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Study Session 12: Fixed Income: Valuation Concepts

Change in steepness and level fixed income

“Consider a portfolio of zero-coupon bonds that mature at different times in the future. Changes in interest rates are not always parallel across maturities, so let’s analyze what happens as rates change across the yield curve. Let’s assume that the portfolio has sensitivities to factors as provided in Exhibit 3. The portfolio has equal weightings in each key rate duration and an effective duration of 4.7. I would like you to assess the impact on the return of the portfolio if rates rise evenly across the curve and also when the curve flattens but does not twist.”

Spot Rates and Forward Rates

Can someone please explain how to derive the spot rates and forward rates if the yield rates are given.

Can someone also please explain in detail, how to solve the problem mentioned below.


A 3 year floating rate bond pays annual coupons of one year LIBOR (set in arrears) and is capped at 5.6%. The one year, two year and three year par yields are 2.5%, 3% and 3.5% respectively and interest rate volatility is 10%. The value of capped floater is closest to:

A. 100.000

B. 105.600

C. 105.921

Arbitrage free, is it dominance or value additivity


I haven’t been sure on how to differentiate between dominance or value additivity arbitrage. At first I thought it is as simple as just checking whether we need to (for example buy multiple bonds and see one/multiple bonds). I thought dominance would be the case only when two bonds have different prices. However, question 11 in the book in The Arbitrage-Free Valuation Framework has got me confused as they considered that arbitrage dominance as the discount rates are different. I mean discount rates will be always different even with value additivity. 

The reason for calibration of binomial tree


I just want to confirm.

We calibrate binomial tree, because in the exercise tasks (or in the market data) we have just spot rates and we need forward rates. Those spot rates are the spot rates from now until a particular maturity. We need forward rates, because current forward rates are the best estimator for the future one-year spot rates. True?

What I don’t understand is that the values of the bonds in the binomial tree seem to be discounted by a “too early forward rate”. Anyone knows the reason why we assign the discount rates “too early”?

OAS for callable and putable bond

hi fellow members,

while practicing, i came across a question regarding if the interest rate volatility declines, what will be its impact on OAS for callable and putable bond for OAS spread.

As per my understanding, the callable bond value would have gone UP and hence OAS should decrease. for putable bond, value should go down and hence OAS should increase.

However the answer mentions OAS should inrease and decrease for callable and putable respectively.

I am confused now ! Can someone please explain the answer.



Mock Exam pm: Fixed Income Q43

CFA Official 2018 Level 2 mock exam PM (Solution p41)


Govt bond with a 3.2%, annual pay coupon maturing in three years. the bond is quoted in the market at $103.50. 

                                               Year 1                       Year 2                         Year 3

Spot Rate                                1.1%                          1.5%                          2.01%

Par Rate                                  1.1%                          1.5%                          2.00%

bond behavior Wiley mock question

“Statement 3: The value of an option-free bond can be positively related to changes in certain short-term par rates if its coupon rate is greater than the market interest rate”

In the answer, this statement is said to be incorrect because “Key rate durations can sometimes be negative (indicating a positive relationship between par rate and bond values) at maturity points that are shorter than the maturity of an option-free bond if the bond has a very low coupon rate or is a zero-coupon bond.”

can someone explain this? im not getting it


Error in CFAI Binomial Interest rate

Has anyone noticed that the CFAI method adds back the coupon twice at each node? 

That’s there method = 0.5×(102.8/1.0456+102.8/1.0456)+2.8

Must be wrong surely?