Interest rate jargon

[wrongsaidfred]

Hi David,

If a Eurodollars contract is quoted at 96, this means that for for the three months after it matures it locks in a rate of 4% that is compunded quarterly on an actual/360 basis. This is the futures rate. After we adjust the rate to continuous and actual/365 and then subtract the convexity adjustment we get the forward rate on a continuously compunded basis.

In this sense, what would be considered the "3 month LIBOR" rate? Is this a futures rate or a forward rate? Is it something else?

Thank you,
Mike

 

[David Harper CFA FRM]

Hi Mike,

As you imply, the Eurodollar futures contract is not the same thing as LIBOR. Rather, the futures contract references (is a derivative on) the underlying LIBOR interest rate; in a way analogous to a corn futures contract references (derives from) underlying corn commodity.

LIBOR itself is a so-called simple (non compounded) interest rate, see http://www.bbalibor.com/technical-aspects/calculating-interest

The futures contract, however, is quarterly ACT/360 (that is two aspects: compound frequency and day count convention).
Please note that the simple rate is not inconsistent with quarterly as long as the instruments are short term (90-day instruments).
For example, if you earn 8% simple interest on $100 per annum over 90-days, you earn 8% * 90/360 * $100; if you "roll this over" each quarter, in a year your earn an effective rate not of 8.0% but rather (1+8%/4)^4; i.e., the simple LIBOR and the quarterly ED futures contract are consistent!
... In this way, LIBOR itself is LIBOR but is "on the same terms" as the forward rate implied by the ED contract (100 - Quote).

The convexity adjustment is a sidebar: there are several methods, Hull happens to employ the "Ho & Lee" adjustment where the adjustment produced is continuous ACT/365. The only reason Hull adjusts the LIBOR is to get them apples -to-apples. (In fact, come to think of it, IMO it would make more sense to convert the convexity adjustment to quarterly ACT/360)

I hope that helps, David

 

[wrongsaidfred]

Hi David,

Thank you for the explanation. I hate to ask this becuase I know I take up a lot of your time, but I am still not quite sure what you mean when you say they are consistent. I see how all of the math works, but what is called what? Is LIBOR 8% for these 90 days or is it 2%? Is the Eurodollar futures contract 92? Is the yearly LIBOR 8.243% (1.02^4)?

I thought the whole reason for the convexity adjustment was that the rate implied by the Eurodollars was a futures rate and cannot be thought of as a forward rate.

Sorry again for all of the questions.

Mike

 

[David Harper CFA FRM]

Hi Mike,

LIBOR is simple but annualized; e.g., quote of 92 corresponds to an 8.0% LIBOR but that is NOT 8% over 90 days but rather 90/360*8% = 2% over the 90-days. Per another thread of ours, we always want to convey in "per annum" rates or it gets confusing. In this case, then, the 8.0% per annum is compounded quarterly so the EFFECTIVE annual rate (aka, effective annual yield) is 1.02^4.

Yes, the convexity adjustment reconciles between a Eurodollar futures rate (which is marked to market) and the equivalent forward rate. I meant it's a sidebar b/c it reconciles derivative (instrument) vs. derivative (instrument). The Eurodollar is a "futures rate" because it is exchange-traded vs. OTC FRA. The compounding math exists in parallel w.r.t. FRA. (we still can call the Eurodollar rate a "forward rate" and often do ... it is a forward rate as opposed to a spot rate ... but it is an exchanged-traded forward rate so we call it a futures rate, but it's not wrong to call it a forward rate in the sense of the time-dimension ... the pricing difference here concerns the liquidity of the futures contract compares to the OTC forward).

Thanks, David

 

[wrongsaidfred]

Thanks again.

Mike