BAC leverage

[Sunrider]

Hi Eric

 

Note that I said "given X" ... so given X USD - which is the basis of what your argument. I.e. you're starting by saying 'take 12 dollars invest it in BAC" or "take 12 dollars and invest it in a Leap ..."

 

So in both the LEAP and the warrant scenario the X will be gone - it's NOT about losing 2 on the LEAP or 5 on the warrant. You'll lose X dollars. Again, I'd have to mull this over a bit but I think structurally from your argument it will always have to come back to this. That is, you will have to make an assumption about a price by some expiration date and, further, you will have to assume that you are investing a fixed sum for which you wish to gain the maximum (i.e. cheapest) leverage.

 

 

Then you've completely misunderstood me.

 

Look, if you invest $12 in the warrant at $5.50 per warrant, then you have 2.18x leverage.  You own upside on 2.18 shares of common.

 

I'm simply saying that to purchase 2.18x leverage it's far cheaper leverage to go with the LEAPS.  Or go with a mixture of common+at-the-money LEAPS until you have 2.18x leverage of upside (equivalent to owning the upside on 2.18 shares of common).

 

I'm not saying go put the entire $12 into the LEAPS right now for 6x leverage with the 2-year LEAPS when the stock is priced at $12.  I'm not an effing idiot  ;D  That would be completely insane!

 

Again - I need to think through your reasoning carefully but the argument that you made, or the way I understood it, did start with take x amount to put at risk and then compare the options? May also relate to the way you define leverage here.

 

Note that I'm not saying that you're wrong to say the LEAPS are "cheaper" (quotation marks because I think cheaper also has to defined in a given context). I largely agree with that. All I'm saying/adding is that there is a good reason for it - that reason being that you're buying optionality for another 1 year 9 months or so vs. 6 years on the warrants. Hielko's point speaks to that as well. In comparing one to the other we do have path dependency since they have different time horizons - if they expired on the same date it would clearly be a very simple exercise. Since they don't, we need to make an assumption of what the stock price will be on the earlier expiration date and we can only make a statement about pro/cons and expensive/cheap in the context of that assumption. That's all I'm saying.

 

Put another way - if the path turns out to be that for whatever reason, BAC trades at 12 in Jan 2015 and you had 12 strike option then you may have been happier holding warrants instead.

 

I don't disagree that as the uncertainty "goes out of the stock" - i.e. ROE > 10% or whatever other measure we will see the warrant (and option) pricing adjust - I think I posted on that a very long time ago where I queried what people thought of the elevated IV in the warrants (>60% at the time, if memory serves ... so it's already come down a bit).

 

I think most people here believe that fundamentally BAC should rise from here and most people don't expect it to materially decline and stay low for two years - so in that scenario, and with enough comfort that the increase will be enough to pay for the time premium, the shorter term option will offer the better payoff/cheaper leverage, as per what you have said.

[Sunrider]

I disagree completely, and this has nothing to do with 'a traders mentality'.

 

You might be willing to hold the LEAP till maturity in 2015, but what's the value of the warrants at that point? You can't compare the 'cost of leverage' if you have no idea how valuable the warrant will be at that point in time. Or you might decide to buy new LEAPs, but how expensive will be rolling your position? You can't know that if you have no assumption on how the distribution of possible shares prices will look like and the probability of the various implied volatilities at that point in time.

 

What you are doing is making a comparison that makes absolutely no sense, sorry.

 

I think this is largely congruent with what I've been trying to say.

[Sunrider]

but I think what he's saying is that the warrants are "ahead" of the common in appreciation and at today's prices the common represents a better value than the warrants.

 

I'm not saying that exactly. 

 

I'm just shopping for cheaper leverage if I can find it.

 

Downside first should be the mantra.  Even when you use leverage, you should first think about the downside.

 

And the downside I'm thinking about with the cost of leverage in those warrants is that Black Scholes will kill off the value of their embedded puts when the stock reprices to "normalized earnings" once the expenses at BAC runoff over the next two years.

 

Ironically people keep thinking I'm missing something with regards to Black Scholes.

 

I fully understand the market relies on Black Scholes and that's why I'm staying the hell away from the warrants for now.  Once the market reprices the BAC common (in two years) I will look again at the warrants after Black Scholes reprices their leverage.

