# Study Session 12: Fixed Income: Valuation Concepts

## OAS and level of interest rate volatility

If the OAS of a straight bond is 48bps, putable bond and callable bond with similar liquidity risk and credit risk compare to the straight bond should also have a OAS of 48bps. Is this correct?

If the above is true, then why during high level of interest rate volatility putable bonds should have a higher OAS? (I understand OAS is a measure of the attractiveness of the bond, and putable bonds protect investors during times of volatility)

I am having trouble bridging the two concepts.

## I seem to find an error on Schweser's QuickSheet

Value of a forward on a coupon-paying bond:

Vt(long) = (St-PVCt) - [FP / (1+Rf)yx(T+t)]

I’m almost certain that it should be (T-t) not (T+t). Could anyone comment on this please?

## Binomial Interst Rate Tree - Schweser Mock Q42

Hi guys,

In Schweser’s Mock there’s a question that asks to calculate the value of a bond with the following information.

Maturity: 3 years

Option: Callable at par in 1 year

Coupon: 2%

Par value \$100

The interest rate tree is

Year 0 = 1.5%

Year 1, upper node = 2.8873%

Year 1, lower node = 1.9354%

## Soft Put vs Hard Put

There is a statement that I do not get;

” a bond with an embedded soft put is redeemable through the issuance of cash, subordinated notes, common stock, or any combination of theses three securities. In contrast, a bond with a hard put is only redeemable using cash.

What does hard put and soft put mean?

How so?

## Pars vs. Spots

what is the difference between par rates and spot rates?

## YTM

What would be the best way to answer this question?

Based on the data in Exhibit 1 and the yield to maturity quoted by the dealer referenced in Module 2, what action should an analyst most likely take with regard to the Treasury bond?

EXHIBIT 1

SELECT SPOT AND FORWARD RATES

Year 1
Year 2
Year 3
Year 4

Spot Rate
0.055

0.0825

Discount Factor

0.8163

## Arbitrage Free Tree to Value Bond

Why is the coupon of 2.8% being used twice in the below rather than just in the numerator/cash flow? This is using the arbitrage free tree to value a bond.

vu,u=0.5×(102.8/1.0456)+(102.8/1.0456)+2.8=101.117

vu,d=vd,u=0.5×(102.8/1.0345)+(102.8/1.0345)+2.8=102.172

vd,d=0.5×(102.8/1.0260)+(102.8/1.0260)+2.8=102.995

## Binomial tree

So I got a little confused with two problems in reading 36 (the arbitrage-free valuation models), problems 10 an 14 in the curriculum. Both bonds are valued by using binomial tree model and they have three year maturity.

In problem 10 they start off with start off by discounting last year cash flow (par + coupon)/forward rate + coupon
In problem 14 they actually start off by not discounting these values; rather, they represent third year cash flow simply as par + coupon.

## Changing Porfolio Duration!

How can a manager reduce the duration of a portfolio, is not is an automatic calculation determined based on the prices and interest of the investments in the portfolio? Or it means that the manager changes the bonds in the portfolio?