Not Understanding Derivatives At All

CFA Level II Derivatives
#1

Hello everyone,

I started the first reading for derivatives last week and I finished reading it, but didn’t understand anything. This is the first reading where a reading has been not understandable.

Also tried doing the example problems, and even after re-reading sections to figure out what the formulas mean, I’m not understanding anything. I find the formulas to be poorly explained and I do not understand what each symbol corresponds to in each formula.

Did anyone else have the same issue? How to fix? What did you do to understand the derivatives section for Level II?

Thanks

#2

Please give me one example of something that’s vexing you.

I might be able to shed some light on it.

#3

Hello S2000magician, I appreciate your willingness to help.

Ok so I am going through the example problems, looking at the formulas, and trying to figure out what the symbols in the formula represent, and how to plug them into the formula for the problems and why the CFAI plugs them in the way they do. I have the most difficult with examples 6-9.

Example 6, #s 2 and 3, Pgs.313-314 (2018 CFA Level II paper textbook):

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Their solution uses this formula: NA { [FRA(0,h,m) - Lh(m) tm ] / [1 + Dh(m) tm] }

Here are my thoughts so far:

Ok so NA = notational amount.

FRA(0,h,m) = I am not quite sure what this means but the CFA book said “fixed forward rate set at time 0 that expires at time h when the underlying Libor deposit has m days to maturity at expiration of the FRA”. This seems a very long way to say a simple thing. I am assuming it is simply the given FRA pricing rate since that is what the problem does. Could you please explain a little bit more about this? Because it becomes important later on for Example Problems 7 and 8.

h = expiration of FRA

m = maturity of the underlying

Lh(m) = ? some sort of Libor rate, I think Lh is the Libor rate at FRA expiration date, so what is the (m) term for? In the solution to the example problem, it looks like the Libor rate at maturity. But then why the h???

Dh = discount rate for the FRA at settlement, or maturity.

tm = fraction of the year until deposit matures observed at the FRa expiration date (ex: 90/360).

Is this correct? Is there a simpler way to think about this? I know the CFA, at least the first test, is very much a memorize and chug exam. I memorized the majority of the formulas for the 1st test without learning too much on how to derive most of them (no time for that), since that is what the exam seems to emphasize (memory vs. understanding). Can I get away with this strategy for the second exam? Because when I try to understand it in too much depth its easy to get lost in it, confused, and unable to apply it to a problem for exam purposes.

When I look at a problem, it seems to me very much that they just want me to figure out which formula or concept to memorize, and then using the right numbers to plug them in, to get the answer.

Example 7:

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They like to use this formula for the solution:

FRA(0,h,m) = { [1 + L0(h+m) th+m] / [1 +L0(h)th] -1 } / tm

Once again the FRA(0,h,m) terms pops up again. They used h=180 and m=90, so FRA(0,180,90). I think that the 180 is because of the 6 months (x3=180days) but I don’t know where the 90 came from or what it means.

L0(h+m) = Its some sort of Libor rate, but they used the 90-day Libor. This means they didn’t do h+m, it looks more like they used something that looks more like Lm…very confusing.

t h+m= ok this is just a fraction; h+m / 360: they used 270/360 because h=180 and m=90

L0(h) = unsure what this means. But they used the 6 month Libor rate.

Also, X x Y FRA means:

X= FRA expiration date

x = by

Y = End of loan peiod.

But I don’t understand how this works in the context of example 7. Shouldn’t this mean that m should be 270 (9 months x 30) instead of 90?

Is there something I am not understanding right about any of the above?

#4

The only difference between what you’re seeing for FRAs here and what you saw for FRAs at Level I is that the discount rate for a payment made 90 days from now may not be the same rate as 90-day LIBOR.

Well, that and the fact that their notation is incredibly stupid.

I suggest that you ignore their notation and simply understand how an FRA works.

