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WIFEWeek in Risk (August 26th)

David Harper CFA FRM

David Harper CFA FRM
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Welcome to our newly upgraded forum, we hope you like it! (did you notice that it's faster? among other advantages ....)

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kate18233

New Member
Would appreciate if the demonstration can be given by using financial calculator instead of excel. For example, to obtain the chapter 6 conversion factor, could you demonstrate how to obtain the PV +0.25 = 125.83 by using financial calculator?

Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
Would appreciate if the demonstration can be given by using financial calculator instead of excel. For example, to obtain the chapter 6 conversion factor, could you demonstrate how to obtain the PV +0.25 = 125.83 by using financial calculator?
Hello @kate18233

Thank you,

Nicole

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
@Nicole Seaman I think @kate18233 refers to (Hull's Chapter 6) the calculation of a US Treasury bond conversion factor, because simultaneously a similar comment was left at this youtube video, see below

We don't currently have calculator videos planned. If the 2019 syllabus does not significantly change (wink wink), then we could add a path of calculator-specific videos ...

kate18233

Hi David, thank you for your quick response. I have figured out the calculation, am quite new to the financial calculator so would appreciate if there is a video that shows essential calculator skills for the exam. Nevertheless, I don't understand why in the (if three) full price (PV) T0 which is around $121.832 + 0.25 where excel indicates is 8% x (100/2) =4 so make it up to total of 125.832. Why it is not 8% x 100 x 3/12 for the second part if i understood the calculation correctly? Thank you. David Harper CFA FRM David Harper CFA FRM Staff member Subscriber Hi @kate18233 It's tricky because the coupon is given by 8%*100/2 =$4.00 coupon every six months, but 3/12 is the amount of time from today to T(0) + 0.25 and if the yield is 6.0% per annum with semi-annual compounding then we compound a full price forward three months with PV*(1+6.0%/2)^(2*3/12) per FV = PV*(1+y/k)^(k*T). So i think this is just a matter of distinguishing the coupon cash flow from compounding.

The reason that Bond #2 is harder to price is that it rounds to 18.25 (nearest 3 months). The calculator cannot, to my knowledge, price the semi-annual bond at 18.25 because it is between coupons; it can price at 18.0 years (ie, 36 semiannual periods) or 18.5 years (ie, 37 semiannual periods). So the displayed 125.832 at T0 + 25, in excel, is simply adding the $4.00 coupon received "immediately" at T0 + 0.25 years to a 18-year bond that starts receiving$4.00 coupons six months later. By combining the two components (immediate coupon plus "standard" in arrears 18-year bond), it prices a 18.0 year bond but with an "extra" coupon paid immediately. Then the next step discounts this price to T0 with $125.832/(1+6%/2)^(0.25*2) =$123.986.

My excel replicates Hull's approach and the calculator approach to the same is:
• Price of 18.0 year bond: 36 N, 3 Y, 4 PMT, 100 FV and CPT PV = -121.8323, but being mindful this is the price of a "standard bond" that pays the first coupon six months later, so this price omits the first actual coupon....
• When in fact, we are pricing the PV in + 0.25 years, where a coupon is paid immediately, which is not included in the -121.8323. so we need to add the $4.00 semi-annual coupon such that price is -125.8323. • Then finally we discount this from T0 + 0.25 to T0 to get 123.986 Alternatively, to reinforce an understanding, we can price this bond as of T - 0.25 years; i.e., three months back in time! At that time, it was an 18.5 year bond which can be priced: • Price of 18.5 year bond: 37 N, 3 Y, 4 PMT, 100 FV and CPT PV = -122.1672 (there is no need to add an extra coupon in this scenario!) • Now we can compound this bond forward six months, from T0 - 0.25 years to T0 + 0.25 years, with 122.1672*(1 + 0.060/2)^(0.5*2) = 122.1672*(1 + 0.060/2) =$125.83. Notice equivalance!
• But we didn't need to go that far, we could have just compounded to today with 122.1672*(1 + 0.060/2)^(0.5) = \$123.986. You see how we can use the calculator on coupon dates (e.g., N = 36, 37) but not really between (N = 36.5). I hope that helps!

Last edited:

kate18233

New Member
Hi @David Harper CFA FRM, thanks so much for the detailed explanation. I appreciate and it helps a lot.

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