Problem 5

This problem is modeled after portfolio management questions on Level 3 of the CFA exam. These questions focus on wealth planning for private clients and include a combination of quantitative analysis and open-answer response.  

You are serving as a financial adviser to a high-net worth client whose marginal tax rate on investment income is 32%. He has $200,000 in cash, and he is considering investing a portion of this capital in bonds. He is choosing between two investment alternatives.

The first alternative is a municipal bond issued by the county where he lives and works. The second alternative is a corporate bond. Both bonds have a face value of $100, mature in four years, pay coupons semiannually, and have an annual coupon rate of 6%. The price of the municipal bond is $97.087. After analyzing both alternatives, you determine that the client would be indifferent between these two bonds on the basis of their after-tax YTMs.

a) Because the two investments are identical in terms of their after-tax returns, your client is leaning towards investing in the municipal bond of his home county to support the local community. As a risk manager, do you agree with your client? Explain briefly.

b) Based on your review of the client’s financial position and risk tolerance, you determine that the portfolio you are discussing should have a modified duration of approximately 2%. A portion of this portfolio will remain in cash to fund his liquidity needs, and the rest of the portfolio will be invested in the corporate bond discussed above. If the modified duration of cash is zero, how many corporate bonds (i.e., the whole number of bonds) should your client purchase at their current market price so that the duration of his portfolio is as close as possible to 2%, but does not exceed 2%?

c) Your client is worried about the high likelihood of interest rate hikes in the near future. Using the duration approximation for his portfolio, find the maximum one-time upward shift in the yield curve that your client would be able to withstand without losing no more than $5,000 in portfolio value? If such a maximum shift does occur immediately, will his actual portfolio value be greater or smaller than what is expected on the basis of the duration approximation? Explain briefly.