Hull 07.03 Pg 183-184 - Financial Markets and Products - PQ set

[Dr. Jayanthi Sankaran]

Hi David/Nicole,

I am very sorry to be posting my query on this separate thread. It so happens that there is no student forum thread for all questions from Hull in this PQ set.

Hull.07.03: A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, 6-month LIBOR is exchanged for 12% per annum (compounded semiannually). The average of the bid-offer rate being exchanged for 6-month LIBOR in swaps of all maturities is currently 10% per annum with continuous compounding. The 6-month LIBOR rate was 9.6% per annum 2 months ago. What is the current value of the swap to the party paying floating? What is its value to the party paying fixed?

Answer 07.03: Although it is very easy to compute the value of the swap - treating it as a portfolio of fixed rate and floating rate bonds, I am finding it very difficult to understand your answer when viewed as a portfolio of FRA's. Unfortunately, I cannot copy paste your answer either

Thanks!
Jayanthi

 

[Nicole Seaman]

Hello @Jayanthi Sankaran

In the case where you do not have a link to the original forum question, you can copy the first sentence of the question and paste into the search box in the forum (or type "A $100 million interest rate" in the box). A quick search brought me to this original question where you can post your question: https://forum.bionicturtle.com/threads/hull-07-03.3783/#post-10042.

Thank you,

Nicole

 

[David Harper CFA FRM]

Thanks @Nicole Manley

@Jayanthi Sankaran the source contains a snapshot of the XLS i used to price (see below). Pricing the bond as two FRAs, in my opinion, is more intuitive because it describes how we typically think of valuing cash flows. What I mean is:

• We first infer the forward rates, which in this case are simply the rates that we expect the floating-rate counterparty to pay
  
• For each future (six month) period, we compute the expected floating-rate payment and the fixed rate payment (which we already know!)
• We net them (subtract one from the other) which is what actually happens; this gives us an expected future netted cash flow
• We discount this stream (of expected net cash flows) to the present value. I hope that helps,

 

[Dr. Jayanthi Sankaran]

Thanks a lot, Nicole - much appreciate it - will do it in the future

Jayanthi

 

[Dr. Jayanthi Sankaran]

Thanks David - much appreciate it. Just one more question: The cash flows at t = 0.25 are floating: $4.80 and Fixed: $6.00. However, is it not true that the actual timing of these cash flows are at 0.333. Ultimately, of course the Net Cash flows are discounted at the discount factor corresponding to 0.333. On one level, I think I understand it, but not completely. Would be grateful if you would explain

Thanks
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran Yes, you are correct! I am sorry, the spreadsheet contains a typo: under the FRA, as you point out, the "Time" intervals should be 0.333 (ie, 4 months) and 0.833 (ie, 10 months) so that they match the time intervals at the top. However, I just looked at the XLS and those lower time intervals are cosmetic, they don't impact the calculations (is why the values are the same, -$1.96376, under both methods). Thanks!

 

[Dr. Jayanthi Sankaran]

Hi David,

Two more questions regarding the above:

(1) How do you get the 10.25% forward semi-annual? I get it by:

(1 + r/2)^0.5 = e^(.10*0.25)
(1 + r/2)^0.5 = e^0.025 = 1.02532
(1 + r/2) = 1.02532^2 = 1.05127
r/2 = 1.05127 - 1 = .05127
r = .05127*2 = .10254 = 10.254%

However, I am not very sure as to the intuition underlying my calculation. Could you please explain this?

(2) For exam purposes, is it important to know the swap valuation using both methods i.e. as a portfolio of bonds, and as a portfolio of forwards?

Thanks!
Jayanthi

 

[Deepak Chitnis]

Hi @Jayanthi Sankaran, you just need to convert foeward rate which is continueose to discrete semi annual like(e^0.10/2-)1*2=0.10254=10.254%. I dont think that we need to know portfolio of forward for the exam purpose, but portfolio bond is testable. But I think david will elaborate more.
Thank you,

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran @Deepak Chitnis is correct, it's just a conversion from the continuous rate of 10.0% given by r_m = m*[exp(r_c/m) - 1], where r_m is discrete rate, r_c is continuous rate, and m = 2 in this case. Similar to your first step, that conversation is found via the equality: exp(r_c) = (1+r_m/m)^m; ie, Hull Chapter 4. Based on history, I tend agree with Deepak: "I dont think that we need to know portfolio of forward for the exam purpose, but portfolio bond is testable. But I think david will elaborate more." Thanks,

 

[Dr. Jayanthi Sankaran]

Thanks David - appreciate it

Jayanthi