Reference no: EM133395657

Wealth Management

Question 1. Suppose that stocks A, B, and C each have the same expected return and standard deviation. Given the following correlation matrix, which portfolio constructed from these stocks has the lowest risk?

                                    Correlation Matrix

            Stock   A         B         C

            A         +1.0

            B         +0.9     +1.0

            C         +0.1     -0.4      +1.0

a. A portfolio equally invested in stocks A and B
b. A portfolio equally invested in stocks A and C
c. A portfolio equally invested in stocks B and C
d. A portfolio totally invested in stock C

Question 2. The risk-free rate of return is 5% and the expected return and standard deviation of the optimal risky (tangency) portfolio are 0.15 and 0.20 respectively? Which of the following portfolio(s) is/are not efficient?

       Portfolio              Expected return                    Standard Deviation

            A                                 0.20                                         0.30

            B                                 0.08                                         0.06

            C                                 0.16                                         0.22

            D                                 0.18                                         0.28

            E                                  0.10                                         0.10    

Question 3. Which of the following statements is/are not true about Roth IRA and Roth 401(k) accounts Contributions to Roth 401(k) accounts are made from after-tax dollars Individuals should have U.S. earned income in order to set up a Roth IRA Roth 401(k) accounts are subject to Required Minimum Distributions after the age of 72 Participation in Roth 401(k) is subject to limits on annual gross income (AGI)
Children with earned income can have Roth IRAs established in their name

Question 4. During the period 2000-2013, the Fidelity Magellan fund (ticker symbol: FMAGX) averaged a (net-of-fees) return of 2.68% per year with an annualized standard deviation equal to 18.36%. During the same period the Vanguard S&P 500 index fund (ticker symbol: VFINX) earned an average (net-of-fees) annual return of 4.02% with a 15.71% annualized standard deviation. Risk free T-bills averaged a return of 1.94% per year over the same period. Calculate the additional portfolio management fee (expressed as a percentage of assets), that the S&P 500 index fund could charge an investor (during this period) and still leave her as well off as being invested in a portfolio that includes the Fidelity Magellan fund and T-bills.

Question 5. Assume that Bob, age 35, earns $200,000 per year, is subject to a tax rate of 32%, and can participate in a qualified 40l(k) plan at work. Alternatively, he could make similar investments with after-tax income in directly owned assets through Fidelity or Vanguard, for example. The plan allows him to elect to have up to 4 percent of his salary contributed to the 401(k) plan before tax, and then his employer will match his elective contribution 50 cents on the dollar.

(a) Assuming Bob elects the full 4 percent salary reduction, what would be his annual taxable salary and the total annual contributions (employee contribution plus employer match) towards his 401(k) account?

(b) Now suppose instead that Bob decides not to participate in the 401(k) plan. Instead, he sets aside the same 4 percent of salary as above, and invests outside the plan in directly owned assets through an investment account, after tax. Assume that he is in the 32 percent marginal federal income tax bracket. What would be his annual taxable salary and the annual amount invested in the directly owned investment account in this case?

(c) Further, assume that Bob can earn a 5 percent annual rate of return (all taxable as ordinary income) on his directly owned assets, and 5 percent in his 401(k) plan account.

What would be the balance in Bob's directly owned investment account after 30 years, assuming he chose to invest in the directly owned assets rather than in the employer-sponsored 401(k) plan?

(Note: For simplicity, assume Bob's salary is $200,000 per year throughout the 30-year period)

(d) Assume, that Bob decided to elect the full 4 percent salary reduction and invest in the 401(k) plan as in part (a) above (rather than in the directly owned investment account). Bob can earn a 5 percent annual rate of return in his 401(k) plan account. Assume further that Bob takes a distribution of the entire balance in his 40l (k) account at age 65 (or in 30 years). What would be the after-tax balance available to him at that point?