1. Identify the parts of the circular-flow diagram immediately involved in the following transactions. a. Mary buys a car from Jaguar for 40,000. b. Jaguar
1. Identify the parts of the circular-flow diagram immediately involved in
the following transactions.
a. Mary buys a car from Jaguar for 40,000.
b. Jaguar pays Joe 2,500/month for work on the assembly line.
c. Joe makes 10 worth of calls on his Vodafone mobile phone.
d. Mary receives 1,000 of dividends on her Vodafone shares.
Consider a discrete stochastic process X"= ], that evolves over an integer time sequence i, for 0 $ 1 2 7. Explain the following terms: (a) A filtration F at time i. (b) A binomial measure Q. (c) The conditional expectation Eo (X] F;) (d) A previsible process o = $; [4] (ii) Explain how, using conditional expectations, you can construct a stochastic process My based on any process X, such that MY satisfies the martingale condition: EQ(M F )= M, for all is j [3] (a) State the Binomial Representation Theorem for a binomial measure Q and martingale process M. (b) Explain briefly how this could be used to price contingent claims on a stock. [4](3 points) You are given the following external cash flows and post-contribution account balances. recorded from the past month: External Cash Inflow Amount Date (beginning of day) December 10, 2019 7,500 December 15, 2019 2,500 Account Balance Date ( end of day) December 1, 2019 75,000 December 10, 2019 77,500 December 15, 2019 80,000 December 31, 2019 90,000 (i) (2 points) Calculate the monthly time-weighted return. Show all work. (ii) (/ point) Explain why time-weighted return might be more appropriate than the money-weighted return. (/ point) Explain the assumptions that support classical immunization theory. (5 points) You have decided to pursue contingent immunization for a portfolio that is currently worth 100 million, with the following: A five-year investment horizon Minimum acceptable return of 4% . . Your firm can immunize its asset portfolio at 6%. All yields provided in this question are quoted on a bond-equivalent yield basis. (i) (1 point) Describe how contingent immunization addresses a shortfall of the classical immunization approach. (ii) (2 points) Calculate the initial dollar safety margin. Show all work.(iii) (2 points) You decide to invest 100 million in 10-year 6% Treasury notes at par. The following present values of cash flows of the 10-year Treasury notes at different discount rates are provided: Discount Rate Present Value of Cash Flows 20% 136,091,106 4% 116,351.433 6% 100,000,000 8% 86.409,674 10% 75.075,579 Calculate the revised dollar safety margin if the yield to maturity suddenly increases to 10%. Show all work. (d) (3 points) Critique the following statements regarding immunization strategies: A. The portfolio manager should strive to rebalance the portfolio more frequently to adjust its duration. B. Dollar duration is a measure of the change in duration for a 0. 1% change in market yields. Furthermore, a portfolio's dollar duration is a weighted average of the dollar durations of the component securities. C. Regardless of the shape of the yield curve, the yield to maturity of a portfolio should roughly approximate the immunization target rate of return
