# Study Session 12: Fixed Income: Valuation Concepts

## Fixed income security as portfolio of zero coupon bonds?

In the text, it shows that:

Using the arbitrage-free approach, any fixed-income security should be thought of as a package or portfolio of zero-coupon bonds

Could someone clarify this conceptually? Eg. How’s a premium bond a portfolio of zero-coupon (discount) bonds?

## Spot rates for corporate bonds

We use spot rates to get an arbitrage-free value for govt bonds (risk- free bonds). But, why do we use the same spot rates to value corporate bonds which carry credit risk ? Shouldn’t we use higher rates?

## Why or how is the binomial interest rate tree a lattice?

This might sound like a weird question, but I don’t understand how the binomial interest rate tree can recombine, for example how are an up down and a down up the same?

I understand that they are the same, say for a stock that is worth $30 with an up and down factor of 1.1 and 0.9, the stock results in the same value when the stock goes up and down, and vice versa. How is this the case in the binomial interest rate tree where an up and down movement is not the same as a down and up movement.

Please help! Let me know if you would like me to rephrase my question.

## CFAI online Fixed Income-Wingaersheek Arbitrage Opportunities Case Scenario

Good day!

May I ask **Q. **Using the backward induction method and the data in Exhibit 2, the value of the bond Hake has been asked to value is *closest* to:

In the solution it says the following for Time 2 value, but why we don’t add the coupon payment of $4 to 99.522/100.726/101.612? Isn’t it making more sense to include the coupon into the valuation?

**Official solution:**

**[ We calculate the present value of the bond at Time 2 using the three forward rates found in Exhibit 2:**

## Return on a LT bond over one year if spot rates develop as predicted by today's forward curve

Can someone please help explain why the return on a bond over one year is always equal to the one-year risk-free rate **if spot rates develop as predicted by today’s forward curve?**

So say for example the 1-year spot rate is 4%.

Why is it that no matter what bond I’m holding–a 2-year, a 5-year, or even a 30-year–after one year, each of those bonds will have earned the 1-year spot of 4%?

I understand that the math works out but I can’t seem to understand the intuition. Any help would be greatly appreciated.

Thanks so much!

## Forward Price Evolution

Assuming an upward sloping yield curve, if a trader believes that the spot rate in one year is going to be lower than the predicted spot rate which is the forward rate (i.e. f(1,1)), then which investment strategy is more profitable for the trader? I know that both of the following strategies provide higher returns:

1) Buy a two year bond and sell after one year

2) Buy a forward contract today to profit from its appreciation in one year

Shouldn’t both these strategies be equal? Or are these not comparable?

## Par Rate and YTM

Hi,

Is the Par Rate & YTM same ? Its confusing.

I hope the YTM is used to construct the Par curve?

Are these statements correct?

Thanks in Advance

## Another OAS question

I know there are a million threads on OAS and I get that it’s the Option Removed spread and the spread you are getting paid for taking the additional risk over the benchmark treasury. There’s a piece in the application that I’m missing and could use some clarity on.

I’m just pulling these numbers out of my ass so they may not work out but hopefully, the point will get across.

## Spot rates and forward rate

When you buy a four year zero coupon bond , you calculate your purchase price by discounting by the 4 year spot rate. And when you sell that 4 year zero coupon after 2 years, how do you calculate the future price, to use it to arrive on returns?

Do you calculate the price (2 years remaining for that 4 year zero coupon) by discounting with 2 year spot rates or you calculate f(2,2) to arrive at that price?

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