 

I don't see how it can be any more obvious -- Black Scholes relies on an efficient market... that reliance gets exposed by undervalued securities that reprice long before warrants expire.  So it's a bizarre case that value investors who don't believe in efficient markets would consider wading into the warrants for a stock they strongly believe to be undervalued. It's like a suicide mission of opportunity cost in the amount they are overpaying for their leverage in the years after the repricing of the common.

 

 

There seems to be quite a bit of emotion here now. Eric - note that I wasn't talking about Black Scholes, nor did I claim that the market was efficient. I'm actually making your 'business man's' argument - what could happen in the time frame and what's my pay-off. The only reason why I mentioned implied volatility is because that's a useful model to think in as well. You call it a cost of leverage, I see it as something built into the price to compensate for uncertainty. Whether the market prices this according to BS or not, I don't know. Whether that's an appropriate model, I don't really know either (I'd tend to say not but that's because I have a specific view on the underlying which is not part of an option pricing model like BS, which has to derive a value across all scenarios without favouring any which one).

 

What I would like to say is that the last bit of what you write above is dangerous. Very dangerous. You implicitly assume that undervaluation will correct in the market in a time frame that suits you. Then your argument is spot on - why pay for more optionality in time than you need? But if the market doesn't cooperate with you in repricing the security in the time frame that suits you, then you got a bit of a problem. Hence I'm saying it's dangerous - you still need to assume things work out the way you expect - otherwise your conclusion may be sub-optimal.

[zippy1]

Put another way - if the path turns out to be that for whatever reason, BAC trades at 12 in Jan 2015 and you had 12 strike option then you may have been happier holding warrants instead.

 

Surinder,

 

        I think what is missed here is that Eric has said that he isnot  comparing class A warrant against 2015 strike 12 call. 

 

        He is really comparing class A warrant against a combination of (BAC common+2015 strike 12 call). So if the stock price stay at 12 in Jan 2015, then the part of portfolio of 2015 call will expire worthlessly but the part withBAC common will still be worth 12 per share.

 

        His argument is both approaches are just ways to gain leverage but a combination of (BAC common+2015 strike 12 call) will be better due to the fact that he is not paying for the "leverage" for the years between 2015 and 2019.

[Sunrider]

Eric,

 

      I really appreciate that you took time to explain this.  I think it makes senses.  This is really any eye-opener for me. 

 

      I finally figured out what you meant on Thursday morning. For the part of my portfolio related to BAC, I restructured it into Jan 15 calls and common instead of class warrants on Thursday morning just in time before the stress test announcement. 

 

      Speaking of lucky timing, the Jan 15 $12 call did get a much bigger kick than the common and the common did get a bigger kick than the class A warrants.

 

        Thanks again for sharing your thoughts.

 

 

Guys,

 

Maybe Hielko and I are the one eyed or the blind or whatever here - but the above worries me a bit.

 

You do not need to assume any sort of Black Scholes magic to see why this behaviour makes sense:

 

The stock moves by a certain percentage, you compare that move to a near term option that is at the money or moving into the money. That option has to react more strongly as it works off a different base (2 dollars vs. 12 dollars - and you've just 'gotten above the threshold' ... in model speak, your delta has gotten much closer to one.

 

The warrant/longer term option doesn't react so fast - why? Well think about it, more time for things to go wrong (or right) - you don't know (unless you do have a view on the stock going to specific level in a specific time - but until such time you just don't know). So in model-speak, the longer term option has a lower gamma, resulting in less move of the delta AND it's not yet at its strike price.

 

What is very possible though, and I agree with Eric here (just that I can't get my head around his cost of leverage analogy) is that the warrant will reprice when the fundamentals clear up - and so it should. There's less uncertainty in the underlying so the market should rationally pay for less uncertainty in setting the warrant price. This -may- however be partially offset by a supply constraint in the warrant that may keep the price elevated (and thus the IV or cost of leverage).

 

 

(and Eric, I think it's also not fair to say that the market prices the warrants based on Black Scholes - especially with these and AIG I would not be surprised if a lot of the behaviour is demand/supply ... the latter a bit restricted perhaps because of Berkowitz et al rather than everyone looking at the model and setting the price there).

 

... just sayin'

 

C.

[zippy1]

Eric,

 

      I really appreciate that you took time to explain this.  I think it makes senses.  This is really any eye-opener for me. 

 

      I finally figured out what you meant on Thursday morning. For the part of my portfolio related to BAC, I restructured it into Jan 15 calls and common instead of class warrants on Thursday morning just in time before the stress test announcement. 

