Option Forumulas

CFA Level III Derivatives
#1

I’m copying & pasting from Word, so I hope this works:

I really had a difficult time with the options section. For whatever reason, I was never able to learn this area in the way that it was taught. So last year I spent the month of September creating my own formula language in an effort to boil things down in a systematic way so that I could memorize them as easily as possible. I was able to list all these formulas on one page of paper using two columns. To memorize them, I printed just the left hand side of the formula (VT = , $ =, etc) and left the formula side blank. Then I made several photocopies of this and would practice my memory of the formula’s by writing them out, in order, in the morning, during coffee breaks, during commercials, and so on. In a few weeks I had it all memorized by heart. I think the key to this working for me was in keeping the ordering consistent for each of the option strategies.

Anyway, I’m sharing this just in case there is anyone else out there that shared my challenge with this and might possibly find this useful. At the bottom I applied this to a butterfly spread problem from one of the 2012 EOC questions.

VT = Value @ expiry

Δ = X or S1

Qc = S-X

Qp = X-S

$ = profit

MP = Max Profit

ML = Max Loss

C = call premium

P = put premium

SoC = So + C

SoP = So + P

QL-H = QL – QH

NP = Net Premium

Covered Call: SC

VT = S1 - Qc

$ = Δ – SoC

MP = X-SoC

ML = So - C

B/E = So - C

Protective Put: BP

VT = S1Qp

$ = Δ – So - P

MP = ∞

ML = SoP - X

B/E = SoP

Bull Call: BCL SCH

VT = QL-H

$ = QL-H + NP

MP = XH-L + NP

ML = NP

B/E = XL - NP

Bear Put: BPH SPL

VT = QH-L

$ = QH-L + NP

MP = XH-L + NP

ML = NP

B/E = XH + NP

Collar: SC BP

VT = S1QP-C

$ = QP-C + S1 – SO + NP

MP = XC - SO

ML = SO - XP

B/E = SO

Straddle: BCP

VT = QCP

$ = QCP + NP

MP = ∞

ML = NP

B/E = X +/- NP

Butterfly: BHL S2M

V0 = -NP

VT = QLH – 2M

$ = VT - VO

MP = XM-L + NP

ML = NP

B/E = XL – NP & 2XM – XL + NP

Box Spread: BCLSCH BPHSPL

VT = XH-L

$ = XH-L + NP

E(V) = (XH-L)/ (1+RF)T

Ok, an example: EOC Question 3Aiii; 3Bi, ii; 3C (from 2012 readings)

Summary:

  • Stock currently $114
  • Construct butterfly spread using calls
  • CL = $8; XL = $110
  • CM = $5; XM = $115
  • CH = $3; XH = $120

3Aiii) determine value at expiration and profit if price of stock at expiration of calls is $115

Answer: S1 = $115; therefore:

VT = QLH – 2M

QL = 115 – 110 = 5

QM = 115 – 115 = 0

QH = 115 – 120 = 0

5 + 0 – 2(0) = 5

$ = VT - VO

VO = -NP

-NP = -(2(5) – 8-3) = 1

$ = 5 – 1 = 4

3Bi,ii)

MP = XM-L + NP = 115 – 110 + (-)1 = 4

ML = NP = -1

3C

B/E = XL – NP & 2XM – XL + NP

  1. 110 - - 1 = 111
  2. (2)(115) – 110 + - 1 = 119
#2

I intend to derive the formula from scratch on exam, keeping in mind the chart shape and the intended strategy.

I can’t never memorise results like this without logic( for the long term). I tend to not sleep well the night before CFA exam and my short-term memory suffers.

What works for me is to have the building blocks and superimpose them on the chart and then work out the various values.

#3

nuts

#4

but admirable

#5

learn how to draw each option and you can figure out the rest using common sense

no need to learn 1000 formulas

#6

You are taking the wrong approach by memorizing formulas. All you need to understand is how a call and put work - all the other strategies are just combinations of the two. Focus on understanding the strategies, not memorizing formulas. Also ,as mcap pointed out, knowing the payoff diagrams is useful.

#7

OMG!!!

#8

Yeah… I think you are doing this wrong…

#9

Well, in all fairness it must have worked for Long Journey since he is now a charterholder. But I’d rather jump off a bridge than memorize those formulas. There are certainly topics that require straight up memorization on the exam (GAAP vs. IFRS and GIPS come to mind), but this is not one of them.

#10

Good grief. Yes ok, I actually agree with you that this was not the best approach and that you were better off if you could work the solution from graphs/first principles. I’m just saying that that approach was causing ME problems and I devised this suboptimal process that worked for me that’s all. I promised myself when I had time I would share it here in case there was anyone that had my same challenge and might find this of any use for them. Then again, I’m sometimes told I’m one of a kind… So, just to recap - this is not a recommendation, it’s just possibly a possible alternative alternative. Most certainly avoid it if you can. LJ

#11

The only question is: why?

Option strategies is a really nice subject and easy to grasp after some preparation. It is amazing why would anyone try to remeber all those formulas instead of understanding the simple rules.