R19.P1.T3.Hull-Chapter 6: Topic-Extract LIBOR Zero Rates

[gargi.adhikari]

In reference to R19.P1.T3.Hull-Chapter 6: Topic-Extract LIBOR Zero Rates:-
Rf ( T2-T1) = [ R2T2- R1T1 ]
=> R2 = [ Rf ( T2-T1) + R1T1 ] / T2
To calculate the last Zero-Rate, we did the following:-

4.994% = [ 491 * 4.893% + 5.5 % ( 589- 491) ] / 589
Based on the Zero Rate and Forward Rate calculations in other chapters, should we not have used 5.6% = as Rf , instead of the prior period's Rf= 5.5 % ...?

 

[ami44]

Hi,

is it possible, that you misread the table?
5.5% is the forward rate from day 491 to day 589. The next forward rate from day 589 onwards is 5.6%.
So 5.5% is the rate to calculate the zerorate up to day 589.

 

[gargi.adhikari]

Thanks @ami44
What you pointed to is absolutely right and hence the point I am trying to make...Please refer Chapter 4- Fin products, Topic : Spot and Forward Rates, Pg # 52 as an example:-
By plugging in the Spot rates for Yr 3 and Yr 4 we get the Forward rate of Yr 4 and ahead and not Yr 3 and ahead....

Whereas in the example above, if we plug in the Zero rates for the 3rd Period (= 4.893%) and the 4th Period (= 4.994%) and reverse check, we will get the Forward rate for the 3rd Period and ahead = 5.5% instead of getting the Forward rate for the 4th Period and ahead= 5.6 %....This happened because we used the 3rd Period Forward Rate instead of the 4th Period and ahead Forward rate of 5.6 % ...

Trying to see the point I might be missing here..... @David Harper CFA FRM ...? Any insights...?

 

[ami44]

In your example you get the forward rate from year 3 to year 4 by using the spotrate of year 3 and the spotrate of year 4. Nothing beyond year 4 happens here.

Maybe the expression "The one year forward rate for year four" is a little misleading here, but it means here the forward rate from year 3 to year 4.

 

[gargi.adhikari]

@ami44 Thanks so very much for pointing this out....I do see the point now...There was indeed a huge gap in my understanding here...Thanks again !

 

[David Harper CFA FRM]

Hi @ami44 and @gargi.adhikari

The study notes (both page 90 and page 52 of your screenshot above) are poorly phrased, sorry. Forward rate semantics are tricky but these don't help

In regard to your red circles on page 52 (i.e., your second screen shot), the reference to the 6.3% forward rate should read:

• the one-year forward rate starting in three years (this follows syntax used in a 2016 GARP practice question, P1.76); or here is also an acceptable alternative:
  
• the three-year into one-year forward rate (this is CFA approach)

Such that the Eurodollar Futures exercise (which is just Hull's Example 6.5) is

• Solving for the 589-day zero rate of 4.994% as a function of the 491-day zero rate of 4.893% and the forward rate for a 90-day period beginning in 491 days (which is equal to 5.50%). This is tricky because this 90-day forward rate is multiplied by 98 days = 589-491 simply because it is solving for (extending to) the 589-day zero.

In case it's interesting, here is CFA part one on this (just because I needed to refer myself):

"Suppose that a dealer agrees to deliver a five-year bond two years into the future for a price of 75 per 100 of par value. The credit risk, liquidity, and tax status of this bond traded in the forward market are the same as the one in the cash market. The forward rate is 5.8372%.
75=100/(1+r)^10, r=0.029186 ×2=0.058372

The notation for forward rates is important to understand. Although finance textbook authors use varying notation, the most common market practice is to name this forward rate the “2y5y”. This is pronounced “the two-year into five-year rate,” or simply “the 2’s, 5’s.” The idea is that the first number (two years) refers to the length of the forward period in years from today and the second number (five years) refers to the tenor of the underlying bond. The tenor is the time-to-maturity for a bond (or a derivative contract). Therefore, 5.8372% is the “2y5y” forward rate for the zero-coupon bond—the five-year yield two years into the future. Note that the bond that will be a five-year zero in two years currently has seven years to maturity. In the money market, the forward rate usually refers to months. For instance, an analyst might inquire about the “1m6m” forward rate on Euribor, which is the rate on six-month Euribor one month into the future.

Implied forward rates (also known as forward yields) are calculated from spot rates. An implied forward rate is a break-even reinvestment rate. It links the return on an investment in a shorter-term zero-coupon bond to the return on an investment in a longer-term zero-coupon bond. Suppose that the shorter-term bond matures in A periods and the longer-term bond matures in B periods. The yields-to-maturity per period on these bonds are denoted z(A) and z(B). The first is an A-period zero-coupon bond trading in the cash market. The second is a B-period zero-coupon cash market bond. The implied forward rate between period A and period B is denoted IFR(A,B–A). It is a forward rate on a security that starts in period A and ends in period B. Its tenor is B – A periods."--- Institute, CFA. 2015 CFA Level I Volume 5 Equity and Fixed Income. Wiley Global Finance, 2014-07-14. VitalBook file

 

[gargi.adhikari]

@David Harper CFA FRM David...as usual...Thank You Thank You Thank You