Derivative strategies

CFA Level II Derivatives
#1

Hi everyone,

Can I check whether we need to know how to compute the profits / max gain / max loss / breakeven for a Bull Put and Bear Call?

The LOS states: “LOS 42.h: Calculate and interpret the value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price at expiration of the following option strategies: bull spread, bear spread, collar, and straddle.”

However, the Schweser material I am studying from does not provide those formulae. They only provide the formulae for Bull Call and Bear Put. If we are required to know them, can something please direct me to a good resource to find those formulae?

Thank you.

#2

I would say yes we should. And my problem is that it takes a ton of time (unless someone is a trader in real life).

I wonder what others say though.

#3

Thanks Moosey, yes I fully agree with you that it takes a ton of time. What’s more it isn’t even remotely related to my line of work :confused:

Could I ask where do we find the payoff formulae for Bull Put and Bear Call?

#4

I’m not on derivatives right now, but when I studied it I created my own notes. Here is what I have on these 2 strategies. I really hope they are right. Sorry for the format this is how it copies from my notes. BULL CALL SPREAD long call with low exercise price XL

short call with high exercise price XH

payoff = – cL + cH + (ST – XL) – (ST – XH) maximum profit: when both called S > X high; or only the long call is called when ST = XH

profit = – cL + cH + XH – XL

maximum loss: when neither option is called

loss = – cL + cH

breakeven price: when only the long call (with low X) is called and the payoff equals to the investment in call premiums

ST = XL + cH – cL

BEAR PUT SPREAD

long put with high exercise price XH

short put with low exercise price XL

payoff = – pH + pL + (XH – ST) – (XL –ST) maximum profit: when both called S < X low

profit = – pH + pL + XH – XL

maximum loss: when neither option is called

loss = – pH + pL

breakeven price: when only the long put (with high X) is called and the payoff equals to the investment in call premiums

ST = XH + pL – pH

#5

Sorry I overlooked your question. As I said I’m not on derivatives right now.

I’m not sure that bull put and bear call exist??? It wouldn’t make sense, would it? These 2 above (bull call and bear put ) do make sense. Where did you come across bull put and bear call?

I’m not a trader either so I might not see the full picture???

#6

You can construct a bull spread with puts or with calls.

You can construct a bear spread with puts or with calls.

I’ve written a series of articles on option strategies for Level III, and I just added them to the Level II menu. The strategies I cover are:

  • Bear spread
  • Box spread
  • Bull spread
  • Butterfly spread
  • (Equity) collar
  • Straddle
  • Strangle
#7

Well. This shows I know nothing… :-((

In this case payoff of a bull put spread should be the same, you buy the put with the lower exercise price and sell the put with the higher.

  • pL + pH - (XL - ST) + (XL - ST)

I somehow thought this structure cannot be realistic.

#8

That’s better.

The profit is the same as the profit from a bull call spread. The payoff is quite different, however (because the initial cost is quite different).

#9

Thanks for the correction S2000!

I meant that the payoff is calculated in the same way, but now I’m a bit puzzled if the profits can be the same?

If I disregard the initial profit (or cost) paying for a put/call and getting the price of a put/call

for a bull call spread if the two calls are exercised I end up with receiving the difference between the two strike prices.

for a bull put spread if the two puts are exercised I end up with paying the difference between the two strike prices.

Not?

#10

If you create a bull spread with calls you’re buying an in-the-money call and selling an out-of-the-money call; you have a positive net cost (i.e., you’re _ paying _ money to establish the position).

If you create a bull spread with puts you’re buying an out-of-the-money put and selling an in-the-money put; you have a negative net cost (i.e., you’re _ receiving _ money to establish the position).

The minimum payoff on a bull call spread is zero and the maximum is the (_ positive _) difference between the strike prices.

The minimum payoff on a bull put spread is the (_ negative _) difference between the strike prices and the maximum is zero.

#11

Thanks Moosey and S2000magician. It sure is confusing :frowning:

Anyway, I found a site that can hopefully help others struggling with the topic. It is called theoptionsguide. You can look at the various payoff diagrams in there and it would talk about the max profits / loss.

#12

My pleasure.

#13

Thanks S2000, your description above was very clear.

#14

The easiest way to remember this is draw the payoffs but first keep few things in mind:

Bull --> means you expect ST (stock price) to go up

Bear --> you expect ST to go down

So in the case of Bull call Spread = Long call (XL) + Short call (XH)

  1. you want Long call exercise price to be low —> because you want it very close to the money so you exercise fast

  2. you want short call exercise price to be high --> you want it far from being in the money

now that you established this logic we can look at the payoff and you have 3 scenarios:

when ST < XL

when XL < ST < XH

when ST > XH

Long Call (XL) Short Call (XH) Premiums Payoff

Start with ST < XL not exercised so = 0 0 CH - CL 0 + 0 + CH - CL

XL < ST < XH ST - XL 0 CH - CL ST - XL + CH - CL

ST > XH ST - XL -(ST - XH) CH - CL XH - XL + CH - CL

Now:

Max Gain ( is when ST goes way high) ==> Max Gain = XH - XL + CH - CL

Max Loss ( Is when ST goes way low) ==> Max Loss = CH - CL

break-even price (is when payoff is equal to zero) ==> ST - XL + CH - CL = 0

ST = XL - CH + CL

i know it looks cumbersome but once you understood the logic above, all you have to do is draw the payoff table (period)

#15

Your last column is labeled incorrectly; it’s _ profit _, not payoff.

#16

Nicolas, thank you so much for this! This makes its so much more easy to remember.