Fixed Income Investment-Binomial Tree

CFA Level II Fixed Income
#1

There was a question in Wiley 2017 morning session, I do not get how did we calculate the par value of the bond by which we constructed the binomial tree.

Brandon Walsh, a new intern hired by Haas, then provides the team with the binomial interest rate tree presented in Exhibit 1. He wants to use the tree to value a floating-rate bond issued by Samdong Industrials Inc. Information regarding the bond issued is provided in Exhibit 2:

Exhibit 1: Binomial Interest Rate Tree Assuming an Interest Rate Volatility of 8% t = 0 --> 0.5430%

t = 1 -->u=2.0908%, d=1.7817%

t = 2 -->u=2.6865%, m=2.2893%, d=1.9508%

Exhibit 2: Three-Year Floating-Rate Note Issued by Samdong Industrials Inc. Coupon=Annual coupon based on 12-month Libor + 320 bps Cap=5.40% Term=Three years

Answer: Based on the data provided in Exhibits 1 and 2, the value of the bond issued by Samdong is closest to: A. $101.528. B. $99.895. C. $99.856. Answer: C

t = 0 -->99.856

t = 1 -->u=99.7416, d=99.9597

t = 2 -->u=99.5405, m=99.9153, d=100

#2

I don’t follow how for t=2, d=100. The coupon payment is 12 month LIBOR + 3.2%, so 1.9508% + 3.2% = $5.15. $105.15 is discounted back at 1.9508% to give $103.14.

#3

The way wiley is doing this is by adding the 3.2% (as denoted by 320bps over libor) to the interest rate tree, such as you would with OAS, and then capping the coupon at 5.4%. The binomial then transforms to:

t = 0 –> 3.7532%

t = 1 –>u=5.2909%, d=4.9817%

t = 2 –>u=5.8893%, m=5.4893%, d=5.1508%

And the result is exactly as the answer:

t = 0 –>99.856

t = 1 –>u=99.7416, d=99.9597

t = 2 –>u=99.5405, m=99.9153, d=100

Remember to cap the coupon + value to 105.4.

#4

There’s no calculation for the par value of a bond, it is 100. The MV at different periods could be below par (less than 100) or above par (more than 100) depending on the ytm and coupon.

#5

Lifesaver! This question puzzled me whole day.