2013 Exam. Q7 Part C and Part D. Fixed Income

CFA Level III Fixed Income
#1

Part C.

I changed the wording, for the question.

Explain why widening of credit spreads may require Bergen to classically immunize the portfolio again?

(he puts 20% allocation on corporate bond as he is implementing a contingent immunization strategy).

Answer key provides that:

Becaues Bergen is allocating 20% of the portfolio to corporate bonds-secruities which are exposed to credit risk- a widening of credit spreads in this scenario would cause the market value of the portfolio to decline, which may be large enough to erase the surplus and thus require the classical immunization again.

My question is:

i) I understand the spread widening effect as

A widening creit spread suggest that an increased in default risk (default risk, right?), thus the risk of corporate bond increases, requires rate of return for the corporate bond increases, market value of corporate bond thus drops, right?

Do I understand it correctly?

ii) In addition, what is the widening spread’s impact on the Treasury bonds?

Part D.

Answer states that no surplus change due to duration effect. However, the convexity of the liabilities is less than that of the assets. Therefore, the decline in value of the liabilities as a result of the yiled curve shift 75 basis points upward will be greater than the decline in value of the assets, thus increasing economic surplus.

I don’t understand why the lower of convexity would result in a greater value of decline.

First of all, is the convexity postive or negative, or does it matter?

Second of all, why does a higher convexity seem to provide less movement in price. Is that always the case?

Lastly, it seems mathematically convexity is the first derivative of duration, and second derivatives of the price of bond with regard to the interest rate, how could this be understand more clearly (like distance, velocity, and acceleration). [http://en.wikipedia.org/wiki/Bond_convexity]

#2

q1: answer - what is the spread compared to? it is to treasury bonds itself. so treasury spread = 0.

q2: change in value of portfolio = -Duration * Change in Rate + Convexity * (Change in Rate)^2

so since duration of asset and liability is the same - Part 1: -Duration * Change in Rate is the same.

Part 2: Asset has a higher convexity that liability. So Asset changes in value MORE - and since surplus = Asset - Liability - the surplus increases.

#3

Less convexity means more price change as compared to high convexity where price change is less then low convexity

#4

I wouldnt worry about it cuz they are not part of this year’s curriculum… read the LOS before answering the question. Allocating Shareholder Capital to Pension Plans has been dropped

#5

Thanks a lot for answering! :slight_smile: I think Part 2, asset has a higher convexity than liability, so Asset changes in value LESS*, and since both are declicing in value because it’s a rate shifting upward, the change in (asset - liability) > 0 because say it was (10-2) and it is now (9.5-1) thus the surplus increases.

Feel free to correct me! Thank you all and good luck tomorrow folks!

#6

Convexity causes duration to underestimate the change in price from a rate decrease and overestimate the change in price from a rate increase. Higher convexity increases these effects.