Can someone please help me understand how did we calculate these Expected Exposures values? I’m not getting it via spot rates or forward rates as mentioned in exhibit 9-10. I’m stuck at this exposures calculation.
It’s the weighted average of the bond values (plus coupon) in the binomial tree used to value the bond.
Here, they don’t give you the tree, so you can’t compute those values yourself.
If you go back to Exhibits 12 and 13, you can see how it’s done. In Exhibit 12, at time t = 1, there are two possible bond values – 98.4920 and 101.0803 – each with a weight of 1/2, plus a coupon of 3.50. The expected exposure is:
\left(\frac12\right)98.4920 + \left(\frac12\right)101.0803 + 3.50 = 103.2862
which is the value we see in Exhibit 3 at time t = 1.
Note that at time t = 2, the weights are 1/4, 1/2, and 1/4, respectively: one path to get to 95.6703, two paths to get to 98.1435, and one path to get to 100.2352. The expected exposure is:
\left(\frac14\right)95.6703 + \left(\frac12\right)98.1435 + \left(\frac14\right)100.2352 + 3.50 = 101.5481
which is the value we see in Exhibit 3 at time t = 2.
At time t = 3, the weights will be, in order, 1/8, 3/8, 3/8, and 1/8.
And so on.
I wrote an article on this: Valuing Risky Bonds | Financial Exam Help 123
You can get access to it (as well as all of my other articles on Level II Fixed Income) here: CFA® Level II Fixed Income Membership | Financial Exam Help 123
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Thanks Bill, it is much helpful. 
My pleasure.
Good to hear.
I’m currently going through it too.
But in the level I, Curriculum defines the EXPECTED EXPOSURE OF A BOND: is equal to bond face value plus accrued interest less the current market value of available colateral.
So in the above example, we assume that bond doesn’t have any collateral, EXPECTED EXPOSURE OF A BOND = Bond face value + accrued interest (AI)
For example, we buy a bond on coupon payment date, so AI =0.
And Expected exposure of a bond = Bond face value = 100. Is there anything wrong here.
They’re a little more sophisticated at Level II. Instead of using the face value of the bond (which won’t be received until the bond matures), they use the present value of the face value.
The exposure is at end of year and includes the coupon due on that date.
So 107.0902 is the value at the end of year 1 including the coupon due at the end of year 1.
End of year 3
Just the par and the coupon due that day = 104
End of year 2
We need to discount the future cash flow using the 3 potential forward rates from the tree in exhibit 10; ie. 3.7026%, 3.0315%, 2.4820% and weight them 0.25, 0.5, 0.25; and then add the coupon.
End of year 1
We need to work another year of the tree. Getting the 2 potential values, taking the average and adding the coupon.
