HomewrkI work out D the discaunt factay for twe years ap o g

HomewrkI work out D, the discaunt factay for twe years ap o gears DPreent value + r rn DF 9000 2 14036 2 HOMEWORK 1 ALL HOMEWORK SHOULD BE SUBMITTED IN CLEARLY LEGIBLE HARD COPY. YOUARE ADVISED TO KEEP A COPY OF THE HOMEWORK I. Ms. Juanita Fotheringay-Murgatroyd has $9000 available to invest. She observes that r2, the interest rate on risk free investments with a term to maturity of two years is 3.6%, while the discount factor for five years is 0.945. (i). Work out DF2, the discount factor for two years. (ii). Work out rs, the interest rate on risk free investments with a term to maturity of (iii. Determine whether or not there are risk free arbitrage opportunities here. Give (iv). Set up an arbitrage table to show how you would realize arbitrage profits. five years reasons. If the rates in the two markets were to remain unchanged, how many round trips would be necessary to make $1 million? If the five-year rate were to remain unchanged, to what level would the two-year rate have to fall for the arbitrage opportunity to vanish? (v). (vi).

Solution

As asked only part ii, iv and vi being answered.

(ii) Let us assume that the interest rate for 5 years is r₅; then the discount factor DF₅ shall be:

DF₅ = 1/(1+r₅)⁵ = 0.945; solving for r₅, we get r₅ = 1.14%

(iv) Given that the investor can borrow for 5 years at a lower rate of 1.14% and invest for 2 years at 3.6%. the arbitrage can be as below:

vi. The two year rate should be such that the present of the 2 year hence value should be at $9000 - let us denote the revised 2 year rate by y%, then it should be:

9000*(1+y)² * 0.945 = 9000; solving for y we get y = 2.87%