Looks like I need a refresher in calculating PV’s… Schweser book 4, SS 12, Q10 - Manager will borrow some money in 6 months for 1 year at LIBOR+150 bps. LIBOR now is 3.5%, but changes one month into the contract to 3%. Calculate amt and direction of credit risk. —>Definitely counterparty faces the credit risk —>to calculate payoff to FRA at beginning of loan(i.e. at 6 months from now) why do we use 3% (spot LIBOR) as the rate instead of 4.5% (spot LIBOR+150 bps ) Please help, I can’t seem to get the discount rates right…
Draw yourself a chart of 6X18 chart. They use 3% (current LIBOR) because we are trying to price the FRA NOW! The 4.5% (Libor+150bps) is the company’s borrowing cost.
Number is little confusing, 3+1.5 is 4.5%.
discount rate should LIBOR + 4.5, you should discount at borrowing cost of the borrower, but to calculate forward rates you use LIBOR spots
The loan saving/or extra cost happen at end of the loan period. We need to discount the saving/or extra cost back to the beginning of the lona period. I belive the discount rate need to be LIBOR. If we are trying to figure out the amount of credit risk and its direction, we are pricing this FRA @ currement market price (LIBOR). CSK, where did you get LIBOR+4.5?
There are two discounting rate. Use LIBOR to discount the saving/cost back for 1yr, (Loan term), then use rfr (I remeber this problem, it should be rfr somewhere) to discount 5 month (6 month FRA, 1 month into it).
I dont have a book, and dont see a problem but in general, you have to use borrowing cost to discount to the beggining of contract. Why? You have to discount by borrowing costs of the manager. Since payment is going to happen on that day (6 months in the future) now you have to discount it by rfr (if you assume it is a bank borrowing cost)
Cool, at least we know what we disagree on. I believe that we use the market rate to discount back to the beginning of the loan term. Also, the payment (in this case) actually happen in 18 month in the future, 6X18 FRA. 6 month is the FRA term, 12 month is the loan term.
i have to disagree with csk for the 12 months loan period. the counterparty of FRA (lehman) may not bear the same borrowing cost as the borrower (ge). to price counterparty’s credit risk, the only fair discount rate should be the prevailing libor rate.
What do you have aganist LEH? 
LEH … let me see. too much ads on its building, that big tv screen is a bit annoying, 30% loss this year, …
rand0m Wrote: ------------------------------------------------------- > LEH … let me see. > > too much ads on its building, > that big tv screen is a bit annoying, > 30% loss this year, > > … LOL, hahahah!!! Good old LEH.
LEH for teh WiN! LEH is like our long lost brother!
ws - I got your point, you are right that we need to discount the value at the end of contract(beginning of loan period) back to today, using the RFR. But still not clear about why use LIBOR instead of (LIBOR+150) for the first calculation. Are you saying that (LIBOR+150) is the borrowing cost of the investor and LIBOR is the borrowing cost of the dealer in between - and that is why we are discounting at LIBOR… sorry… just not getting it…
Wolly i will come home and check CFAI books, they have example like this
I would just delete this one from schweser, makes no sense to me: they get the pv (in 5 months) of the FRA at maturity (which would be correct, I guess) using 3%, which is current LIBOR… Why “current LIBOR” to get that pv (in 5 months)? I mean, you should use a one year rate starting in 5 months, which seems more like a forward rate and not “current libor is 3%” as they say, without even mentioning what tenor they are talking about… then the thing is even worse, because they take the pv (today) of that using “the risk free rate of 2.8%”… again no tenor, not anything… “the risk free rate”… cool but I think that even the 25k are not correct, although not sure about this: According to them, the result of the FRA (in 5 months + 12 months) is 5% (FRA rate) - 4.5% (3% LIBOR + 150%)… what? I don´t get it: I understand that if he has to pay floating in the other loan, at LIBOR + 150 bps, he doesn´t want interest rates to go up, that is the reason why he enters into the FRA. But the payoff of the FRA would be calculated as the present value of LIBOR - 5% (times whatever days / 360). Why do they use 5% - 4.5%? That way they are incorporating the terms of his other loan into his FRA contract (done perhaps with other counterparty, which is not even mentioned). But that is not the correct payoff of the FRA. Even more, “one month into the contract” means that the loan has not even been taken… For me, this is either wrong or incomplete. And, also, please correct me if wrong, but FRA calculations are nowhere in the level III curriculum, right? thx
