Question

1a) What can we learn from CARA,IARA and DARA?

b) What can we learn from CRRA,IRRA and DRRA?

Answer 1

The concept of CRRA, IRRA, and DRRA on Risk aversion of an Individual and Its initial Wealth.

Assume function of Wealth A (W). Utility Function U which measures Risk Aversion.

Now in CARA, (Constant Absolute Risk Aversion)

A'(w)=0  With  Implies that with change in Wealth there is no effect of change in risk aversion.

Now in DARA, (Decreasing Absolute Risk Aversion)

A'(w) < 0 Implies that with reduction in wealth Risk aversion also reduced

Now in IARA, (INcreasing Absolute Risk Aversion)

A'(w) > 0 Implies that with Increase in wealth Risk aversion also Increased

Assume an example Two People, First One is Wealthy and second One is Poor. A(W1) > A(W2). Both of the people having same same risk aversion and expected return.

But, during recession in economy both of them made loss of certain percentage. But the notional loss will make more impact to the poor people as compared to wealthy people. So the poor one will invest in more risk free investment means its risk aversion will reduced.

This is an example of DARA.

If that guy did not change any investment decision it will be an example of CARA.

If that guy invest more in risky stocks to cover up the loss  it will be an example of IARA.