Question

Question 2 [Forward and Spot Prices: 30%]

Assume that the underlying asset/stock is an investment asset. The information of the forward price and stock price is provided below:           

Forward price	F0	$450
Stock/Spot Price	S0	$430
Maturity date of Forward Contract (1 year)	T	1
Risk-free Rate	r	4%

Question 2 - Part A [10%]

Given the above information, show that there is an Arbitrage Opportunity between the Forward price and the Spot price.

Question 2 - Part B [20%]

Construct and demonstrate the Arbitrage Strategy (i.e., Cash-and-Carry Strategy or Reverse Cash-and-Carry Strategy) based on the above information and your result in Part (A).

In addition, compute the Arbitrage Profit of this arbitrage strategy.

Answer 1

F_{​​​​​​0}​​​​​ = $450

S_{​​​​​​0}​​​​​ = $430

T = 1 year

r = 4%

1)

ST = Expected price after 1 year

ST = S_{​​​​​​0} * (1+r)^T

ST = $430 * 1.04^1

ST = $447.2

We can see that ST and F0 are not similar, so there is a mispricing. That can be exploited to earn arnitrage profits by traders.

2)

ST = $447.2

F0 = $450

We can use CASH AND CARRY arbitrage strategy here. As we can buy cash the stock and hold till 1 year incurring total cost of $447.2. Simultaneously we sell the future @ $450

Strategy:

Buy Cash Stock @ $430

Sell Futures @ $450

ARBITRAGE PROFIT:

Sell Futures @ $450

Less: Buy Spot @ $430

Less: Holding Cost $17.2

($430 * 4%)

Arbitrage Profit $2.8

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