Question

Suppose the market price of the security from question 2 is $700. Is there an arbitrage opportunity? If “yes”, please specify actions that should be taken to perform the arbitrage (be very specific, indicate all cash flows associated with the arbitrage) and state arbitrage profit. Please provide the solutions to the following questions in the box below. Back up your answers with calculations.

[This is question 2 with the answer]

Q2: Suppose a security generates the following risk free cash flows: $250, $150, and $350 at the end of the first, second and third years after the issuance. Find the security’s fair price at the time of the issue if risk free interest rate is 4%. Please provide the solutions to the following questions in the box below. Back up your answers with calculations.

A: Payment 1 = 250, Payment 2 = 150, Payment 3 = 350, interest = 4%

250*(1/1.04) => 250 * .9615384615 = PV of year 1: $240.38
150* (.9615384615 /1.04) => 150*.924556213= PV of year 2 : $138.68
350* (.924556213/1.04) => 350*.8889963587= PV of year 3 : $311.15
Fair Price = 240.38 + 138.68 + 311.15 = $690.22

Answer 1

If the market price of the asset is $700 as against the fair price of $690.22, there are arbitrage opportunities present and the following actions can be taken

1. Sell short the asset today (assuming that selling short is permissible) at $700

2. Investing $700 received in the following way

a) $240.38 invested for 1 year at 4%

b) $138.68 invested for 2 years at 4%

c) $311.15 invested for 3 years a

d) Remaining amount of $9.78 is arbitrage profit

3. After one year $240.38 will mature to become $240.38*1.04 = $250 and paid to the buyer

4. After two years. $138.68 will mature to become $138.68 *1.04^2 = $150 and paid to buyer

5. After two years. $1311.15 will mature to become $311.15 *1.04^3 = $350 and paid to buyer

So, the strategy generates an arbitrage cahflow of $9.78 today and there are no cashflows at any future points of time.