Blog Week in Risk (August 26th)

David Harper CFA FRM

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

New Practice Questions
New YouTube
In the Forum This Week (selected only)
External

Economics and world
Banks
Cyber and data science
Quantitative
  • Materials for Teaching Applied Statistics https://trtl.bz/2BB2l0e Wonderful resource, this teacher's "dedication and energy are apparent in the materials"
  • Exploring correlations in R with corrr https://drsimonj.svbtle.com/exploring-correlations-in-r-with-corrr This is such a cool package that simplifies correlation analysis
  • Pearson’s Correlation, Linear Regression, And Why ‘Beta’ Grossly Underestimates Portfolio Sensitivity To Market Returns https://trtl.bz/2Na892p This article explains relationship that are fundamental (useful) in the FRM P1.T2 and P2.T6
  • Transforming skewed data https://trtl.bz/2LgWrkx
  • Power Law, Broccoli, and Billionaires (medium.com) https://trtl.bz/2P5gSTY "Scale invariance is also a defining feature one of the most important mathematical functions in modern society — power law."
  • Understanding Probability Theory with Dungeons and Dragons (Chapter 1: Independent Events & The Binomial Distribution) https://trtl.bz/2P4zcg6
Risk/FRM
Investing
Other
 

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 CFA & 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

Can you please be more specific about which link you are referring to? If it is one of our forum links that are listed above, please comment directly in that forum thread.

Thank you,

Nicole
 

David Harper CFA FRM

David Harper CFA FRM
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

New Member
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
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:
Top