# Futures

A stock is currently priced at \$110 and will pay a \$2 dividend in 85 days and is expected to pay a \$2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to: A) \$110.06. B) \$110.00. C) \$110.20. I see how Schweser did it, there has to be a simpler way.

Spot Price = 110 PV of first dividend = 2/(1.08)^(85/365) = 1.96447443 PV of second dividend = 2.20/(1.08)^(176/365) = 2.119854 Spot Less Dividends = 110 - 1.96447443 - 2.119854 = 105.9156712 Futures Price = 105.9156712 * (1.08)^(182/365) = 110.0591906 So is the answer A?

PVD = 2/(1.08)^(85/365) + 2.2/(1.08)^(176/365) = 4.08427 FP = (110 - 4.08427)(1.08)^(182/365) = 110.0592517 = A ?

Same calcs here. A

Well, that is the same way Schweser has it. Another formula to remember.

So * (1+rf)^T - FVD = (So-PVD) * (1+rf)^T Right?

^ correct

I would personally like to know it the way SwaptionGamma and CLT2 did it. It makes sense, and is only 2 or three steps.

Seriously, FUCK Schweser how the hell are they going to make the answers so damn close round to the wrong decimal place (even though you know how to do the calc properly) and get the wrong answer! Your knowledge of the pricing should be tested not how well/lucky you get in the decimal place to which you choose to round your answer!

CLT2 Wrote: ------------------------------------------------------- > Spot Price = 110 > > PV of first dividend = 2/(1.08)^(85/365) = > 1.96447443 > > PV of second dividend = 2.20/(1.08)^(176/365) = > 2.119854 > > Spot Less Dividends = 110 - 1.96447443 - 2.119854 > = 105.9156712 > > Futures Price = 105.9156712 * (1.08)^(182/365) = > 110.0591906 > > > So is the answer A? This is the best way. CLT2 broke the steps down instead of placing them all in a mile long equation. This helps keep order as well. Schweser does it like this except it is all one long equation.

What is the value of a 6.00% 1x4 (30 days x 120 days) forward rate agreement (FRA) with a principal amount of \$2,000,000, 10 days after initiation if L10(110) is 6.15% and L10(20) is 6.05%? A) \$767.40. B) \$700.00. C) \$745.76.

C (1+(.0615(110/360))/(1+(.0605(20/360))-1=.01538 [.01538-(.06*(360/4))]*2,000,000=760 760/(1+.0615*(110/360))=745.98

R(110) = 1.01879 R(20) = 1.003361 1.01879/1.003361 - 1 = 0.01538 0.01538*360/90 = 0.06152 (0.06152 - 0.06)*90/360 = 0.00038 0.00038/1.01879*2000000 = 745.98297980 = C?

Step 1- 1/ (1+ .0605 * (20/360)) =0.996650148 Step 2- 1+ (.06*(90/360) = 1.015 Step 3- 1+ (.0615*(110/360) = 1.01879167 Step 4- 1.015/1.01879167 = .99627827 Step 5- .996650148 - .99627827 = .000371877286 .000371877286 * 2000000 = 743.75 Closest answer is C

R(110) = 1.01879 R(20) = 1.003361 1.01879/1.003361 - 1 = 0.01538 0.01538*360/90 = 0.06152 (.01538 - .015) * 2,000,000 = 760 760/1.01879 = 745.98 So C

CLT2 Wrote: ------------------------------------------------------- > Step 1- 1/ (1+ .0605 * (20/360)) =0.996650148 > > Step 2- 1+ (.06*(90/360) = 1.015 > > Step 3- 1+ (.0615*(110/360) = 1.01879167 > > Step 4- 1.015/1.01879167 = .99627827 > > Step 5- .996650148 - .99627827 = .000371877286 > > > > .000371877286 * 2000000 = 743.75 > > Closest answer is C nice. \$745.76 is some retarded approximation due to rounding. if answer a) was \$743.75 and answer b) was \$745.76, b) would be wrong. that questions sucks, in summary

Yes, the rounding is within the 0.00038, which is the de-annualized difference in rates. If you use 3-4 more decimals of precision you will get 743.75, otherwise you get 745.76.