CT7 - Question 5.10

[london]

I'm probably missing something trival here - but why does the utility function not satisy all requirements - the solution says that its because U''(x) = 0 - but why is that a problem ?
Thanks.

 

[Graham Aylott]

It's nothing more complicated than a violation of the assumption that investors are risk-averse, i.e. U''(x) < 0.

U''(x) = 0 corresponds to an investor being risk-neutral (see page 14 of Chapter 5), whereas economists always assume that in real-life investors:

- prefer more (wealth) to less (wealth), i.e. U'(x)>0

- are risk-averse, i.e. U''(x)<0.

 

[london]

ok - thanks very much !

 

[london]

CT7 - Question 6.8 - 2nd order stochastic dominance

Hi,
Another question - could someone talk me through the numerical answers to question 6.8 which talks about 2nd order stochastic dominance for two different assets U and V. Also, I would I calculate the variances of assets U and V in this case ?
Thanks again for any help.

 

[Graham Aylott]

The mean returns are calculated as follows:

E = 0.25 * [6 + 7 + 8 + 9] = 7.5%
E[V] = 0.75 * 7 + 0.25 * 9 = 7.5%

So, the two assets have the same mean return.

The variance of returns for Asset U can be found as:

V = 0.25 * [(6)^2 + (7)^2 + (8)^2 + (9)^2] - (7.5)^2 = 1.25

The variance of returns for Asset V can be found as:

V[V] = 0.75 * (7)^2 + 0.25 * (9)^2 - (7.5)^2 = 0.75

So, U has a greater variance than V.

Hence, an investor who prefers more to less and is risk-averse will choose V over U.