# Simple value of a Forward contract at an intermediate time question

I am taking "Financial Engineering and Risk Management Part I" from Columbia University on coursera and I got a seemingly simple question wrong on the first quiz. This is all based on the no-arbitrage arguments. Here is the question:

During the lesson we constructed a portfolio to try to get the value of a forward at an intermediate time. Here is what we got:

What was missing at this point was how to get F(t) and F(0). A few slides back we did:

Ok so now I have all of the ingredients for this forward soup. I got the forward price at time zero with the stock price at time zero divided by the discount for the whole period (two 6 month periods so its squared). Then I got the forward price at 6 months by taking the price at 6 months and dividing it by the discount for one six month period. I took the difference between the two and multiplied it by the discount factor for six months (between t and T). I ended up rounding off to 27. What am I doing wrong? Below is a picture of my calculations (I did not round any intermediate calculations). I'm more of a pencil and paper guy but if you want I can type it all up.

Also, Happy New Year to you all!

• What was the correct answer to the question? Based on the formula above 125*(1.05) the answer should be 131.25. But that does not seem to be the correct answer. – user17400 Sep 1 '15 at 16:06

Always take care that you got the compounding frequency right. I recommend you take a deeper look at http://breakingdownfinance.com/finance-topics/derivative-valuation/forward-contract/ . You can download an excel file here and take a deeper look at the formula. You can also give in the compounding frequency as input.

In case of doubt, or as a standard procedure, you could first start transform it to continuous compounding and use this to discount to avoid mistakes.

• Got it with the spreadsheet too. Thanks for the link. – GHStein Jan 2 '15 at 18:31

Your discount factors are not inverted properly. Intuitively, df(0,T) should be a number between 0 and 1. For example, if r=0 then there is no discount so df = 1. If r > 0, then discount is going to be less than 1.

Your formula for df will always be greater than 1. Check the formula given by the prof on the last slide titled "Term structure of interest rates" for the PDF on linear pricing in week 2.

If we compound semi-annually and we have half year to go, then the current forward price is $$F = S \left(1+\frac{r}{2}\right) = 125 \left(1+\frac{0.10}{2}\right)$$ Isn't it as simple as that?

• Yes it was a simple algebraic mistake. That's what I get for not taking breaks! Thanks. – GHStein Jan 2 '15 at 18:22

Correct answer to the question is 20.

F_o= 100*(1+.1/2)^2=110.25 ....forward price at time 0(future value of 100 stock at time t=1 yr) F_t=125*(1+.1/2)=131.25 .....forward price at time t ( future value of 125 at time t=1/2yr down the line) d(t,T)=1/(1+.1/2)=.9523 f_t=(F_t-F_o)*d(t,T)=20