 

      Speaking of lucky timing, the Jan 15 $12 call did get a much bigger kick than the common and the common did get a bigger kick than the class A warrants.

 

        Thanks again for sharing your thoughts.

 

 

Guys,

 

Maybe Hielko and I are the one eyed or the blind or whatever here - but the above worries me a bit.

 

You do not need to assume any sort of Black Scholes magic to see why this behaviour makes sense:

 

The stock moves by a certain percentage, you compare that move to a near term option that is at the money or moving into the money. That option has to react more strongly as it works off a different base (2 dollars vs. 12 dollars - and you've just 'gotten above the threshold' ... in model speak, your delta has gotten much closer to one.

 

 

Sunrider,

 

        Longer date warrants at 6 years is not longer dated than common (being perpetual), are they?  The base of warrant being ~$5.5 is not larger than $12 of common, is it?

 

        So based on what you said, why did common move more than warrant?

 

        Just curious?!

[Hielko]

So how can you claim the X is cheaper than Y if you don't know the cost of X?

 

I do know the worst case cost of X over two years but I don't know the worst case cost of Y (and I'm going to be defensively minded and not take that risk!).  I've calculated "X" already in this thread.

 

Let X be the LEAPS -- over a two year period the leverage will cost me 10% annualized

Let Y be the Warrantss -- over a 6 year period the leverage will cost me 13% annualized

 

I know I can't do worse than 10% annualized if I go with the LEAPS.

 

I could take a gamble and hope that somehow the Warrants will decay at less than 13% annualized rate, but that's getting pretty damned hopeful.  Because if it decays at LESS than 13% rate, it only means the next 4 years will be a higher than 13% rate.  So operating on the greater fool theory, then yes go right ahead and hope you can sell those warrants for a higher cost of leverage in two years time.  Best of luck, because warrant holders are expecting the stock to rise (why else are they in this game?). 

 

Once the stock rises, it's going to crush the value of the leverage embedded in the put.

 

It's a terrible strategy for somebody who is expecting the stock to swing high to the upside (they have a strong opinion of present common stock undervaluation).

 

Black Scholes only understands that the market is efficient.

I have not said anywhere in this thread that Black and Scholes is the appropriate model to value options, and that it works for valueing options and warrants with a long maturity. In fact: I specifically stated that it is not suitable. That doesn't mean that you cannot learn anything from basic options theory. Theta (time) decay is not a linear function. Calculation the cost of leverage as a 13% annualized function for the warrants is fundamentally completely flawed!

 

This is how theta decay looks like:

 

http://optionalpha.com/wp-content/uploads/2010/11/Option-Theta-Time-Decay.jpg

And this is not the only thing about options that is not linear...

 

I fully understand the market relies on Black Scholes and that's why I'm staying the hell away from the warrants for now.  Once the market reprices the BAC common (in two years) I will look again at the warrants after Black Scholes reprices their leverage.

We are not living in 1980 anymore.

 

[Sunrider]

Put another way - if the path turns out to be that for whatever reason, BAC trades at 12 in Jan 2015 and you had 12 strike option then you may have been happier holding warrants instead.

 

Surinder,

 

        I think what is missed here is that Eric has said that he isnot  comparing class A warrant against 2015 strike 12 call. 

 

        He is really comparing class A warrant against a combination of (BAC common+2015 strike 12 call). So if the stock price stay at 12 in Jan 2015, then the part of portfolio of 2015 call will expire worthlessly but the part withBAC common will still be worth 12 per share.

 

        His argument is both approaches are just ways to gain leverage but a combination of (BAC common+2015 strike 12 call) will be better due to the fact that he is not paying for the "leverage" for the years between 2015 and 2019.

 

Hi Zippy

 

Thanks - I think this is an important point. As per my above posts I agree that -to that horizon- taking the LEAP is the cheaper way to go. What I am saying is that if I look at this as an investment with a certain downside and in the context of having a certain portfolio amount (or allocation) then I must consider not just the scenarios that I need to have come true but also the ones that I don't want to make that decision. So, let's say, we take the above and I'm still left with the common - that's cool, I've basically paid for the put in the LEAPS and I will have paid some value in the warrants for their puts (to use Eric's description).

