Indifference Curves

Answer 1

We need to match each client to the most approprate portfolio and this can be done by incorporating the numerical risk tolerance score.

Utility = expected return - risk of portfolio

Where risk of the portfolio = Portfolio STDEV / risk tolerance factor.

The highest level of utility, i.e. the largest value of the three portfolios is the optimal asset mix.

For Miss A = Portfolio 1

For Miss B = Portfolio 3

This is because Ms A is less risk tolerant so she prefers the lower risk portfolio.

Ms B is more risk tolerant so she prefers the higher risk portfolio.

This is becuause the formula acts as a risk penalty.

Answer 2

1. Risk aversion is the inverse of risk tolerance
   
   1. RA = 1/ RT
   2. Annie = 0.333
   3. Sophie = 0.125
2. The optimal portfolio mix:
   
3. The utility from a portfolio increases as the expected rate of return increase and it decreases when the variance increases. The formula acts as a risk penalty. The calculation gives an investment suitability and client utility per portfolio.
4. Merits:
   
   1. Combines an objective investment risk with subjective risk tolerance to arrive at a more holistic risk penatly to the investment return of a portfolio.
   2. Easy to calc and explain
   3. Is a means of allocation people to different investment portfolios who may not have hugely different investment objectives.
5. Drawbacks:
   
   1. Does not include risk need or risk capacity
   2. Scaling is sometimes subjectively added

Answer 3

we can say a utility score as a certainty rate

it is the rate that if earned with certainty would provide a utility score equivalent to that of the portfolio in question - adjusted for the risk factor

A portolio is only desirable if its CE returns exceeds that of the risk free alternative, if it not larger than the portfolio will be rejected.

The concept suggests that as households hold lots of risk free assets that they must have high risk aversion.