Answer to Question #220031 in Financial Math for Favor

Question

A stock currently trades at R84 and the interest rate is 1.25%. The 6-month forward
price of this stock is quoted at R85. Construct an arbitrage strategy given this scenario

Answer 1

To construct an arbitrage strategy, we will first se what is arbitrage. 

Arbitrage is the act of buying a same security from one place where price is low and simultaneously selling it in other market where price is high. Arbitrage allows for risk free profit.

An arbitrage involving derivatives include buying where price is low, be if future/forward or spot market and selling where price is high.

To construct an arbitrage strategy, we will do the following:

First, we will borrow at 1.25% interest rate for 6 months and use the funds to buy the stock at R84.

Simultaneously we will sell the forward contract at R85.

After 6 months, we will receive R85 as we agreed to sell the stock for R85 in 6 months. 

We will use R85 received to payoff the loan taken of R84.

First we will have to find the interest rate for 6 months, For that we will raise the annual interest rate to the time period of loan.

So,

6 month Interest rate = (1+0.0125)^6/12

= (1.0125)^0.5

= 1.00623059

= 0.00623059

= 0.623% (rounded to three decimal places)

Thus,

Interest rate for 6 month will be 0.623%.

So after 6 months, we will have to pay back the original borrowed amount, that is R84, plus interest at 0.623059%.

So,

Total amount repayment = 84 * (1+0.00623)

= 84 * (1.00623)

= 84.52336955

= 84.523 (rounded to two decimal places)

Thus,

Total amount repaid is R84.523.

We sold the stock for R85, We are repaying R84.523. So the difference between two is our profit.

Profit = R85 - R84.523

= 0.477

= 0.48 (rounded to two decimal places)

Thus,

Our profit from the arbitrage strategy will be R0.48.

Summary of strategy

• Borrow R84 to buy the stock

• Sell the forward contract at R85

• After 6 months, sell the stock at R85 (as agreed in forward) and receive R85

• Repay the borrowed fund with interest (R84.523)

• Earn the profit on difference (85 - 84.523 = 0.48)