Just wanted to ask…in Example 3 from Reading 43 (Arb Free Valuation Framework - Volume V Pg 289) it gives the standard formula for finding a bond value at a node taking the values and coupons at the two different levels of assumed rates and averaging them…
However, in Example 3 it applies that formula for example at Node2 and then without discounting adds the full coupon payment made at Time 2 as well: .5 X [105/1.08 + 105/1.08] + 5 = Bond Value of 102.2222 without adding the undiscounted coupon pmt and just applying the formula I would get 97.22 as the bond value.
In all the Schweser example questions I’ve done, none of them account for the coupon pmt made at the nodal point of valuation…rather they would just appply the standard formula here of .5 X [105/1.08 + 105/1.08] for that 97.22 value.
Does anyone know what I am missing…or how I would I know which approach to take for the coupon pmt that is being made at the nodal point of valuation?
Each period is going to have a coupon. You will be starting with your maturity year which is principal + coupon, then discounting at the respective forward rate given one year before than. From there you will then add another coupon and repeat the process. You have to take the average of the upper and lower nodes of course, but the point is every node is going to have a coupon added to it (coupon for that year) after you get the PV.
value time t -1 = (.5*(VUt + CouponUt + VDt + CouponDt))/(1 + Forward rate given in year t-1)
V = Value determined from taking PV of U & L nodes in T + 1
Coupons are made at the end of each period so you have to add and discount them to the beginning of each period.
The exception is you don’t add a coupon at time 0 because that is technically the beginning of time 1 and therefore no coupon is paid during that time.
I’m refering to the Exhibit 9 in Reading 43 Volume 5 of the CFAI books on Page 289. It shows a binomial tree for pricing for a bond with par of 100 and coupon of 5 and for example at Time 2 it has this:
.5 X [(105/1.08 + 105/1.08)] + 5 = 102.2222 for the bond value.
It says to note that in addition a coupon payment will be made at Time 2, so it has a 5 coupon payment that is NOT discounted in the valuation formula which is in addition to the coupon pmts being discounted in the formula “.5 X (105/1.08 + 105/1.08).”
The practice problems I’ve done with Schweser for bond valuation at Node 2 do not include any undiscounted coupon payment in the bond valuation (they just follow the formula but the CFAI ones seem to do that ( for example Problem 4 on Page 305). There is an undiscounted pmt included in the calculation of the bond at the node.
Yes, I understand why it is not discounted (it happens at that time). In the Schweser questions I’ve done they seem to ignore the coupon being made at the point of valuation though rather than including them in the calculated present value whereas the CFAI practice questions seem to include them. SO…does it not seem like these are two different approaches to the same type of problem that give different answers?
It’s seriously like the is book making this harder than it needs to be, maybe they got the team in from IKEA to write this section of the book. Could someone smarter and no doubt better looking than me help me and others understand this by way of example using Q10 in reading 43, page 307 of the IKEA Instructions CFA textbook.
In reading 43 Q 10, I have tried adopting both of the below formulas and I get different answers
Formula 1
0.5 *{ [(VH+C) / (1+R)] + [VL + C] / (1+R)] }
Formula 2
0.5*{ [VH / (1+R)] + [(VL / (1+R)] } + C
Formula 2 is used in the textbook to answer reading 43, question 10 - answer seems to be 109.0085. If I apply formula 1 I get answer 108.84 (not including the coupon at time 1 here)…
Are formulas 1 and 2 both expected to yeild different answers when it comes to valuation. In reading 43 the textbook seems to apply formula 2, then in reading 44 they seem to love using formula 1. Why oh why??
Please help me unlock and harness the power of these formulas…
Bond value at a node = 0.50 ×[VH +C/ (1+i) + VL +C/(1+i)]
0.5 × [(105/1.08 + 105/1.08)] + 5 = 102.2222 0.5 × [(105/1.06 + 105/1.06)] + 5 = 104.0566 0.5 × [(105/1.04 + 105/1.04)] + 5 = 105.9615 The formula above is not consistent with the calculations given below (Exhibit 9, CFAI book) Still can’t figure out which formula to use. Any help or insight would be great!
After going back and asking Schweser I believe it is because the curriculum treatment is done under the invoice price method where the formula is executed but then that current coupon payment at point of valuation is added in… Below is my question in quotes and the response to it from Schweser was yes.
"So when you say Invoice Price you mean that the full accrued interest, or in this case full coupon payment made at the point of valuation is simply added to the result of the formula .50 X [(VH + C)/(1+r) + (VL + C)/(1 + r)] PLUS CURRENT COUPON PMT, right? All the sample problems in the CFAI curriculum seem to add in that current coupon so for example in the problem I cited above (Exhibit 9 in Reading 43) the answer is 97.22 if I just follow the formula but it states that the correct answer is 102.22 and notes that the current $5 coupon is added to the formula to get the final price.
This bothered me for a while but I found the solution and created an account to post this. It lies under exhibit 8 of reading 43. The rates given are annual rates which are effective at the beginning of the year. Therefore you need to add the coupon after discounting. Same with question 10 in the reading 43 EOC. Annual rates were given hence the coupns are added after. For normal bonds, the valuation is done as normal by adding the coupon first before discounting.