CM2, Chapter 2, Practice Question 1.2 (ii), Page no.37

[rrustogi]

Hi,
Per the question, It has been asked to explain C's holding of risky assets will change as his wealth decrease.
In theory, When A'(w) and R'(w). i.e first derivative of Absolute risk aversion and Relative risk aversion is greater than 0, it exhibits increasing absolute/relative risk aversion. Then why in this question, with decrease in wealth and A'(w) and R'(w) >0 answer states that there will be decrease in risk aversion.
Is it because of solvency level exception, as in investor with decreasing wealth invests increased share of wealth in order to get back the wealth.
Please help!!

 

[Steve Hales]

Hi
For a function of wealth f(w), assume that f'(w)>0.
This means that as w increases so f(w) increases, but it must also mean that as w decreases so f(w) decreases.
Is this what you meant?

 

[rrustogi]

Thanks for responding.
Not really. My question is per theory A'(w)>0 leads to increasing risk aversion and hence decreased investment then why in this question this principle isn't being followed.

 

[Steve Hales]

I see what you mean! In practice, utility functions which lead to A'(w)>0 aren't realistic and don't model typical investor behaviour.
We could try to construct a narrative around it, such as someone trying to invest their way out of imminent insolvency (by using risky assets), but even that feels like a stretch.