Question 1

Your Company, manager of the Gigantic Mutual Fund, knows that her fund currently is well diversified and that it has a CAPM beta of 1.0 The risk-free rate is 8% and the CAPM risk premium of 6.2%. She has been learning about measures of risk and knows that there are (at least) two factors: changes in industrial production index, ₁ and unexpected inflation, ₂ The APT equation is

E(R_i) R_f = [₁ R_f]b_i1 + [₂ R_f]b_i2,

E(R_i) = 0.08 + [0.05]b_i1 + [0.11]b_i2.

Required

1. If his portfolio currently has a sensitivity to the first factor of b_i1= -0.5, what is its sensitivity to unexpected inflation?

2. If she rebalances her portfolio to keep the same expected return but reduce her exposure to inflation to zero (i.e., bi₁= 0) what will its sensitivity to the first factor become?

In addition, Your Company wish to establish a PhD University Scholarship of GHc 2,000 paid at the end of each year for deserving students as an alumnus at the School you attended. You would like to make a lump-sum gift to the school to fund the scholarship into infinity. The school's treasurer assures you that they will earn 7.5% every year continually.

Required:

a) How much must your company give the school today to fund the proposed scholarship programme?

b) If you allow the amount of the scholarship to increase annually after the first end of year by 3% per year, how much must you give the school now to fund scholarship programme?

e) Compare, contrast and discuss the difference in your response to parts (a) and (b)

f) Your company Human Resource department has just notified you that you have less than three years to retirement and you need to save GHc 37,000 over the next 15years to fund your three-year-old pension daughter university education. If you make equal annual end-of-year deposits into an investment that earns 7% annual interest, how large must this deposit be