 

Start with

(a) 12.57 + 2.57 so I'm long 2 shares

(b) 2 x 5.50 so I'm also long 2 shares with 4.02 in cash left over; assume cash earns nothing for the next 2 years

 

We get to Jan 2015

Good scenario - stock at 20:

(a) 20 - 12.57 + 8-2.57= 12.98

(b) 4.02 + (20- 13.3 - 5.5)x2 = 4.02 + 2.4 = 6.42 + remaining value in the warrants (<- and this is what Eric debates, saying it will have a proportionally much lower value than what we see at the moment because uncertainty has been reduced)

 

Bad scenario - stock at 11.99:

(a) 11.99 + 0 = 11.99

(b) 4.02 + 2 x 5.5 = 15.02 (<- there's an assumption here that time decay doesn't matter much or is offset by some increase in uncertainty, however, you see that you can assume a loss in warrant value of 1.51, going back down to 4, to be in the same situation as in (a)

 

Right - so I hope I didn't mess up any numbers so far. This basically just shows what we intuitively know to be true: If we have a good scenario then we're better off with short term options so that we don't pay for the optionality of stuff happening after our cut-off. You can call this "cheapness". If we're in not such a good scenario then we've lost a little more (given assumptions above, which one can debate) because we refused to pay for said optionality. You could, of course, say that you can then rinse and repeat in both scenarios (well only for a really because in b you don't need to do anything). So say the unlikely happens and we sit at 12 in four year's time, with the same sort of parameters you would've lost another 2, etc.

 

Now let's say I want to not compare on an "equal leverage" basis but on a risk/return for money invested (as per above, some amount of money/portion of portfolio invested in BAC) - again let's start as above:

(a) 12.54 + 2.45 = 15.02 total invested for long 2 shares

(b) 15.02/5.5 = 2.73 shares long (i.e. more leverage, clearly)

 

Good scenario (20):

(a) as above

(b) (20-13.30-5.50)x2.73 = 3.276 pay-off + TV remaining in warrants (we could ask ourselves how much TV there would have to be to put us in an equal position: 12.98 - 3.276 = 9.704 / 2.73 = 3.55. So with warrants repricing no lower than 3.55 at that LEAP expiry date we'd be in the same position).

© 15.02/2.45 = 6.13 shares long (i.e. all LEAPS)

 

Bad scenario (11.99):

(a) as above, 11.99

(b) 2.73 x warrant price at that date. Using Eric's sensible argument that the warrant price should come down as the market refuses to pay for leverage (or as I would say for uncertainty) and turning it around in that it will not reduce the price if there is remaining uncertainty, I'd say that I would expect the warrants to trade right about where they trade now, ignoring loss of time value. (i.e. we'd be in a 11.99 scenario only if uncertainty remains, earnings don't normalise, etc.). So if that's the case, with warrants trading at 5.5, we'd be back where we started. For us to end up with the same value as in (a) warrants could be re-priced down to 15.02-11.99=3.03, divide by 2.73 warrants gives about 1.10, so could reprice down to about 4.4.

© you're dead and lost the 15.02.

 

By the way, the assumptions around the warrant pricing at LEAP expiry above, are in my view, reasonable - but happy to debate it. In any event, it comes back to the point Hielko made previously that there is path dependence - because we are comparing options across different dates of expiry. To make a statement about pay-offs or cheapness we need to assume a price at a date.

 

This has become rather long but I thought I'd spell it out with numbers and I hope I covered all the potential scenarios and starting points. All I've been trying to say - and what the above shows - is that if you are certain that BAC will be above 15.02 in Jan 2015 then LEAPS or LEAPS + common would be a better way to go. If you have a queasy feeling in your stomach that there is a sufficient chance of BAC trading below 11.99 then adjust the above preference to some other mix (more common, less LEAPS or more warrants). What I tried to say in my original post is that this MUST be so in all but a completely dysfunctional market and, further, that the strategy proposed does make sense largely under the set of scenarios that sees BAC above strike + option cost. If you believe in that then of course you should not pay for optionality beyond LEAP expiry. In fact you should then go all-in on the LEAPS. This is perfectly rational given the assumption - it implies BAC has made good progress, etc. etc.

 

Call this a cost of leverage or cost of optionality that you are paying (or not paying) - the results, I think, are the same and the arguments largely parallel.

 

So for those who are horribly confused by options, Black Scholes, etc. and find Eric's cost of leverage analogy more intuitive: by all means go with that one - it's right. Just be aware that you still need the market to cooperate with you. How much damage is done when it doesn't will - quite intuitively - come back to how much leverage you have taken on. The only complication being that you have a choice of decreasing risk (at a cost, of course) by choosing the warrants. It is not possible to make a statement about whether the warrants are more expensive than the LEAPS (or any sort of combinations), without assuming a stock price at the LEAP expiry. (Sadly.) :)

 

Hielko - would you agree with the above?

