EC3114 - Financial Economics I Vinay P NUNDLALL Problem Set 1 - Solutions Question 1 a) In the lecture we claimed that the price of financial assets grow continuously and hence returns are better calculated as : r = In (Pt) - In (Pt-1) Write the expression for Pt in terms of Pt-1 and r Answer: Manipulate the expression for returns to obtain: Pt r=ln P. t-1 P1 e = P 1-1 Pt=e' Pt-1 b) there are two investments available. Project A requires an initial capital investment of £800, and returns a cashflow of £1,200 in two years Project B requires £900, and returns a cashflow of £1,300 in two years. Assume an annual discrete rate of return, for each project. Calculate r and decide which is the best project to choose for a rational investor. Answer: The capital will grow, over n years, at the discrete rate of r per annum Therefore for Project A: £1,200 = £800 *(1 + r)2 r=(10) -1=0.2247 or 22.4f1% For Project B, r= -1=0.2019 or 20.19% 1,300 900 0.5 As Project A yields higher returns, a rational investor should choose Project A rather than Project B. 1
c) An investor has a utility of wealth function of the form: U(x) = ln(x), where x is wealth. The investor has an implied discount rate of r Suppose the investor is faced with the choice of inheriting £800 today, or £1,200 next period. Deduce the implied discount rate of this investor if she is indifferent between £800 today and £1,200 next period. Answer: The investor is indifferent if U(800)= 1 (U(1200 1+r In 1200 r= In 800 -1=0.0607 or 6.0f1% d) What type of implied discount rate (or time preference rate) will an impatient investor have? Answer: A quite high rate. For an impatient investor, consumption (or wealth) now is more important than in the future. Question 2 Suppose you short sell 100 shares of Harrier Group on the LSE, now selling at £16 per share. a. What is your maximum possible loss? In principle, potential losses are unbounded, growing directly with increases in the price of Harrier. b. Is Short Sale allowed everywhere in the financial markets? Why or why not? In naked short selling, there is no broker involved. You sell shares you don't own or don't confirm to own. Transactions of trades associated with the short may not complete in time because the seller doesn't actually own the shares. Short sale is allowed for both rising and falling stocks in the NYSE since 2007. However, naked short sales (selling stocks that have not been borrowed yet) are not allowed. 2
In many exchanges (such as those in Australia, India, Western Europe), naked short sales are also banned. Question 3 Joe Trader opens a brokerage account and purchases 600 shares of Galactic Steel at $f15 per share. He borrows $18,000 from his broker to help pay for the purchase. The interest rate on the loan is 9%. a. What is the rate of