Question

3. You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of 10% and a standard deviation of 16%. The other is a fund that is actively managed by your broker. This fund has an expected return of 15% and a standard deviation of 20%. The risk-free rate is currently 7%. Answer the questions below based on this information. a. What is the slope of the Capital Market Line? b. What is the slope of the Capital Allocation Line offered by your broker's fund? c. Draw the CML and the CAL on one graph. d. What is the maximum fee your broker could charge and still leave you as well off as if you had invested in the passive market fund? (Assume that the fee would be a percentage of the investment in the broker's fund, and would be deducted at the end of the year.) e. How would it affect the graph if the broker were to charge the full amount of the fee? 4. You are a financial adviser consulting with a potential individual client on investing. To measure her risk aversion, you ask her to compare the following investments: Investment Expected return E() Standard deviation 10.5% 10.1% 6% 8.2% 19.8% 18% 17.9% 20.45% 25.4% 30.39 Her response is 2<1<4=5<3 (a<b means b is preferred to a, and a-b means a is as good as b). Assume that her utility function is U = E(r) - 0.5A0, where A is the risk- aversion parameter. a. What is the value of your client's risk aversion parameter A? (4 points) b. Calculate the utility for the five portfolios, and check whether the assumed utility function is consistent with your client's response? (4 points)

Answer 1

Slope of Capital Market Line ,

For Passive Market portfolio,
Expected Return = 10%
Standard Deviation SD = 16%
Risk-free Rate = 7%
Slope of CML = (10% - 07%) / 16% = 0.1875
Ans a: Slope of Capital Market Line For Passive Market portfolio 0.1875

CAL (Capital Allocation Line) differ from CML (Capital Market Line ) in sense of passive fund vs Actively managing of fund.

Actively Managed Fund,
Expected Return = 15%
Standard Deviation SD = 20%
Slope of CAL = (15% - 07%) / 20% = 0.4
Ans b : Slope of Capital Allocation Line offered by the brokers Fund 0.4

Ans c .: CML and CAL graph

Y axis Depicts Expected Return, X Axis - Standard Deviation.

Fund. CAL Actively managed £ Fund Passive тем 16% 20%

Now if the broker charges a fee equals to f% then the Return of the fund will reduce to (15-f)%. But to maintain the attractiveness of the broker's fund its slope should be higher than CML slope (0.1875).
Slope of CAL with fees = (Expected Return - Riskfree Rate) / SD = (15-f - 7)/20
So,
(15-f - 7)/20 = 0.1875
15 - f = 10.75
f = 4.25
Ans d : maximum fee the broker can charge = 4.25%