 

Cheers - C.

 

P.S.: I'm pretty sure I mucked up a calculation or number somewhere but I hope the gist of the argument/demonstration is clear :)

P.P.S.: By "right" above re cost of leverage analogy I mean that it gives directionally the right answer in this specific case and under the assumptions made - not that it's the right answer/approach in all cases, scenarios, assumptions, etc.

 

 

[Sunrider]

Eric,

 

      I really appreciate that you took time to explain this.  I think it makes senses.  This is really any eye-opener for me. 

 

      I finally figured out what you meant on Thursday morning. For the part of my portfolio related to BAC, I restructured it into Jan 15 calls and common instead of class warrants on Thursday morning just in time before the stress test announcement. 

 

      Speaking of lucky timing, the Jan 15 $12 call did get a much bigger kick than the common and the common did get a bigger kick than the class A warrants.

 

        Thanks again for sharing your thoughts.

 

 

Guys,

 

Maybe Hielko and I are the one eyed or the blind or whatever here - but the above worries me a bit.

 

You do not need to assume any sort of Black Scholes magic to see why this behaviour makes sense:

 

The stock moves by a certain percentage, you compare that move to a near term option that is at the money or moving into the money. That option has to react more strongly as it works off a different base (2 dollars vs. 12 dollars - and you've just 'gotten above the threshold' ... in model speak, your delta has gotten much closer to one.

 

 

Sunrider,

 

        Longer date warrants at 6 years is not longer dated than common (being perpetual), are they?  The base of warrant being ~$5.5 is not larger than $12 of common, is it?

 

        So based on what you said, why did common move more than warrant?

 

        Just curious?!

 

Yes ... but no optionality in the common.

 

Or alternatively: the common stock's delta is already 1 and that will not change.

 

As per Hielko's other post - pretty much nothing here will behave linearly (whether you consider this in a context of a model or just intuitively ... well unless you - personally - believe that uncertainty itself is a linear 'thing'). Of course there's one exception: the common will behave linearly ;-) but we knew that already.

 

Cheers C.

 

 

[Hielko]

Hielko - would you agree with the above?

Conceptually I agree with the fact that we have to consider different possible paths :). But there are many more possible scenario's that also matter. Options are unfortunately not easy...

 

Quick remark:

 

We get to Jan 2015

Good scenario - stock at 20:

(a) 20 - 12.57 + 8-2.57= 12.98

(b) 4.02 + (20- 13.3 - 5.5)x2 = 4.02 + 2.4 = 6.42 + remaining value in the warrants (<- and this is what Eric debates, saying it will have a proportionally much lower value than what we see at the moment because uncertainty has been reduced)

If the stock price will be up a lot on Jan 2015 Eric is right that the warrants will have lost of lot of extrinsic value, there is not a lot of optionality left when options/warrants are deep in the money. The big difference is of course that the warrants can do well in the end even when the share price isn't doing well on Jan 2015.

[writser]

I have to agree with the minority here. Option payouts are not linear (just look at their payout graph). Ericopoly's calculations for calculating the cost of leverage assume linearity. Hence these calculations make no sense and should not be used to guide your investment approach. I'm not saying Black Scholes is the holy grail but it's a better tool for valuing options than comparing buying stock to buying stock on margin. If this wasn't the case then why isn't everybody using these back-of-the-envelope calculations to arb the US option market? Things like volatility term structure and volatility smiles are no imaginary constructs and they should not be ignored.

 

And the worst thing about this topic is that, even though the strategy delivers extremely satisfying results to Eric,  it might give inexperienced investors a reason to believe that you can make 50% per annum by trading in and out of options. Truth is that that is mostly a fool's game where the money is made by the market makers, brokers and arbitrageurs. If WEB was on this board he would not participate in this thread, he'd be looking at all investment topics and that's what we should do as well imo.

 

My 2 ct.

[ERICOPOLY]

If the stock price will be up a lot on Jan 2015 Eric is right that the warrants will have lost of lot of extrinsic value, there is not a lot of optionality left when options/warrants are deep in the money.

 

And this risk is unnecessary is my point.  We can instead contain the cost of premium decay to no more than 10% annualized cost of leverage by going with the LEAPS.

