# Derivatives: Forward Contract

360 words (1 pages) Business Question

12th Jun 2020 Business Question Reference this

Disclaimer: This work has been submitted by a student. This is not an example of the work produced by our Essay Writing Service. You can view samples of our professional work here.

Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of BusinessTeacher.org.

## Question

A stock has an expectation to pay a dividend of \$1 per share in 2 months and \$1.20 in five months. The price of the stock is \$80, and the risk-free rate is 8% per year with continuous compounding for all maturities. An investor has taken a short position in an 8 month forward contract on the stock. 3 months later, the price of the stock is \$78 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

-> Forward price at the start of short position The present value of an income stream with compounding is given by: P = Ie-rT Where, r is the risk-free rate and T is time left to receive payment. The risk-free rate, r, is 8%. Present value of \$1 dividend due in 2 months = 1e-0.08(2/12) = 0.9868 Present value of \$1.20 dividend due in 5 months = 1.20e-0.08(5/12) = 1.1606 Total present value of two dividends = 0.9868 + 1.1606 = 2.1474 Forward price, F0, is calculated as below: F0 = (Share price – Present value of dividends)erT Share price is \$80. The forward contract is for 8 months. Substituting values in the above equation: F0 = (80 – 2.1474)e0.08(8/12) = \$82.1175 -> Three months later Value of the short position After three months, only one dividend of \$1.2 is due in two months. Present value of \$1.2 dividend due in 2 months = 1.2e-0.08(2/12) = 1.1841 Share price at the end of three months is \$78. Five months before the expiry, present value of F0 is calculated below: Present value of F0 = 82.1175e-0.08(5/12) = \$79.4253 Present value of investment to acquire a share = Current share price – Present value of dividend = 78 – 1.1841 Since the investor has a short position, value of the short forward contract, f, is given by the following calculation: f = Present value of forward F0 – (Current share price – Present value of dividend) = 79.4253 – (78 – 1.1841) = \$2.6094 Forward price at the end of three months, F1, with five months to expiry is calculated below: F1 = (78 – 1.1841)e0.08(5/12) = \$79.4196

## Related Services

View all

### DMCA / Removal Request

If you are the original writer of this question and no longer wish to have your work published on the UKDiss.com website then please:

Related Services