# Study Session 16: Fixed Income: Analysis of Risk

## Understanding Defeasance

So let’s say I am a borrower. I pay 6% interest on the mortgage I have on my commercial property. I decide to repay my loan balance say $100.

But because of defeasance provision I have to “provide sufficient funds for the servicer to invest in a portfolio of government securities to replicate the cash flows that would exist in the absence of prepayment.”

But then these government securities will pay a lower rate than the mortgage, say 2%? So that means that in order for the cash flows to be the same, I would have to provide $300 so that again $6 is the same cash flow.

## Return on Capital

Can someone explain how is this ratio calculated?

An what does it means? (like higher better, lower worse)

## Having a Hard Time to Understand Fundamental of Credit Analysis

I figured this los so hard:

g. calculate and interpret financial ratios used in credit analysis;

It`s way too many formulas and the interpretation for each one is not easy, some are better when the number is small, some better when it`s big. I just can`t remember this formulas (I`m having a hard time because the accounting terms are not so familiar with my language that is portguese too, unlikely everything I have been reading until now)

This is on Fixed Income last reading, I don`t studied FRA yet, so I don`t have much basis what`s going on,

## Duration - Reading 46-FI

Could someone help me to understand this concept?

Q: For large changes in yield, which of the following statements about using duration to estimate price changes is *most accurate*? Duration alone:

A: overestimates the increase in price for decreases in yield.

B: overestimates the increase in price for increases in yield.

C: underestimates the increase in price for decreases in yield.

Correct answer: C

## Reading 46 ■ Understanding Fixed-Income Risk and Return

Hi,

Need a suggestion: Is it better to memorize the formulas before going to the back of the curriculum questions or solve them looking at them and then memorize once get a hang of the language etc?

I have done the reading 46 “Understanding Fixed-Income Risk and Return” and keep on getting the mix of a few conceptual formulas.

## Macaulay duration (MacDur)

I have a question about the weight calculation. For the weights I got

w_{1} = .0556

w_{2} = .0514

w_{3} = .8415

Am I wrong? If so, how do you get the weights from the answer key?

An investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond’s Macaulay duration is *closest* to:

## Effective Convexity Question

See practice question below - in the solution why does PV0 change in the denominator (it appears they have just dropped a 9)?

Thanks in advance!

## Modified duration and Money duration

Hi!

I am having troubles studying about Modified duration and Money duration, and hoping to get some helps.

1. Modified duration can be used to measure the percentage price change upon absolute change in YTM. I am confused about YTM here. Modified duration can be shown as

Modified duration = (dP/P)/d(1+r)

And I think the r here represents periodic interest rate.

## Effective Duration = Modified Duration when Yield Curve is Flat? (for option-free bond)

Hey all!

Why is it that if the yield curve is flat, the effective duration will be equal to the modified duration for an option-free bond?

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