 

Risk control!  We can alternatively hope that the warrants cost more than 13% annualized for the leverage in 2015, but that is the game of the greater fool (per Greater Fool's Theory).  So you are engaging in that game if you think the warrants are the way to go because they have a shot of costing less than the options over the first two years.  Okay, let's take the chance!  Why???

 

That's a game I'm not even going to consider playing with options.  You might get lucky, but do you feel lucky?

 

 

The big difference is of course that the warrants can do well in the end even when the share price isn't doing well on Jan 2015.

 

Again, it's relative to what we know costs only 10% per annum in decay.  The question isn't if they'll make money in the end, or if they'll beat the common in the end...  the question is if they'll beat the alternative forms of leverage in the end.

 

And once again, they are more risky in the first place because you have to put more money on the table to get the same amount of leverage.  What if the common is only priced at $5 in two years?

 

[ERICOPOLY]

Option payouts are not linear (just look at their payout graph). Ericopoly's calculations for calculating the cost of leverage assume linearity.

 

Look, I'm making an assumption that the warrants will decay at 13% annualized -- yes, that's linearity.

 

Presumably you claim this is unfair and that maybe they'll only decay at 7% annualized for the first two years.

 

Okay, then think about this... if that's true, then for the remaining 4 years the embedded cost of leverage is even higher than the 13% that it is today.

 

This is the Greater Fool's Theory game.  Don't worry if it's expensive -- perhaps we can sell it (the premium cost of years 3-6) to somebody for even more down the road!!!

 

It's outside of my DNA to think of that kind of outcome as the reason why we should pick the warrants over the LEAPS.

 

But that's your only rebuttal to my "linear thinking" and from this you conclude the calculations "make no sense and should not be used to guide your investment approach". 

 

[Sunrider]

If the stock price will be up a lot on Jan 2015 Eric is right that the warrants will have lost of lot of extrinsic value, there is not a lot of optionality left when options/warrants are deep in the money.

 

And this risk is unnecessary is my point.  We can instead contain the cost of premium decay to no more than 10% annualized cost of leverage by going with the LEAPS.

 

Risk control!  We can alternatively hope that the warrants cost more than 13% annualized for the leverage in 2015, but that is the game of the greater fool (per Greater Fool's Theory).  So you are engaging in that game if you think the warrants are the way to go because they have a shot of costing less than the options over the first two years.  Okay, let's take the chance!  Why???

 

No no no. :) That's not at all the argument - it's not about them having a shot at 'costing' less than options 'over the first two years', it's about the fact that you may kill yourself in those two years and not live to fight another day! I think we're pretty much all agreed here that if we were 100% certain that BAC would trade at above strike + cost of LEAP at LEAP expiration we'd be all-in on the LEAPS, not the warrants. Trouble is, whilst I hope that will be the case, I don't know if it will and I can only put a subjective probability on that outcome.

 

Oh and I feel lucky most days! (Because I'm here, not with respect to the market.)

 

Re your point about trading at 5 - yes, if that's the case then you lose in a constellations - but the value you invested in the warrants will have not declined proportionally the same was as that value invested in the options, and you still have four years left for Mr. Market to come to his senses.

 

It's not about saying warrants are the way to go - only each person can make that call for themselves. And they can only make that call under an assumed price at LEAP expiration (if that's the alternative) or at warrant expiration AND the path taken by the stock price between LEAP and warrant expiration (if you assume rolls).

 

Cheers.

 

 

[ERICOPOLY]

No no no. :) That's not at all the argument - it's not about them having a shot at 'costing' less than options 'over the first two years', it's about the fact that you may kill yourself in those two years and not live to fight another day!

 

The worst case is the 10% cost of leverage decay over two years.

 

So if that means "kill yourself", then you are risking much more decay in the warrants.  So are you going to take a Post Office with you on your way out of this life if that happens?

 

[zippy1]

Sunrider,

 

          Thank you for a nice and detailed explanation. 

          Thinking through these "scenarios" are quite interesting.  I used to do Monte Carlo years ago.  One day when I retire I should get into this more.

 

 

 

          best regards,

 

          Zippy.

[ERICOPOLY]

 

Start with

(a) 12.57 + 2.57 so I'm long 2 shares

(b) 2 x 5.50 so I'm also long 2 shares with 4.02 in cash left over; assume cash earns nothing for the next 2 years

 

 

You are comparing "ALL IN" strategy to one where a lot of cash is not even invested.

