Economics of financial markets part 2
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Economics of financial markets part 2
11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 making has been limited to a single date. In chapter 10 several intertemporal aspects of asset price determination were studied, but individual maximizing decisions were neglected. In this chapter the optimizing choices of investors return to the foreground. As a consequence, ii is possible lo addr Economics of financial markets part 2 ess questions about how investors’ portfolios are affected by the opportunity to change their asset holdings in the future, or to consume some of theiEconomics of financial markets part 2
r wealth, or to add to their investments from a flow of saving.Although the analysis of investment decisions becomes more complicated in a multiperiod11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 H|= I-11.1where E[-] is an expectations operator reflecting the beliefs of the investor, f j is the rate of return on asset /■ (j = 1.2,and H is a random variable that depends on each investor’s risk preferences, The EVR remains the focus of attention in portfolio selection, and the inclusion of tim Economics of financial markets part 2 e subscripts makes explicit the role of the dates at which decisions arc made or information becomes available. Most importantly, in the multiperiod cEconomics of financial markets part 2
hoice setting, H can be given a particular and precise interpretation as a stochastic discount factor.Several new dimensions are added to the analysis11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 ize the allocation of consumption among different goods and across time. Here, the accumulation of wealth is an intermediate objective, a stepping stone towards the consumption of goods and services; the optimal choice of consumption according to preferences is assumedIntertemporal choice and the eq Economics of financial markets part 2 uity premium puzzle251to be the ultimate aim of individual decisions. Section 11.1 begins with a review of a two-period world for which the future isEconomics of financial markets part 2
certain. Simplistic though this must seem, the principles generalize readily to a world with uncertainty, many assets and long time horizons; the exte11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 e portfolio decisions of investors. The famous equity premium puzzle is explored in section 11.4. while section 11.5 shows how the capital asset pricing model can be extended to allow for investors’ intertemporal planning.11.1Consumption and investment in a two-period world with certaintyThe allocat Economics of financial markets part 2 ion of consumption over lime introduces, by implication, a saving decision - a second way in which wealth can be accumulated or depleted (the first waEconomics of financial markets part 2
y being via the return on assets). Each individual’s decisions can. in principle, be extended to include labour supply and. consequently, a new source11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 eglects labour/leisure choices. Also, sources of income other than the return on assets are ignored in this section. Finally, it is assumed that goods al each dale can be aggregated into a single ‘consumption’ good each unit of which has a price equal to one unit of account (so that changes in the g Economics of financial markets part 2 eneral price level are neglected). Each of these assumptions can be relaxed without sacrificing the fundamental insights of the analysis.In elementaryEconomics of financial markets part 2
microeconomics the intertemporal consumption decision is modelled by assuming that the individual chooses consumption Cj in (he present period and co11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 nasmuch as ct and ct 11 differ from the endowments in Ĩ and t + 1. (he individual saves or borrows between the present. /. and the future, 14-1. Here it is assumed that the endowment takes the form of wealth. IV;. available at the present, date Í. (Presumably, IV; was accumulated in the past - i.c. Economics of financial markets part 2 dates prior to /.) The difference between wealth and current consumption, VV; — C;. represents saving (if positive) or borrowing (if negative).1Il isEconomics of financial markets part 2
assumed provisionally that wealth is transferred between t and t + 1 at a given, certain interest rale. /;+I. Hence, wealth at the start of the next p11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 umed to be zero, so that ‘saving’ is used in an unconventional way to refer to wealth net of current consumption.252The economics of financial marketsdate 14-1. equals H'z+| =(14- rz+|)(Wf — Cz). Given that all wealth is consumed at /4- 1. the individual’s budget constraint is simplyC/+l=(l+r/+l)(VG Economics of financial markets part 2 )-11.2In this framework each ‘dale’. Ĩ. denotes the start of the time period, and consumption in period Ĩ takes place between dale Ĩ and dale 7 4-1. AEconomics of financial markets part 2
lso, the rale of return. r,+i, corresponds to wealth accumulated in the period immediately preceding dale /4-1. These timing conventions arc maintaine11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 utility function U(Ct, cz+|). For little reason other than tractability and case of interpretation, it is assumed that the utility function lakes the formỈ/(C„ Cr+1) = "(Ct) + Ỗ«(C,+I)-11.3where <5 < I denotes a subjective discount factor, which reflects the rate at which the individual weights futu Economics of financial markets part 2 re consumption relative to the present.2 Sometimes the subjective trade-off between the present and the future is expressed by the ’rate of lime prefeEconomics of financial markets part 2
rence’, defined as (1/Ổ) — 1.The function //(•) applies to consumption in just one lime period and is sometimes called the ‘felicity function’ to dist11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 for consumption in the present compared with the future. Marginal utility is assumed to be positive but diminishing: iT(•) > 0. «"(•) < 0. at each level of consumption.Figure 11.1 depicts an optimum, al L. for the consumer. Just as in elementary consumer theory, E denotes a tangency between the budg Economics of financial markets part 2 et constraint (the line joining wz and (1 4->7+1 )VVZ) and an indifference curve - the highest that can be attained subject lo the budget constraint.FEconomics of financial markets part 2
or the purposes of this chapter the relevant implication of figure 11.1 is the condition that defines the tangency - i.e. the necessary, or first-orde11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 ividual transfers one ‘small’ unit of wealth from the present period to the next. This results in a loss of utility, equal to the marginal utility of forgone consumption, in the present. By the next date wealth will have grown in2 The 5 parameter should not be confused with discount factors derived Economics of financial markets part 2 from market interest rales. Here Ổ reflects an aspect of preTerences, and only in rather special equilibria will Ỗ equal a market discount factor.•’ TEconomics of financial markets part 2
he distinction between the utility function and the felicity function is neglected except where ambiguity may result.4By definition, an interior maxim11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 een consumption ‘today*, c,. and consumption ■tomorrow', Cxl|. rhe choice is made to maximize utility subject to a wealth constraint, liach indifference curve is drawn for a given level of utility. The line joining W' and (I +/*f|i)VV; represents the wealth constraint. Point £ depicts the point of m Economics of financial markets part 2 aximum utility, such that consumption is allocated to reach the highest possible indifference curve without violating the wealth constraint. The tangeEconomics of financial markets part 2
ncy al E defines the necessary', or first-order, condition for a maximum of utility.proportion lo the interest rate. The increment to wealth yields a 11Intertemporal choice and the equity premium puzzleOverviewWhile all financial decisions involve the future, in earlier chapters individual decision Economics of financial markets part 2 s the gain of utility (in the future) equals the loss (in the present), utility cannot be at a maximum.More formally, a necessary condition for an interior optimum is that Economics of financial markets part 2Gọi ngay
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