No Arbitrage Price - Futures Contract. ( Reading 40, question 1).

CFA Level II
#1

Hi, The CFA uses the following formula for the No Arbitrage Price of the futures contract.

FP = (Current Price + AIo - PVcoupon) x (1+Rf)^T

And then they add AIt to the qouted futures price.

Is it correct that it is supposed to be a +?

From doing the Schweser practice questions I found the following formula to work:

FP = (Current Price +(or-?) AIo - PVcoupon) x (1+Rf)^T - AIt

So the difference here is that they deduct AIt from the arbitrage free forward price instead of adding it to the qouted futures price.

The difference will be the same, but I will end up with different arbitrage free and actual values. Which ones is correct?

Why do they not deduct AIt in the CFA formula but instead add it to the Qouted Futures Price. ?

#2

Adding AI at t = 0 to the clean price, and then subtracting AI at t = T at the end is the correct way to calculate the futures prices when starting with a bond quote that doesn’t include AI.

#3

Thank you for the reply.

Okay, then I understand that adding AI at t = 0 is correct.

However at T, the CFAI does not subtract AI from the No Arbitrage Futures Price. Instead they add it to the Qouted futures Price.

Which method is correct?

#4

[quote=“Thammer”]

Thank you for the reply.

Okay, then I understand that adding AI at t = 0 is correct.

However at T, the CFAI does not subtract AI from the No Arbitrage Futures Price. Instead they add it to the Qouted futures Price.

Which method is correct?

This is what they did:

  2. Quoted Futures Price: 125. Conversion Factor: 0.90
    1. Value of futures qouted price: 125 * 0.90 = 112.50
    2. Accrued interest at expiration: 0.20
    1. – Why do they add the accrued interest here? 
3. Futures contract value at expiration: 112.70
  1. No Arbitrage Futures Price:
  2. FT = (So + AIo - PVcoupon) x (1+Rf)^T
  3. FT = (112 + 0.08 – 0) x (1.003)^3/12 = 112.1640
    1. Why do they not deduct the accrued interest here?
#5

See post above. Apologize for multiple posts.

#6

I don’t understand why they’re doing it that way (maybe someone else can chime in on this), but I can work it out algebraically. So remember that the quoted futures prices is the price after the conversion factor adjustment has been made. So:

Quoted futures price = 1/(Conversion Factor) * Futures Price.

125 = 1/0.90 * Futures price

which becomes:

112.50 = futures price w/ AI at t = T, and then you subtract the AI at t = T to find what the futures price is before adding back AI at t = T, or [(Bo(Y+T) + AI(t) - PV of CI)]*(1+Rf)^T

#7

I appreciate your reply.

We will end up with the same arbitrage opportunity. But different Qouted Futures price and Arbitrage Free Value of Forward Contract.

It would be great to have it cleared up, because a question about the value of the Arbitrage Free Value of Forward Contract seams likely.