CFA Level I, Deri­va­ti­ves — Pri­ce vs. Value of a For­ward Con­tract — MC Question

You own a stock pri­ced at €104, and you have a for­ward con­tract to sell the stock at €100 in one year. The risk free rate is given by 5 per­cent per year. What can be said about the value and the pri­ce of the for­ward contract? 

A. The value of the for­ward con­tract is equal to €-8.76, but its pri­ce is €100.

B. The value of the for­ward con­tract is equal to €100, but its pri­ce is €-8.76.

C. The value of the for­ward con­tract as well as its pri­ce are both given by €-8.76.

Solu­ti­on: A. is correct.

We con­sider

• the value of a con­tract and 
• the pri­ce of a contract.

The value of a con­tract is equal to the amount of wealth repre­sen­ted by owning a con­tract whe­re­as its pri­ce is one of the terms the par­ties agree on when crea­ting the contract.

1. We first con­sider the share pri­ce of €104 in peri­od 0. 
2. This pri­ce will be €100 in year T. 
3. Then, the­re is a for­ward con­tract in peri­od 0, 
4. it is worth 100/(1 + r + del­ta) = 100/(1 + 0.05 + 0) = 100/1.05 = €95.2381, becau­se we  have a del­ta equal to zero, sin­ce we con­sider a ris­kless inte­rest rate. 
5. So, again, we get €95.2381 when con­side­ring the share as well as the for­ward con­tract, i.e. the sum of both. 
6. The­r­e­fo­re, which num­ber do we have to sub­tract from €104 to get €95.2381? The ans­wer is €8.76.