ABSTRACT
A conditional version of the CAPM is applied to the returns of emerging markets and the results are compared with those obtained in developed markets. Conditional refers to the use of conditioning information, some information set Zt−1 to calculate expected moments and to test properly the intertemporal capital asset pricing model (ICAPM) as a relation between expected returns and ex-ante risk. e conditional version of the Sharpe (1964) and Lintner (1965) asset-pricing model restricts the conditionally expected return on an asset to be proportional to its covariance with the market portfolio. e proportionality factor is the price of covariance risk which is the expected compensation that the investor receives for taking on a unit of covariance risk. e model is given as
[ ] Cov
Var[ ] mt t
E r E r r r
r −
Ω⎡ ⎤ ⎡ ⎤Ω = Ω⎣ ⎦ ⎣ ⎦Ω (7.1)
where rjt is the return on a portfolio of country j equity from time t − 1 to t in
excess of the risk return rmt is the excess return on the world market portfolio Ωt−1 is the information set that investors use to set prices
e ratio of the conditionally expected return on the market index E[rmt|Ωt−1] to the conditional of the market index Var[rmt|Ωt−1] is the world price of covariance.* Harvey fi rst specifi ed a model of the conditional fi rst moment and assumed that investors process information using a linear fi lter:
− −− = δ +1 1 jtjt t t jR r Z u (7.2)
− =1 0( )jt tE u | Z (7.3)
where ujt is the investor’s error for the return on assets j Zt−1 is a row of vector of predetermined instrumental variables, which
are known to the investor δj is a column vector of time invariant forecast coeffi cients
Given the assumption on the conditional fi rst moment, Equation 7.1 can be rewritten as
δ ⎡ ⎤δ = ⎣ ⎦⎡ ⎤⎣ ⎦ 1
Z Z E u u |z
E u |z (7.4)
where umt is the investor’s forecast error on the world market portfolio
2 1|mt tE u Z −⎡ ⎤⎣ ⎦ is the conditional variance
⎡ ⎤⎣ ⎦1|jt mt tE u u Z is the conditional
Next, multiply both sides of the Equation 7.4 by the conditional variance
1 1 1 1mt t j t jt mt t m tE u Z Z E u u Z Z− − − −⎡ ⎤ ⎡ ⎤δ = δ⎣ ⎦ ⎣ ⎦ (7.5)
Notice that the conditionally expected returns on the market and country portfolio are moved inside the expectation operators. is can be done because they are known conditional on the information Zt−1. e deviation from the expectation is
− −= δ − δ 2
where hjt is the disturbance that should be unrelated to the information under the null hypothesis that the model is true. hjt is a pricing error which implies that the model is overpriced when hjt is negative and under priced when hjt is positive.
