According to Merton (1973) inter-temporal capital asset pricing model (ICAPM), the conditional expected excess return on the stock market should be a linear function of the stock market's conditional variance as well as a hedging component which captures the investor's motive to hedge for future investment opportunities: where Et[Rt+1] and Vart[Rt+1] are the expectation and the variance of the market excess return which are conditional on the information available at the beginning of the return period denoted as time t, while ÃÆ’MF,t is the conditional covariance between the expected excess return and variation in the investment opportunity set. J (W,F,t) is the indirect utility function in wealth W and any variables F, describing the evolution of the investment opportunity set over time. The term [-JwwW/Jw] is associated with the coefficient of relative risk aversion which is usually assumed to be positive, whereas the other term is the adjustment to the conditional risk premium arising from innovations to the state variables that describe variation in the investment opportunity set. Since Jw is positive, the sign of the adjustment component is determined by (1) By ignoring the hedging component under certain circumstances, the original ICPAM extends to a more general model which can be approximately expressed as where ÃŽÂ³ describes the coefficient of relative risk aversion of the representative investor and ÃŽÂ¼ should be equal to zero. To put it another way, the investor who bears more risk would require higher risk premium for compensation. This risk-return trade-off is known as the "first fundamental law of finance" in financial economics (Ghysels, Santa-Clara and Valkanov, 2005). However, in spite of the great contribution of Merton's research, it is exploratory which does not include hypotheses test. This positive risk-return trade-off has been proved to be hard to find in the data by previous literature. The main difficulty in testing the ICAPM relation is the way to filter the unobservable market conditional variance from the raw data of past returns. Thus, the conflicting findings of past empirical literature result mostly from the different approaches to model the conditional variance. Generally, it can be classificated into three types of models namely ARIMA, GARCH type models, Markov switching models and a pretty new approach-MIDAS. The remainder part of this section reviews the representative work with each type of models more specifically. French, Schwert and Stambaugh (1987) find evidence that the expected market risk premium is positively related to the predictable stock market volatility in a generalized autoregressive conditional heteroskedasticity (GARCH) approach. Also, they observe a strong negative relation between unexpected stock market returns and unexpected change in the stock market volatility which they interpret as the indirect proof of a positive ex ante risk-return relation by using a univariate autoregressive integrated-moving average (ARIMA) model. To start with, they decompose estimates of monthly volatility into predictable and unpredictable components by ARIMA model. The variance of monthly return is computed as the sum of the squared daily returns added by twice the sum of the products of adjacent returns, owing to the autocorrelation of daily returns especially at lag one caused by non-synchronous trading of securities (Fisher 1966, Scholes and Williams 1977):

# The use of Inter-Temporal Capital Asset Pricing Model conditions in the market

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