Wolly Wrote: ------------------------------------------------------- > ws - I got your point, you are right that we need > to discount the value at the end of > contract(beginning of loan period) back to today, > using the RFR. But still not clear about why use > LIBOR instead of (LIBOR+150) for the first > calculation. Are you saying that (LIBOR+150) is > the borrowing cost of the investor and LIBOR is > the borrowing cost of the dealer in between - and > that is why we are discounting at LIBOR… > > sorry… just not getting it… To me, the whole calcuation is the same thing as pricing a FRA at current market rate. You use LIBOR+1.5 and FRA reference rate to determine if you save or lost money by entering the the FRA. You use LIBOR to price a on-going FRA. Why? What if the investor(borrow) want to get out the FRA 1 month into it? He need to pay the dealer or counterparty to get out. To price an instrument, you have to use market rate…not your borrowing rate…in this case, your borrowing rate is irrevelent to the pricing of FRA. This helps??
That makes sense. Thanks…
hala_madrid…I read your post. Not sure what you are confused with. However, FRA is very much like future. Bottom line is, are you better or worse after you enter a FRA? The FRA rate is 5% in this case, borrowing cost is LIBOR+1.5%, As FRA expires, looking at the LIBOR at THAT time, if LIBOR is 6, your borrowing cost is 6+1.5=7.5%, you will be happy to fulfill your obligation to take out the loan at 5% stated in FRA. (You are better with FRA). However, if LIBOR is only at 2%, your borrowing cost is only 2+1.5=3.5%, you will be like "damn, I still have to borrow at 5% (FRA)? " Yes. you do. FRA cost you nothing to enter, however, it cost you money to get out before contract expires. That is why we use market LIBOR to price the FRA, so the party who is worse off can pay the party who is better off to terminate the FRA.
100% agree, ws Perhaps my previous post was confusing. My point is: 1. Payoff of the 1 year FRA at maturity will be: notional x (LIBOR - 5%) 2. Interest on the loan will be: notional x (LIBOR + 150 bps) 3. So basically you will get (LIBOR - 5%) - (LIBOR + 150 bps) = -5% - 150 bps = -6.5% 4. With the FRA, you effectively locked 6.5% as your interest cost. As you say, if LIBOR goes down, worse for you because you would have locked in a higher rate (and viceversa, if LIBOR goes up, better for you because you would have locked in a lower rate) 5. But my point is that, one month into the FRA contract (so, 5 months until you get the loan, and 17 months until expiry of the FRA), the only credit risk in this situation is the one associated with the FRA, as the loan doesn´t even exist. So the calculation of “5% - 4.5%” they do makes no sense to me, as you should only take into account the FRA payoff which is LIBOR - 5% (so 4.5% would not be included) 6. Regardles of the “amount” of credit risk at maturity, even assuming that “5% - 4.5%” as they use is correct, the discount rates the use to get the pv of that also don´t make sense. First, because they use “current LIBOR” to get the value in 5 months of the final settlement (which would happen in 17 months), which by definition should be done using a forward rate (I guess some 12 rate in 5 months time), not “current LIBOR”. And secondly, because once they get that “value in 5 months”, to get the pv today they use “current risk free rate” of 2.8% (again, without specifying what is that “risk free rate”, tenor, etc) Anyway, as I said, I would not spend a lot of time on this one, as I think this is not in the curriculum thx