Three months ago an investor opened a short position on the 9-month forward contract on a non- dividend paying stock index that was then worth 1 000

3 Months Ago:

Stock Index Price = 1000

Position in Forward Contract = Short

Time to Maturity = 9 Months

3 Month Interest Rate = 5%

6 Month Interest Rate = 6%

9 Month Interest Rate = 7%

As per Expectations Theory,

Forward Rate (6 Months after 3 Months) = Log(e^{9 Months Rate * 9 / 12} / e^{3 Months Rate * 3 / 12}) * (No. of Months in a Year / (Longer Time - Shorter Time))

F (3 v 9) = Log(e^{7% * 9 / 12} / e^{5% * 3 / 12}) * (12 / (9 - 3))

F (3 v 9) = 8.00%

Thus, expected Forward Rate for 6 months after 3 months is 8% p.a.

As per no arbitrage arguements,

Forward Price = Stock Index Price * e ^{9 Months Interest Rate * Time to Maturity / 12}

Forward Price = 1000 * e ^{7% * 9 / 12}

Forward Price = 1053.90

So, Forward Price 3 months ago i.e. position entry time should be 1053.90.

Now:

Stock Index Now = 1040

Remaining Time to Maturity = 6 Months (9 - 3 = 6 Months)

6 Months Interest Rate = 8% p.a. (Since this expected forward rates come true, we can say that 6 months interest rate now is 8% p.a..)

As per no arbitrage arguements,

Forward Price Now = Stock Index Price * e ^{6 Months Interest Rate * Time to Maturity / 12}

Forward Price = 1040 * e ^{8% * 6 / 12}

Forward Price = 1082.44

So, Forward Price now should be 1082.44.

Value of Forward Contract = Forward Entry Price - Forward Price Now

Value of Forward Contract = 1053.90 - 1082.44

Value of Forward Contract = - 28.54

Thus, value of forward contract today would be - 28.54.