$100000 should be invested by the client in optimum portfolio. The optimum portfolio is the portfolio which provide the investor highest utility.

$100000 should be invested by the client in optimum portfolio. The optimum portfolio is the portfolio which provide the investor highest utility. As we know that Higher the expected return, higher the utility and higher the standard deviation, lower the utility. So, the best portfolio is the one with the highest return and lowest risk. However, this is not possible in well functioning financial market. We will find that higher return comes at the expense of higher risk.

For instance:

Suppose there are 6 portfolios available in market to invest $100000 by client. These are as follows:

                                      1                        2                       3                     4                           5                          6

Expected Return:       18%                 20%                  30%                30%                      34%                      35%

Standard deviation:   7%                      6%                 10%                 11%                     11%                         11%

We can choose efficient portfolios out of above 6 portfolios.  In above example, P2,P3 and P6 are efficient portfolios. Efficient portfolios are those portfolios which is same for all investors.But optimum portfolios depend on person to person depending on their risk appetite.

We can draw efficient frontier joining efficient portfolios.

Out of the efficient portfolios, the optimum portfolio for investor is one having the lowest co-efficient of variation. co-efficient of variation is given by:

P2: CV = 6/20 *100 = 30%

P3: CV = 10/30 *100 = 33.33%

P6: CV = 11/35* 100 =31.43%

P2 is the optimum portfolio and investor should invest his $100000 in P2. 

The question is where would portfolio P2 lie on the efficient frontier?