Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

CFA Events Calendar

View full calendar

Recommended Discussions

See how our partners can help you ace your CFA exams.

Question on Kaplan's question on Binomial Trees

An example of a standard tree used by FIData is given in Figure 2.

Figure 2: Binomial Interest Rate Tree

Year 0Year 1
4.5749%7.1826%
5.3210%

FIData's website uses rates in Figure 2 to value a two-year, 5% annual-pay coupon bond with a par value of $1,000 using the backward induction method.


The question is: Using the backward induction method, the value of the 5% annual-pay bond using the interest rate tree given in the three bonds in Figure 2 is closest to:

A)$900.
B)$945.
C)$993.

So I averaged node U2 (1005/1.071826) and node L2 (1005/1.05321) to come up with 943.6846.  Then I discounted that by the year 0 rate of 4.5749% and came up with 907.1819.  I answered A.  

Kaplan says the answer is C.  Their explanation is:  The value of the 5%, two-year annual pay $1000 par bond is $992.88.

I find that explanation underwhelming.  Can someone help me out here?  Where did I screw up?

Comments

  • Hi @BobBarkerPlaysPlinko, here's my method:

    I've ignored the $ value of the bond for now, and work on a % basis (of par) to simplify things:

    Using your definition of nodes:
    U2 = 105/1.071826 = 97.9637
    L2 = 105/105321 = 99.6952

    Then fair value of bond today, V0 = 0.5 * [(97.9637+5)/1.045749] + 0.5 * [(99.6952+5)/1.045749]
                                                        = 0.5 * [98.4593+100.1150]
                                                        = 99.2872

    So 99.2872% of a par value of $1,000 should be $993, i.e. answer C. 

    Hope this helps!

Sign In or Register to comment.