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Portfolio Choice and Life Insurance

Portfolio Choice and Life Insurance
Author: Moshe A. Milevsky
Publisher:
Total Pages: 31
Release: 2009
Genre:
ISBN:

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We study a class of portfolio choice problems that combine life insurance and labor income under constant relative risk aversion preferences (CRRA) preferences for consumption, within the optimal control framework pioneered by Merton (1969, 1971). Our model differs from previous research by (i) focusing attention on the correlation between human capital and financial capital, and (ii) modeling the utility of the family as opposed to separating consumption and bequest. From a technical point of view we show how the underlying Hamilton-Jacobi-Bellman (HJB) equation can be simplified using a similarity reduction technique, which then allows for the implementation of an efficient numerical solution. And, for reasonable financial economic parameter values, a closed-form approximation is derived which greatly simplifies the numerical calculations. A variety of example illustrating our numerical algorithm are also provided. Our main qualitative result is that households whose primary breadwinner's wages are negatively correlated with financial market returns, should optimally purchase more life insurance and can afford to take more risky positions with their financial portfolio. In addition, we find that the optimal face value of life insurance is remarkably insensitive to the family's risk aversion.


Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

Dynamic Portfolio Choice with Stochastic Wage and Life Insurance
Author: Xudong Zeng
Publisher:
Total Pages: 20
Release: 2015
Genre:
ISBN:

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We study optimal insurance, consumption and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing CARA utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses the life insurance and the investment together to hedge the risk from the stochastic wage.


Strategic Asset Allocation

Strategic Asset Allocation
Author: John Y. Campbell
Publisher: OUP Oxford
Total Pages: 272
Release: 2002-01-03
Genre: Business & Economics
ISBN: 019160691X

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Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.


Behavioral Aspects of Household Portfolio Choice

Behavioral Aspects of Household Portfolio Choice
Author: In Do Hwang
Publisher:
Total Pages: 91
Release: 2017
Genre:
ISBN:

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This paper investigates how loss-aversion affects individuals' decisions on savings and insurance purchase. Specifically, this paper empirically tests if prospect theory's loss aversion decreases insurance demand and increases savings demand. Prospect theory predicts that boundedly rational consumers may view pure protection insurance, such as term-life insurance, as a risky investment because the insured may lose premiums if a bad event does not occur within the pre-specified term. Hence, those who are fairly sensitive to the potential loss choose not to buy term-life insurance. Instead, they may choose a more safe option to prepare for uncertain future events by increasing precautionary saving. This paper tests such prediction using individual-level data from the Health and Retirement Study (HRS) and finds empirical evidence consistent with the prediction: loss-averse individuals are less likely to own term-life insurance and more likely to own whole-life insurance, which serves as a partial savings instrument. These individuals also hold a higher level of wealth than others, suggesting that they tend to save more (presumably for precautionary motives), all other things being equal.


Optimal Portfolio Selection with Life Insurance Under Inflation Risk

Optimal Portfolio Selection with Life Insurance Under Inflation Risk
Author: Minsuk Kwak
Publisher:
Total Pages:
Release: 2014
Genre:
ISBN:

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This paper investigates a continuous-time optimal consumption, investment, and life insurance decision problem of a family under inflation risk. In the financial market, there is a liquid inflation-linked index bond market which can be utilized to hedge the inflation risk. The explicit solutions for the optimal strategies including consumption rate, investment for each financial asset, and life insurance premium are derived for constant relative risk aversion (CRRA) utility case using martingale approach. The roles of an index bond are investigated and it is verified that they depend on market parameters. We analyze the effects of market parameters on the optimal strategies with focus on the demand for index bond and optimal life insurance premium. Especially, the change of inflation rate has considerable impact on optimal life insurance premium.


Portfolio Choice and Mortality-Contingent Claims

Portfolio Choice and Mortality-Contingent Claims
Author: Huang Huaxiong
Publisher:
Total Pages: 24
Release: 2009
Genre:
ISBN:

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We solve a portfolio choice problem that includes mortality-contingent claims and labor income under general HARA preferences. Our contribution beyond existing literature is to (i) focus on the covariance between shocks to human capital and financial capital, to (ii) model the utility of a family with basic needs, (iii) include life insurance and pension annuity claims in one unified life-cycle model. Our solution employs a similarity reduction mapping which reduces the two dimensional HJB equation into one dimension. This allows for the implementation of a quick numerical scheme. And, when shocks to human capital and financial capital are perfectly correlated, a closed-form expression is obtained as a special case.


Portfolio Choice With Puts

Portfolio Choice With Puts
Author: Moshe A. Milevsky
Publisher:
Total Pages: 32
Release: 2008
Genre:
ISBN:

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In this paper we investigate the actual portfolio choice and asset allocation behavior of individuals who acquire insurance in the form of an out - of - the - money long dated put option on their investment funds. We compare their allocations against those who do not elect and pay for this type of protection; dubbed a longevity put. Using a unique database of nearly a million variable annuity (VA) policyholders collected by seven different insurance companies, we find that these investors take on 5% to 30% additional risky/equity exposure when the longevity put option is selected. And, when this longevity put option is not purchased - so the investment portfolio resembles a conventional mutual fund - we confirm the classical life-cycle age phased reduction in equity.We offer a rudimentary model of utility - maximizing behavior in the presence of this longevity put that indeed justifies the increased allocation to risk, provided the investor is willing, able and understands to exercise the annuity option if - and - when it matures in the money. This, of course, is debatable given the long standing body of evidence - first documented by Modigliani(1986) - that individuals intensely dislike annuitization despite its welfare enhancing properties.Regardless, we believe our paper is the first to examine actual asset allocations within variable annuity policies, which is currently a $1.5 trillion dollar market in the U.S. and is expected to grow as aging baby boomers take control of their own retirement assets.