The underlying on an FRA is a pair of loans (not one loan as is commonly, incorrectly, stated): one long, one short, one fixed, one floating. The long position in an FRA receives the floating rate and pays the fixed rate; the short position in an FRA receives the fixed rate and pays the floating rate. (The easiest way to remember this, in my opinion, is to compare it to a forward contract. In a forward contract (on, say, gold), the long position gains when the price of the underlying increases, and loses when it decreases. In an FRA, the long position gains when the floating rate (which is the only thing that can change on an FRA) increases, and loses when it decreases.)

In a 1 × 4 FRA, the loan period starts in 1 (30-day) month and ends in 4 (30-day) months, so the loan period is 3 (= 4 − 1) 30-day months, or 90 days. If there were two real loans, they would pay off at the end of the loan period. An FRA pays off at the beginning of the loan period, so the final loan payment is discounted back from the end of the loan period to the beginning of the loan period. Usually, the discount rate is the prevailing LIBOR rate for the loan period; however, they’ve thrown in this silly discount rate to complicate things. Whatever.

So, for Example 6, the fixed rate is 0.60% (annually), the floating rate is 0.55% (annually), and the discount rate is 0.40% (annually). Thirty days from now, you will (in essence) enter into a loan to borrow £10 million for 90 days at 0.60%, and (in essence) enter into another loan to lend £10 million for 90 days at 0.55%. If it were settled at the end of the loan period, you would pay (90 days after the start of the loan, or 120 days from today)

(0.60% − 0.55%)(90/360)(£10 million) = −£1,250

Because it is settled at the beginning of the loan period, you have to discount that payment for 90 days at 0.40%:

−£1,250/[1 + 0.40%(90/360)] = −£1,248.75

Pretty exciting, eh?

#5

Example 7 is nothing more than calculating forward rates, which you did at Level I.

Once again, ignore the stupid notation.

In words: if you invest for 6 months at the 6-month spot rate (s6), then for another 3 months at the 3-month forward rate starting 6 months from today (3f6) (for a total investment period of 9 months), you get the same interest as if you had invested for 9 months at the 9-month spot rate (s9).

For effective rates,

(1 + s6)6/12(1 + 3f6)3/12 = (1 + s9)9/12

For nominal rates, such as LIBOR:

[1 + s6(6/12)][1 + 3f6(3/12)] = [1 + s9(9/12)]

A little algebra:

[1 + s6(6/12)][1 + 3f6(3/12)] = [1 + s9(9/12)]

1 + 3f6(3/12) = [1 + s9(9/12)] / [1 + s6(6/12)]

3f6(3/12) = [1 + s9(9/12)] / [1 + s6(6/12)] − 1

3f6 = ([1 + s9(9/12)] / [1 + s6(6/12)] – 1)(12/3)

So,

3f6 = ([1 + 1.75%(9/12)] / [1 + 1.5%(6/12)] – 1)(12/3)

= [(1.013125 / 1.0075) – 1] (4)

= 2.2333%

#6

Thank you S2000Magician!!! You just saved me a few hours of re-reading the textbook…again.

I deeply appreciate your help.

#7

My pleasure.

#8

Follow these steps…

  1. pick up your CFAI LII derivatives textbook

  2. burn it

  3. go on Mark Meldrum’s website and buy his derivatives section

  4. let the master wizard perform his magic on your feeble mind

#9

With all due respect, that’s _ my _ bailiwick.

#10

I have to agree with another post: markmeldrum.com. His videos and notes are tremendous on Derivatives. As he says, “this is just moving stuff around time lines.” Do the EOCs and blue boxes, then use his Review video for each chapter which goes over each EOC question for that chapter. Don’t skip any of the videos. Buy the notes package as well. Then, you still won’t get 50% of it(theoretically you will, but that’s not the same as knocking of answers without much thinking) but if you use Analyst Notes (subscribe to that as well!) and do 10 of the Derivatives questions at a time and eep doing them till you can do all 140 or so, in about a week they’ll be second nature. The CFA notation is horrible and Meldrum goes out of his way to critique it and give a much simpler way to understand the whole topic esp of Pricing and Valuation. You’ll be able to do it in your sleep. Seriously.