 

I believe a more fair comparison would be:

 

(a)  2.57x2 with $10 in cash left over so I'm long 2 shares

(b)  5.50x2 with $4.02 in cash left over so I'm long 2 shares

 

There, now that both strategies each have a put per share, we can compare them.

 

After all, if you've already made a decision to hedge each share of upside (in order to leave cash on side), it's only a matter now of deciding how we can contain the cost of leverage.

 

 

(also, it's 5.69 cost of the warrant today at yesterday's close.  you've updated the cost of the $12 call since this discussion began when it was $2.10 and was at-the-money.  It's now slightly in the money, and the warrant costs a bit more now.  It's 5.69 now.)

 

 

 

 

 

 

[Sunrider]

No no no. :) That's not at all the argument - it's not about them having a shot at 'costing' less than options 'over the first two years', it's about the fact that you may kill yourself in those two years and not live to fight another day!

 

The worst case is the 10% cost of leverage decay over two years.

 

So if that means "kill yourself", then you are risking much more decay in the warrants.  So are you going to take a Post Office with you on your way out of this life if that happens?

 

Sorry - I don't understand the post office metaphor?

 

I think we just have different views/things we're focussing on. If I chose to put some money in LEAPS vs. some money in Warrants then the worst that can happen is that I lose all of the money in the LEAPS and some money in the warrants. The proportional loss will be smaller in the warrants (easy, since you're comparing against a 100% loss in the LEAPS). And there's nothing magical to any of this - you either pay up for more optionality or you don't. Whether the markup for more optionality is justified can only be determined ex-post facto, once we know which scenario occurred. Before that we can pick a price at a point in time and figure out what's cheaper or not if that price materialises. To make this a fair comparison, we'd have to roll forward our assumption and play the game a few times until we match the warrant expiration date with our option rolls.  Adding stock to either of these will change the numbers but not that principle. As I said, if you're 100% sure of the stock going up then the choice is clear, no argument to be had.

 

 

[Sunrider]

 

Start with

(a) 12.57 + 2.57 so I'm long 2 shares

(b) 2 x 5.50 so I'm also long 2 shares with 4.02 in cash left over; assume cash earns nothing for the next 2 years

 

 

You are comparing "ALL IN" strategy to one where a lot of cash is not even invested.

 

I believe a more fair comparison would be:

 

(a)  2.57x2 with $10 in cash left over so I'm long 2 shares

(b)  5.50x2 with $4.02 in cash left over so I'm long 2 shares

 

There, now that both strategies each have a put per share, we can compare them.

 

After all, if you've already made a decision to hedge each share of upside (in order to leave cash on side), it's only a matter now of deciding how we can contain the cost of leverage.

 

 

(also, it's 5.69 cost of the warrant today at yesterday's close.  you've updated the cost of the $12 call since this discussion began when it was $2.10 and was at-the-money.  It's now slightly in the money, and the warrant costs a bit more now.  It's 5.69 now.)

 

Ok, fair enough - so we'd change (a) to 2x2.57 and 10 in cash

 

Good scenario (20):

(a) 10+(8-2.57)x2 = 20.86

(b) as before, so less than above and assumption about market value of warrants required

 

Bad scenario (11.99)

(a) 10 + 0 = 10

(b) as before, also an assumption of the market value required, but likely that uncertainty will not have subsided and thus 'cost of leverage' remains elevated.

 

Either way - if you're right on the upside you win more with the LEAPS (both because you pay for less optionality so your cost base is lower = more leverage and because you risk re-pricing to the downside for the warrants as uncertainty subsides). If you're wrong on the upside (and depending on how wrong), you will likely be happier with the warrants as are much less likely to have re-priced to the downside.

 

There's no magic bullet. There's no solution that gives an optimal trade-off in all scenarios. You have to craft your strategy according to your beliefs. You believe BAC will be substantially higher than today - so you chose the LEAPS (and that makes absolute sense). Someone else believes that there is also some chance that BAC will remain at this level or decline a bit before increasing substantially as earnings normalise in, perhaps, 2015/16, consequently they may be happier having some exposure to 2015 through LEAPS (or common or both) and some exposure to the period after that.

 

Cheerio.

 

C.

[Sunrider]

Put another way - the conversation of where do I find the cheapest form of leverage only makes sense once you've picked the scenario (price by expiry and/or price path from here to warrant expiry). If that scenario then does not play out, you will have likely chosen a sub-optimal composition for your portfolio given the scenario that is actually realised.

