-standard preferences,a large number of assets with arbitrary return distribution,and, most importantly, a large number of state variables withpotentially path-dependent or non-stationary dynamics. The methodis flexible enough to accommodate intermediate consumption,portfolio constraints, parameter and model uncertainty, andlearning. We first establish the properties of the method forthe portfolio choice between a stock index and cash when thestock returns are either iid or predictable by the dividendyield. We then explore the problem of an investor who takesinto account the predictability of returns but is uncertainabout the parameters of the data generating process. The investorchooses the portfolio anticipating that future data realizationswill contain useful information to learn about the true parametervalues.     

Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choiceproblems, up to the solution of an ordinary differential equation(ODE), when the asset returns are quadratic and the agent hasa constant relative risk aversion (CRRA) coefficient. My solutionincludes as special cases many existing explicit solutions ofdynamic portfolio choice problems. I also present three applicationsthat are not in the literature. Application 1 is the bond portfolioselection problem when bond returns are described by "quadraticterm structure models." Application 2 is the stock portfolioselection problem when stock return volatility is stochasticas in Heston model. Application 3 is a bond and stock portfolioselection problem when the interest rate is stochastic and stockreturns display stochastic volatility. (JEL G11)     

An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs

The presence of any friction in financial markets qualitatively changes the nature of the optimization problem faced by an investor. It requires one to either act or do nothing, an issue which, of course, does not arise in frictionless situations. The investor considered here accumulates wealth without consuming until some terminal point in time when he consumes all. His objective is to maximize the expected utility derived from that terminal consumption. We postpone the terminal point far into the future to obtain a stationary portfolio rule. The portfolio policy is in the form of two control barriers between which portfolio proportions are allowed to fluctuate. We show how to calculate them.     

投资组合保险策略的运作原理

保本基金与组合保险策略 投资组合保险1理论起源于20世纪80年代的美国.由伯克利大学金融学教授Hayne E Leland和Mark Rubinstein创始的这项技术自1983年被首次应用于Wells Fargo Investment Advisors、AetnaLife、Casualty三家金融机构的投资管理运作实践中,并在80年代中期得到蓬勃发展.该理论对于较不愿承受风险的投资者或处于下跌的市况来说.是一种很好的投资策略.     

组合保险策略的实证检验

组合保险策略概述 组合保险策略核心思想是,通过静态或者动态资产配置策略的使用,将股票组合损失锁定在一定范围内,同时仍致力追求股市上涨时带来的收益.根据策略设计依据不同,组合保险策略可分为两大类:一类是依据Black、Scholes(BS,1973)提出的期权定价公式所衍生出的基于期权的组合保险(option-based portfolio insurance,OBPI)策略,包括欧式保护性卖权策略、复制性卖权策略;另一类则是依据投资者本身风险偏好以及承风险担能力设定一些简单的参数所形成的组合保险策略,包括固定比例组合保险(constant proportion portfolioinsurance,CPPI)策略、时间不变性组合保险(time-invariant portfolioprotection,TIPP)策略.     

Equilibrium Analysis of Portfolio Insurance

A martingale approach is used to characterize general equilibrium in the presence of portfolio insurance. Insurers sell to noninsurers in bad states, and general equilibrium requires that the risk premium rises to induce noninsurers to increase their holdings. We show that portfolio insurance increases price volatility, causes mean reversion in asset returns, raises the Sharpe ratio and volatility in bad states, and causes volatility to be correlated with volume. We also explain why out-of-the-money S&P 500 put options trade at a higher volatility than do in-the-money puts.     

Systemic Risk and International Portfolio Choice

Returns on international equities are characterized by jumps; moreover, these jumps tend to occur at the same time across countries leading to systemic risk. We capture these stylized facts using a multivariate system of jump‐diffusion processes where the arrival of jumps is simultaneous across assets. We then determine an investor's optimal portfolio for this model of returns. Systemic risk has two effects: One, it reduces the gains from diversification and two, it penalizes investors for holding levered positions. We find that the loss resulting from diminished diversification is small, while that from holding very highly levered positions is large.