Spread change and spread duration

CFA Level III
#1

If Bond B has a spread change from 325bps to 285bps, while Bond C has spread change from 475bps to 400bps… And the spread durations are 5.5 and 4.3 respectively.

Assuming the portfolios are 50% in B and 50% in C, the relative change in value due to the spread change formula is = change in S x SD.

The answer shows:

Average spread change: 0.5 (285-325) + 0.5(400-475) = 58bps Average spread D: 0.5(5.5) + 0.5(4.3) = 4.90 So the change in price is .58 x 4.9 = 2.84%

However, I calculated it individually… why doesn’t this work?

Bond b: (285-325)5.5 = 2.2% Bond c: (400-475)4.3 = 3.225%

So the average is (2.2 + 3.225)/2 = 2.71%

Is this an algebra problem?

#2

Their answer is wrong (and their approach is stupid); yours in correct.

Where did you get this question?

(Oh, and you can consider it either an algebra problem or an arithmetic problem.)

#3

This is from Schweser notes, a blue box problem. The actual problem is:

An investor with a 1-year holding period is analyzing 4 single rating indexes. Each index uses bonds that all have the same credit rating.

Index Rating (numeric value)

Current OAS, bp

Projected OAS, bp

Projected Credit Loss %, (p x L)

Spread D

A (1)

275

250

0.01

4.5

BBB (2)

325

285

0.04

5.5

BB (3)

475

400

0.12

4.3

B (4)

625

499

0.37

5.8

The numeric value in parentheses after the letter rating is used by the investor to determine arithmetic weighted average portfolio credit value.

  1. Calculate the expected annual excess return for a portfolio weighted 50/50 in Index BBB and BB.

Answer:

Average portfolio starting OAS: 0.5(325) + 0.5(475) = 400 bp

Average portfolio spread change: 0.5(285 − 325) + 0.5(400 − 475) = 58 bp decline

Average portfolio credit losses: 0.5(4) + 0.5(12) = 8 bp loss

Average portfolio spread D: 0.5(5.5) + 0.5(4.3) = 4.90

Expected excess return: 1(400) + 4.9(58) – 8 = 676 bp

*** The bolded part is the one I was questioning.

#4

It’s wrong.

I’ll check the curriculum to see if they have it wrong as well.

#5

The curriculum doesn’t have an example of (or a question on) the expected excess return of a portfolio of bonds, so the error is all on Schweser’s part.

I hate it when question writers try to be clever and end up doing something stupid. The curriculum’s difficult enough for candidates when everything they’re told is true. When they get something wrong, it makes it all the worse.

By the way, the question to ask is this: why would you multiply Bond B’s spread duration by Bond C’s spread change (and vice versa)?