 

Another poster made a good point - you've done well for yourself with the option trading. Congratulations. Why did you do well? Not because you chose the cheapest form of leverage. You did well because you called the movement of the underlying correctly. For this I very much congratulate you. I've not been as right in making the calls on the price movement so I'm looking for some measure of robustness in my allocation decisions - as I said above, all a very personal choice at the end of the day.

 

C.

 

Edit: Sorry - to be very clear - the above is not in any way tongue-in-cheek or cynical, etc. I really do congratulate you on your success.

[ERICOPOLY]

No no no. :) That's not at all the argument - it's not about them having a shot at 'costing' less than options 'over the first two years', it's about the fact that you may kill yourself in those two years and not live to fight another day!

 

The worst case is the 10% cost of leverage decay over two years.

 

So if that means "kill yourself", then you are risking much more decay in the warrants.  So are you going to take a Post Office with you on your way out of this life if that happens?

 

Sorry - I don't understand the post office metaphor?

 

I think we just have different views/things we're focussing on. If I chose to put some money in LEAPS vs. some money in Warrants then the worst that can happen is that I lose all of the money in the LEAPS and some money in the warrants. The proportional loss will be smaller in the warrants (easy, since you're comparing against a 100% loss in the LEAPS). And there's nothing magical to any of this - you either pay up for more optionality or you don't. Whether the markup for more optionality is justified can only be determined ex-post facto, once we know which scenario occurred. Before that we can pick a price at a point in time and figure out what's cheaper or not if that price materialises. To make this a fair comparison, we'd have to roll forward our assumption and play the game a few times until we match the warrant expiration date with our option rolls.  Adding stock to either of these will change the numbers but not that principle. As I said, if you're 100% sure of the stock going up then the choice is clear, no argument to be had.

 

Regarding the post office metaphor:

People "go postal" in America -- they walk into a Post Office and shoot the postal workers, then they shoot themselves. 

 

Losing 100% of the options is okay because we're prepared to lose it.  We know upfront what we're losing. 

 

The only way that feels relatively more painful than with the warrants is if the warrants decline by a lesser absolute dollar value.  But if the warrants decline by a lesser absolute dollar value, then by definition the remaining time value in the warrant is rising in cost of leverage per annum.  So once again, if that's the plan and that's the reason for going with the warrant, then it's the greater fool theory at work! 

 

And the warrants of course can decline by a larger dollar value over two years than the options.

 

Your argument sounds a bit like saying I ate 100% of my slice of pizza but you only ate 10% of your entire pizza.  Thus, I ate more pizza than you because 100% is greater than 10%.

[no_free_lunch]

If WEB was on this board he would not participate in this thread, he'd be looking at all investment topics and that's what we should do as well imo.

 

+1 well said.

[writser]

Ericopoly , in the worst case is that there is another 2009-style crisis in 2015, all your $12 calls expire worthless and immediately afterwards the stock rises back to 50. In which case the guy with the warrants will be far, far, far better off. The fact that you have this extra 'optionality' in the warrants means that they should always trade at a premium. Your model ignores this possibility (and I get the feeling that you do not worry about it either) and thus you end up buying short term at the money calls because these have the lowest implied volatility. In English: these are the cheapest options because they are the easiest to price and the least risky to sell (and thus the riskiest to buy).

 

Imho, this has nothing to do with 'playing the fool's game'. The options market has evolved to transfer risks between market participants. I think that your pricing model ignores risk completely and that you confuse it with the cost of leverage. So when you say you swapped into an option position with a lower cost of leverage, you actually just bought a cheaper option portfolio that sets you up to get screwed when something strange happens like in 2009.

 

So yeah, pretty much what Sunrider said (but he was much more to the point and much faster).

[ERICOPOLY]

Either way - if you're right on the upside you win more with the LEAPS (both because you pay for less optionality so your cost base is lower = more leverage and because you risk re-pricing to the downside for the warrants as uncertainty subsides).

 

The cost base being lower does not equal more leverage.

 

1 warrant is 1x leverage

1 LEAP is 1x leverage

 

The businessman thinks about how many shares of upside he wants.  When he decides it's more than he can afford with buying straight common on cash, he then things about how to finance the leverage.

 

So if he wants 1.5x leverage, he scratches his head and puts pen to paper to decide whether the leverage is cheaper by mixing warrants and common, or mixing LEAPS and common.

 

 

[writser]

the intelligent investor would also worry about margin calls (in case he would lever up without options) and the possibility of permanent loss of capital because his derivatives positions expire worthless.