# NYU COR1-GB 2311 - The Intertemporal CAPM (16 pages)

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**View the full content.**## The Intertemporal CAPM

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## The Intertemporal CAPM

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- Cor1-Gb 2311 - Foundations of Finance

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Lecture 5 Foundations of Finance Lecture 5 The Intertemporal CAPM ICAPM a Multifactor Model I II III IV V VI VII VIII IX Reading ICAPM Assumptions When do individuals care about more than expected return and standard deviation Examples Tastes and Preferences with a Long term Investment Horizon Portfolio Choice Individual Assets CAPM vs ICAPM Numerical Example 0 Lecture 5 Foundations of Finance Lecture 5 The Intertemporal CAPM ICAPM a Multifactor Model I Reading A BKM Chapter 10 Section 10 4 B BKM Chapter 27 Section 27 2 II ICAPM Assumptions 1 Same as CAPM except can not represent individual tastes and preferences in E R R space When do individuals care about more than expected return and standard deviation A single period setting 1 returns are not normally distributed and individual utility depends on more than expected portfolio return and standard deviation B multiperiod setting 1 returns are not normally distributed and individual utility depends on more than expected portfolio return and standard deviation 2 individual preferences in the future depend on the state of the world at the end of this period 3 expected return and covariances of returns in future periods depends on the state of the world at the end of this period e g predictable returns III 1 Lecture 5 IV Foundations of Finance Examples A Predictable Returns 1 It has been empirically documented that expected stock returns over a period depend on variables known at the start of the period e g dividend yield on the S P 500 at the start of period t DP start t see Lecture 2 2 A high S P500 dividend yield at the start of this month implies high expected returns on stocks this month 3 So a high S P500 dividend yield at the end of this month implies high expected returns on stocks next month 4 Thus S P500 dividend yield at the end of this month is a state variable that individuals care about when making portfolio decisions today B Human capital value 1 An unexpectedly poorer economy at the end of the month implies a larger negative shock to human capital value over the month a the negative shock to human wealth is due to an increased probability of a low bonus or worse job loss 2 Thus the state of the economy at the end of t is positively related to the shock to human capital value over t 3 Suppose a macroeconomic indicator MI end t summarizes the state of the economy at the end of t the economy at the end of t is better for higher MI end t 4 A sufficiently risk averse individual likes a portfolio whose return over t Rp t has a low or negative covariance with a the shock to the individual s human capital over t b the state of the economy at the end of t c MI end t 5 The macroeconomic indicator MI end t is a state variable the individual cares about when making portfolio decisions at the start of t 2 Lecture 5 V Foundations of Finance Tastes and Preferences with a Long term Investment Horizon A Example 1 Today is the start of February 2 An unexpected low MI at the end of February implies an unexpectedly poor economy at the end of February 3 An unexpectedly poorer economy at the end of the February implies a larger negative shock to human capital value over the month 4 The macroeconomic indicator MI end Feb is a state variable the individual cares about when making portfolio decisions at the start of February 5 A sufficiently risk averse individual likes a portfolio whose return over February Rp Feb has a low or negative covariance with a the shock to the individual s human capital over February b the state of the economy at the end of February c MI end Feb B In general if an individual cares about a macroeconomic indicator MI end t then can only fully represent an individual s tastes and preferences for her period t portfolio return using E R t R t R t MI end t C Even more generally if individuals care about a set of K state variables s1 end t sK end t then can only fully represent an individual s tastes and preferences for her period t portfolio return using E R t R t R t s1 end t R t sK end t 3 Lecture 5 VI Foundations of Finance Portfolio Choice A Since individual s care about more than expected return and standard deviation of return individuals no longer hold combinations of the riskfree asset and the tangency portfolio 1 i e individuals no longer hold portfolios on efficient part of the MVF for the N risky assets and the riskless 2 i e individuals no longer hold portfolios on the Capital Allocation Line for the tangency portfolio B Thus in the ICAPM since individuals no longer necessarily hold combinations of the riskfree asset and the tangency portfolio the market portfolio is no longer necessarily the tangency portfolio C Example cont 1 Today is the start of February 2 The tangency portfolio on the MVF for the N risky assets may have a high covariance with MI at the end of February 3 Thus an individual may prefer to hold a portfolio in February not on capital allocation line for the tangency portfolio but which has a very low covariance with MI at the end of February D However it is possible to show that in equilibrium all individuals irrespective of tastes and preferences hold a combination of 1 the riskfree asset 2 the market portfolio 3 K hedging portfolios Rh1 Rh2 RhK one for each state variable E Thus the ICAPM is a generalization of the CAPM F Example cont 1 Today is the start of February 2 The tangency portfolio on the MVF may have a high covariance with MI at the end of February 3 All individuals hold combinations of a the riskfree asset b the market portfolio c a portfolio whose return RMI Feb hedges shocks to human capital value over February 4 Lecture 5 VII Foundations of Finance Individual Assets A Recall that the market portfolio is no longer necessarily the tangency portfolio so the market need not lie on the positive sloped part of the MVF for the N risky assets B Minimum variance mathematics then tells us that there need not be a linear relation between expected return and Beta with respect to the market portfolio i e assets need not all lie on the SML E Ri U Rf i M E RM Rf C Instead if individuals care about the covariance of portfolio return with a set of state variables s1 s2 sK returns and the state variables are multivariate normally distributed then can show that the following holds for all assets and portfolios of assets E Ri Rf i M M i s1 s1 i s2 s2 i sK sK where M s1 s2 sK are constants that are the same for all assets and portfolios and i sk for k 1 2 K and …

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