# Study Session 12: Fixed Income: Valuation Concepts

## Reading 35 - 3.4 Constructing the Binomial Interest Rate Tree - what to know?

What do we really need to know from this section?

The LOS reads “describe the process of calibrating a binomial interest rate tree to match a specific term structure”, but this section gets quite detailed mathematically. I don’t want to spend too much time on calculations that will not be tested. My main takeway is that, through iterative calculations, one can fit the interest rate tree to the current yield curve of a benchmark bond assuming a certain interest rate volatility.

Does anyone have a summary of the key takeaways that we should know?

## Calculating the Forward Rate Model Simplistically

I’m working through the Fixed Income section on calculating Forward Rates and want to simplify how to approach these questions with a minimal amount of formulas.

I’ll write out the formulas below with including the page numbers. To help I’ve used X to denote multiply.

The CFAI text gives an initial formula: **Equation 4** (pg 8) as *[1 + r(T* + T)] ^{(T*+T)} = [1 + r(T*)]^{T}* X [1 + f(T*,T)]^{(T)}*

## Difference between price and value of bond

Curriculum Reading 35 # 13 , 14

what is the difference between the question of value and price of the bond?

and doesn’t the price of the bond equal to discounted price + coupon?

## Difference between YTM and Spot rate

I am confused with the difference between YTM and spot rate.

ex) Reading 35 Aribtrage-Free Valuation Framework #2

Why can’t we discount the cash flow to the YTM of 1.25%, 1.5%, 1.7% ?

I do not understand the part that 1) calculate each spot rate 2) discount with this number

## Effective Convexity

I’ve been having trouble understanding convexity conceptually, but I think I might be starting to understand it.

## Question on the Steepness or flattening of the Yield curve

Dear All

Please let me know if my understanding is correct:

1. If the Short Term rates increases more than the rates on the longer term tenor, then it is Flattening of the Yield curve - due to level and steepness

2. If the Short term rates decreases more than the rates on the Longer term tenor, then it is Steepening of the Yield curve due to level and Steepness

Please do let me know if the above is correct

Thanks

## Fixed Income - Relationship between future spot and forward rates

Thus, if a trader expects that the future spot rate will be lower than what is predicted by the prevailing forward rate, the forward contract value is expected to increase. To capitalize on this expectation, the trader would buy the forward contract. Conversely, if the trader expects the future spot rate to be higher than what is predicted by the existing forward rate, then the forward contract value is expected to decrease. In this case, the trader would sell the forward contract.

## Bootstrapping

IN the CFAI book it is mentioned for boot strapping:

[question removed by moderator]

**If they are zero coupon bonds than why** **do they have coupon payments of 0.059? **

**Thanks**

## Fixed Income Binomial Tree

Will the question in the main CFA exam ask us to construct the binomial tree or will the tree be given?

Thanks

## Callable and Puttable Bond Curve Questions

Hi,

I’ve a question about the price v.s. yield curve of callable and puttable bonds. The callable bond will show a negative convexity at lower yield and its price will be lower than the straight bond, and the puttable bond will show a more positive convexity at higher yield and its price will be higher than the straight bond.

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