Question

A share of Amazon stock is currently selling for $1,405. You plan to purchase your first share in one year in honor of your 22nd birthday. You are concerned that the price will rise by then. To hedge this risk, you enter into a forward contract to buy one share of Amazon stock in one year. Assume that the risk-free rate is 3.5% (APR, semi-annual compounding). • Calculate the appropriate price at which you can contract to buy the asset in one year. Assume continous compounding. • Assume that eight months into the contract, interest rates increased by 75bp and the AMZN stock price is $1,400. Calculate your gain or loss from the forward contract. Assume continous compounding. • Suppose that at expiration, the price of the stock is $1,500. Calculate your gain or loss from the forward contract.

Answer 1

When the underlying asset in the forward contract does not pay any dividends, the forward price can be calculated using the following formula:

F = S x e^(r x t)

Where:

F = the contract's forward price

S = the underlying asset's current spot price

e = the mathematical irrational constant approximated by 2.7183

r = the risk-free rate that applies to the life of the forward contract

t = the delivery date in years

In this example a APR is provided as 3.5

The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate. Calculated as:

Nominal interest rate = 3.4451%

puuting nominal rate into the formula F = S x e^(r x t)

=1,405*e^(.034451 x 1) =forward price for one year

=1,405*1.03505

=1454.24

b)eight months into the contract

r=3.4451%+.75%=4.951%

t=8/12=.666

putting into formula

F = S x e^(r x t)

=1,405*e^(.04951 x .6666) =forward price for eight months

=1,405*1.0335=1452

stock price = 1400

hence loss = 1452-1400=52

we have calculate assuming continous componding

At the end of year one the price is 1500

gain =1500-1454.24=45.76