In the utility function: U = E(r) - (1/2)(A)(S^2), what is the significance of A?
A is the risk aversion coefficient. This determines the proportion to be invested in optimal risky portfolio and the proportion to be invested in risk free asset. Higher the risk aversion coefficient A, lower will be the proportion in optimal risky portfolio and higher the proportion in risk free asset. In other words, A determines the risk premium an investor would want to invest in a particular security. It measures the utility gained/lost from our wealth. It can be used to compare different individuals to draw conclusions about their differences in risk aversion.
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