Simplified from a QBank vignette: * Annualized 90-day LIBOR is 7.6%. * Globos’ economists expect annualized 90-day LIBOR to rise to 7.9% over the next 60 days. The value of a 150-day, $1,000,000 eurodollar add-on yield futures contract at expiration is closest to: What’s your approach to this question?
25$ per tick (0.01%) per million contract here .3% is the change 25 \* 0.3/0.01= 25 \* 30 = 750
The ans from QBank: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~To calculate the expiration value of a 150-day eurodollar futures contract using 90-day LIBOR, the only interest rate provided that works for the contract, we do the following: Divide $1,000,000 by (1 + expected 90-day LIBOR, 60 days from now). If expected annualized LIBOR is 7.9%, the actual interest rate expected for the 90-day period is 1.92%, or (1 + 7.9%).25 − 1. Thus, the expiration value is closest to 981,171.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ My understanding is: 1) at expiration E futures = the deposit valued using L-90 at that time (ie 7.9%) 2) using $1 / (1+L-90) to determine the yield at t-60 3) multiple 1m to the yield to obtain the result My uncertain point is why L-90 at t60 is (1+7.9%)^0.25 but not (1+7.9%/4)? Is this because of the market practice or we can have some explanation on this? Thanks.
can u please provide the question ID?
88875 Q5 many thanks!!
There is no explanation anywhere in the Schweser notes. They just mention L90 in the notes itself, but no worked example to provide any further information. I will go home and look up the text itself to see if this is something they have over there. Usually - when it comes to LIBOR stuff - they use the /4 convention. Is it the “Add-on” yield part in the question, or that it is related to a Future - because of which they are using the ^1/4 convention here, I am not sure…
I think if the period is less than a year - we De-annualize the rate…by multiplying rate r by days/ 360 OR months/ 12 and use (1 + deannualized rate ) as discount factor. If the period is greater than one year say 1.5 years. We can use the annualized rate and the discount factor would be (1+r)^1.5
charu – here it is 0.25 year difference between 1/(1+0.079/4) = 0.980632508 and 1/(1.079)^.25 = .981170854 For a 1 Million notional: 980633 and 981171 From the answers in the question - both would have pointed to the same choice - that is not a problem from this question’s standpoint, but from a general principal, what is the RIGHT way…? The above also seems to be some kind of generalization we are making – is there any place in the CFAI book that talks specifically on this issue, how to tackle it, is the bigger question in my mind. I am planning on reviewing Futures today, so will look at that in the text later…
Thank for your responses, CP and charu. I have checked the CFAI text (V6 p.100) No specific example but the formula there also use the n/360 convention. My impression is when dealing with LIBOR, we will use n/360 to determine the exact rate to use. Just like swap, we always use 1/(1 + L*m/360) to determine each period is discount factor, right? Appreciate someone can help me out here! Thanks thanks!
The convention for LIBOR style rates is 1+ r*m/360 - says so in CFAI text - footnotes pg 41. Note it mentions "LIBOR style " - from that one can conclude they mean T-Bills too. Anyway I have a more fundamental question. In problem above, given lack of information why is expected future rate a better indicator to spot rate? The way I look at this: (1+r150)= (1+r60)(1+f90). Since no information on r60 they have approximated to f90 But we can also look at it this way (1+r150)=(1+r90)(1+f60). We have r90. So why is f90 better sunstituition than r90 for r150?