Question

# The 60 year old group is indifferent between investing all of their assets in either the...

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.

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

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