### CFA Practice Question

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### CFA Practice Question

Two bonds differ in their provisions for early retirement. Bond A is a five-year serial bond. Bond B contains a sinking fund provision requiring the issuer to provide the trustee with sufficient funds to retire 20% of the original principal each year for five years. The sinking fund provision calls for the trustee to select the serial numbers of bonds to be retired by random assignment. Neither bond is callable.

I. The timing and size of bond A's promised payments are known with certainty.
II. There is a 20% chance that an investment position in bond B will be reversed after the first year.
III. The probability that an investment position in bond B will be reversed before maturity increases as time to maturity decreases.
Correct Answer: I, II and III

The indenture of a serial bond specifies the size and timing of promised payments. The sinking fund provision of the bond described in this problem adds uncertainty as to the number of cash flows to be received by the bond owner.

User Comment
wldu Why III? Can anyone explain?
EK65 III is correct because:
Year 1: the probability to be redeemed is 20% and maturity is 5 years
Year 2: another 20% should be redeemed but out of the remaining 80% outstanding the probability is actually 25% (20/80) and maturity is now 4 years
Year 3: the total percentage of bonds to be redeemed is 20/60 =33% of all outstanding bonds and the maturity is now 3 years
etc.
yanpz Why II is correct? After 1st year, only 80% bonds are left, so another 20% out of 80% should be 25% chance.
jnashville II is correct because if you are the bondholder and the issuer sets aside 20% for sinking fund, the bondholder has a 20% (1 IN 5) probability that their bonds will be retired by the sinking fund.
danlan Suppose the face value of bond is 1000\$, the first year, bond issuer deposits 200\$, change of reverse is 20%;
Second year, deposit is still 200\$, principal becomes 800\$, chance of reverse is 25%;
Then the chance will become 1/3, 1/2 and 100%.
fanfanli In real life, do funds often get retired to maintain a sinking fund?

I was under the impression that these provisions were typically deposited in a secure account whilst all bonds stayed in issue.
jasonkwk what is a investment position?
houstcarr reversing a position is a poor choice of wording in the question. typically in trading, when you reverse a position it means you change from long to short (or vice versa)