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ESSAY. Write your answer in the space provided or on a separate sheet of paper.

ID: 2750100 • Letter: E

Question

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

1) The Century 22 fund has invested in a portfolio of mortgaged backed securities that has a current market value of $245 million. The duration of this portfolio of mortgaged back securities is 14.7 years. The fund has borrowed to purchase these securities, and the current value of its liabilities (i.e., the current value of the bonds Century 22 has issued) is $160 million. The duration of these liabilities is 5.4 years. What is the initial duration of the equity for the Century 22 fund?

2) Luther Industries needs to borrow $50 million in cash. Currently long-term AAA rates are 9%. Luther can borrow at 9.75% given its current credit rating. Luther is expecting interest rates to fall over the next few years, so it would prefer to borrow at the short-term rates and refinance after rates have dropped. Luther management is afraid, however, that its credit rating may fall which could greatly increase the spread the firm must pay on new borrowings. How can Luther benefit from the expected decline in future interest rates without exposure to the risk of the potential future changes to its credit ratings bring?

Explanation / Answer

Answer (1)

Market Value of Assets MVA = $ 245 Million

Duration of Assets DA = 14.7 years

Market Value of Liabilities MVL = $ 160 Million

Duration of Liabilities DL = 5.4 years

Market Value of Equity = Market Value of Assets - Market Value of Liabilities

                                            = $ 245 Million - $ 160 Million = $ 85 Million

Duration Gap DGAP = DA – (MVL/MVA) * DL

DGAP = 14.7 - (160/245) * 5.4

             = 14.7 – 0.65306122 * 5.4

             = 14.7 – 3.52653

             = 11.17 years

For an immunized portfolio   DGAP = 0

Therefore initial duration of Equity = 11.17 years

Answer (2)

Luther can issue long term bonds at 9.75% with a call option with a horizon of the time period during which the interest rates are expected to fall.

In case the interest rates fall, and there is no change in their credit ratings then the company can call the existing bonds and reissue at a lower rate

In case the interest rates do not fall or there is a lower of credit ratings, they can continue with their existing bond issue till maturity at the rate of 9.75%