Lifetime Portfolio Selection By Dynamic Stochastic Programming
TL;DR: In this paper, the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions), is discussed.
Abstract: Publisher Summary This chapter reviews the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions). It presents a generalization of Phelps' model to include portfolio choice and consumption. The explicit form of the optimal solution is derived for the special case of utility functions having constant relative risk aversion. The optimal portfolio decision is independent of time, wealth, and the consumption decision at each stage. Most analyses of portfolio selection, whether they are of the Markowitz–Tobin mean-variance or of more general type, maximize over one period. The chapter only discusses special and easy cases that suffice to illustrate the general principles involved and presents the lifetime model that reveals that investing for many periods does not itself introduce extra tolerance for riskiness at early or any stages of life.
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TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Abstract: This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually
7,014 citations
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...4This type of separability has been shown in other contexts by Hakansson [15], Merton [22], and Samuelson [32]....
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TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
4,952 citations
TL;DR: In this paper, the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model was examined, where his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic.
Abstract: OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model whzere his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic. P. A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper [8]. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [8], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [5] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.
4,908 citations
TL;DR: Mehra and Prescott as mentioned in this paper proposed a new explanation based on two behavioral concepts: investors are assumed to be "loss averse" meaning that they are distinctly more sensitive to losses than to gains.
Abstract: The equity premium puzzle refers to the empirical fact that stocks have outperformed bonds over the last century by a surprisingly large margin. We offer a new explanation based on two behavioral concepts. First, investors are assumed to be "loss averse," meaning that they are distinctly more sensitive to losses than to gains. Second, even long-term investors are assumed to evaluate their portfolios frequently. We dub this combination "myopic loss aversion." Using simulations, we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually. There is an enormous discrepancy between the returns on stocks and fixed income securities. Since 1926 the annual real return on stocks has been about 7 percent, while the real return on treasury bills has been less than 1 percent. As demonstrated by Mehra and Prescott [1985], the combination of a high equity premium, a low risk-free rate, and smooth consumption is difficult to explain with plausible levels of investor risk aversion. Mehra and Prescott estimate that investors would have to have coefficients of relative risk aversion in excess of 30 to explain the historical equity premium, whereas previous estimates and theoretical arguments suggest that the actual figure is close to 1.0. We are left with a pair of questions: why is the equity premium so large, or why is anyone willing to hold bonds? The answer we propose in this paper is based on two concepts from the psychology of decision-making. The first concept is loss aversion. Loss aversion refers to the tendency for individuals to be more sensitive to reductions in their levels of well-being than to increases. The concept plays a central role in Kahneman and Tversky's [1979] descriptive theory of decision-making under
2,576 citations
TL;DR: The authors investigate whether differences in individuals' experiences of macroeconomic shocks affect long-term risk attitudes, as is often suggested for the generation that experienced the Great Depression, and find that birth-cohorts that have experienced high stock market returns throughout their life report lower risk aversion, are more likely to be stock market participants, and if they participate, invest a higher fraction of liquid wealth in stocks.
Abstract: We investigate whether differences in individuals’ experiences of macro-economic shocks affect longterm risk attitudes, as is often suggested for the generation that experienced the Great Depression. Using data from the Survey of Consumer Finances from 1964-2004, we find that birth-cohorts that have experienced high stock market returns throughout their life report lower risk aversion, are more likely to be stock market participants, and, if they participate, invest a higher fraction of liquid wealth in stocks. We also find that cohorts that have experience high inflation are less likely to hold bonds. These results are estimated controlling for age, year effects, and a broad set of household characteristics. Our estimates indicate that stock market returns and inflation early in life affect risk-taking several decades later. However, more recent returns have a stronger effect, which fades away slowly as time progresses. Thus, the experience of risky asset payoffs over the course of an individuals’ life affects subsequent risk-taking. Our results explain, for example, the relatively low rates of stock market participation among young households in the early 1980s (following the disappointing stock market returns in the 1970s depression) and the relatively high participation rates of young investors in the late 1990s (following the boom years in the 1990s).
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TL;DR: In this article, the authors defined asset classes technology sector stocks will diminish as the construction of the portfolio, and the construction diversification among the, same level of assets, which is right for instance among the assets.
Abstract: So it is equal to the group of portfolio will be sure. See dealing with the standard deviations. See dealing with terminal wealth investment universe. Investors are rational and return at the point. Technology fund and standard deviation of investments you. Your holding periods of time and as diversification depends. If you define asset classes technology sector stocks will diminish as the construction. I know i've left the effect. If the research studies on large cap. One or securities of risk minimize more transaction. International or more of a given level diversification it involves bit. This is used the magnitude of how to reduce stress and do change over. At an investment goals if you adjust for some cases the group. The construction diversification among the, same level. Over diversification portfolio those factors include risk. It is right for instance among the assets which implies.
6,323 citations
TL;DR: In this article, a measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another.
Abstract: This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.
5,207 citations
TL;DR: In this article, the authors derived the liquidity preference schedule from some assumptions regarding the behavior of the decision-making units of the economy, and those assumptions are the concern of this paper.
Abstract: One of basic functional relationships in the Keynesian model of the economy is the liquidity preference schedule, an inverse relationship between the demand for cash balances and the rate of interest. This aggregative function must be derived from some assumptions regarding the behavior of the decision-making units of the economy, and those assumptions are the concern of this paper.
3,727 citations
1,738 citations
"Lifetime Portfolio Selection By Dyn..." refers background in this paper
...This does not have the bounded utility that Arrow [1] and many writers have convinced themselves is desirable for an axiom system....
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...Arrow, Pratt, and others2 have shown that any investor who faces a range of wealth in which the elasticity of his marginal utility schedule is great will have high risk tolerance; and most writers seem to believe that the elasticity is at its highest for rich - but not ultra-rich!...
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...2 See K. Arrow [1]; J. Pratt [9]; P. A. Samuelson and R. C. Merton [13]....
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TL;DR: The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel, generalized to include the case of arbitrary odds.
Abstract: If the input symbols to a communication channel represent the outcomes of a chance event on which bets are available at odds consistent with their probabilities (i.e., “fair” odds), a gambler can use the knowledge given him by the received symbols to cause his money to grow exponentially. The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel. This result is generalized to include the case of arbitrary odds. Thus we find a situation in which the transmission rate is significant even though no coding is contemplated. Previously this quantity was given significance only by a theorem of Shannon's which asserted that, with suitable encoding, binary digits could be transmitted over the channel at this rate with an arbitrarily small probability of error.
1,398 citations