Question

The 60 year old group is indifferent between investing all of their assets in either the risk-free asset (given an interest rate of 1.5%) or in the stock market (the market has a risk premium of 6.35% and a standard deviation of 17.6%).

• Use this calculation to estimate the risk aversion (A) of the 60 year old group. Assume that our investors have utility preferences expressed as ? = ?(?) − 0.5A(standard deviation)^2.

Answer 1

Answer :

Calculation of  risk aversion (A) of the 60 year old group :

? = ?(?) − 0.5A(standard deviation)^2.

where ,

U = Interest rate of Risk free asset i.e 0.015

?(?) = Expected Return of stock market = Risk free interest rate + Risk Premium

   = 1.5% + 6.35%

=7.85% or 0.0785

Standard Deviation = 17.6% or 0.176

0.015 = 0.0785 − 0.5A(0.176)^2.

0.5A*0.030976 = 0.0785 - 0.015

0.015488 A = 0.0635

A = 0.0635 / 0.015488

= 4.0999 or 4.10 or 4