Computation of present value of expected loss

CFA Level II
#1

This year a new section on Credit Analysis Models has been added in the syllabus. One of the topics is Present value of the expected loss.

I am unable to understand the computation involved in that case.

Can some please explain the concept?

Thanks

#2

I’m with you on this one. Equally lost! Would really like it if someone could help out

#3

Hey BigShark,

I figured out that PV (risk-free) = CF/(1+rf)^n while PV(risky) = CF/(1+total yield)^n

My confusion is that the formula for PV(risky) is slightly different in the official CFA book and the one by Schweser. Schweser uses PV(risky) = PV(risk-free)/(1+total yield)^n

Hope it helps!

#4

thats not the formula for risky, the Kaplan books comes up with weird values. The risk free formula is right but risky is wrong. Or is the book wrong? I dont get this either

#5

Do we need to know this?

#6

If it shows up on the exam, I would say yes. wink

There’s an LOS for it: calculate and interpret the present value of the expected loss on a bond over a given time horizon;

Although I wouldn’t try to plug and chug a formula for it.

  1. Add the credit spread to the risk free rate to get the total yield at each coupon date using the term structure (rates will have to be given)

  2. Calculate the discount factors for both the risk free yield and the total yield (risk free yield + credit spread) at each coupon date

BA II Plus keystrokes for PV factors: 1) (rate x years to payment) 2) 2ND e^x3) 1/x

  1. Multiply those discount factors by each cash flow to get the present values of the cash flows, then add them up.

  2. (The sum of the PVs of your Risk Free cash flows) - (The sum of the PVs of your Total cash flows) = The PV of the expected loss

Basically you’re comparing the credit-adjusted value (risk-free rate + the spread) of the bond to the risk-free value (risk-free rate only) of the bond.

#7

@Jay – wow, nice.

I spent a fair bit of time on that reading, but honestly viewed it as conceptual. the blue boxes were presented like ANOVA tables – they did all the math and asked you to interpret.

But given the LOS, you’re right. Coud be a question 5% of people are prepared for.

#8

Well if it shows up, at least some of us forum goers will be ready. You don’t want to know how long I poured over the curriculum example trying to figure out where their numbers were coming from. Then two months later I completely forgot how to do it. Then Bill included a slide on it in his Wiley class and it reminded me to get back and look at it again.

#9

The question is: did the slide (two slides, actually) help at all?

#10

Jay im a bit lost could you kindly give a numerical example pls?

#11

On the 2016 official curriculum browse to Reading 46.6.3 Blue Box Example 8. There is a table of calculations (one row only). Spend 15-20 minutes analysing the table (use Excel if necessary) and it could be the best 20 minutes spent in your studies… :slight_smile:

#12

Most definitely. yes

#13

The present value of expected loss is simply the difference in price of a risk-free bond and a risky bond assuming other variables are identical (same maturity, same coupon, etc)

Feel free to correct me if I’m wrong.

#14

QQ from stated above, where:

BA II Plus keystrokes for PV factors: 1) (rate x years to payment) 2) 2ND e^x3) 1/x

Where does the 1/x come from? I don’t see this mentioned anywhere in the readings

#15

Nothing fancy here - it’s just discounting using a continuously compounded rate

e^(-rate * t) = 1 / e^(rate * t)