BAC leverage

[ERICOPOLY]

I may be looking at this the wrong way - but I am getting a 2-year option leverage cost that is a bit above the warrants. 

 

25 is the warrant-common break-even - ignoring the dividend readjustment but also ignoring dividends on the common - which is probably the right way to look at it (the readjustments should cancel each other out).  That implies an annualized cost of leverage of about 13%.

 

The two-year option at $2.10, ignoring dividends, gives you a 10% cost of leverage.  But the two-year options don't benefit from the dividend adjustment.  So the leverage cost of the options is 10% plus lost dividends over the next two years.

 

If you wanted to make an apples-apples comparison, one could use the post-adjustment strike and shares/warrant and compare that to the options.  Guessing at an $11 strike and 1.2 shares/warrant I get a break-even at $19 versus the common stock - implying a leverage cost of 8% plus lost dividends over the next 6 years (stock price at 12.06, warrant price at 5.54 as write).

 

Now of course we don't expect the bulk of the capital return in the next two years - so the 2015 options look ok in that regard.  But unless I am way off, the warrants look a little cheaper than the options.

 

EDIT: since you're paying for dividend protection up front, options could be cheaper over the next two years since serious dividends won't kick in until later.

 

Is this totally wrong?

 

 

Put it this way...

 

If $2.10 is the cost of the 2015 $12 strike call at a cost of leverage rate of 10% annualized, then at a 13% rate it would cost what... roughly 60 cents more (I'm not being exact, just winging it after 4 drinks in Death Valley and no calculator).

 

I have 60 cents of cash still in my pocket from paying a 10% rate instead of a 13% rate.

 

So I decide to invest that 60 cents in the stock at $12 per share.

 

Call it... a certain dividend that I get paid upfront.

 

Meanwhile, other people buying the warrants are implicitly speculating that the dividend over the next two years will exceed 60 cents.  So confident are they that they are paying the 60 cents upfront, hoping to get a dividend that exceeds 60 cents.  They'll lose money on that if it comes in below 60 cents (cumulatively over two years).

 

But it's better.  My way, I'm investing my 60 cents into the stock at $12 per share.

 

The warrant holder?  Maybe a some of the dividend gets invested at $12, maybe some at $15, maybe a good chunk of the 2nd year dividend gets invested at $18.

 

Hmm...  a 45 cent dividend invested at $18 is no better than a 30 cent dividend at $12.

 

Does anyone really want to throw away a certain 60 cents dividend reinvested at $12 today just to gamble on a bigger dividend that will probably get invested at a much higher price? 

 

So yes, the warrants ostensibly have "dividend protection" -- me, since I have the calls at 10% cost of leverage I have that approximate 60 cent dividend already invested in the stock at $12.

 

 

 

 

[ERICOPOLY]

Sorry, I know we have a new thread, but I just wanted throw my 2 cents in here.

 

I couldn't really follow Eric's idea about the 13% as the cost of borrowing, so I thought about it a different way, that seems to make sense to me, would like to hear your thoughts.

 

When you buy a warrant, you're essentially paying the premium $5.65 and the present value of the $1.30 difference between the strike and the current price ($13.30 strike minus $12.00 current price). So the total cost is somewhere around $6.85. This cost allows you to borrow the $12.00 (that you would have otherwise needed to pay to purchase the stock) for 5.8 years, which works out to around a 10% borrowing cost.

 

 

We all agree that if we are to tread water (for no net gain nor net loss) on borrowed money, the investment must compound at the rate at which interest is paid.  Right?

 

So if you have borrowed money at 13%, in order to break even you must have your asset compound at a 13% rate.

 

Well, keeping that in mind, first figure out the point where the BAC common and the BAC warrant wind up the same.  The breakeven point where one is no better than the other is $25.  Given that one is no better than the other, then at that point the asset must have compounded at the rate of borrowed money.

 

And $12 (today's common stock price) compounds at 13% rate for 6 years in order to reach $25.

 

 

[ERICOPOLY]

Plus, don't forget for you US taxpayers, they'll tax you on your warrant dividend adjustments even though it's a "cashless" dividend.

 

My (approximate) 60 cent "dividend" is tax-free.  That's worth a lot more than 60 cents in a California taxable account.

 

[meiroy]

 

Ericopoly,

 

1. You mentioned that you also prefer the AIG warrants which come at a lower cost (~8%)? In this sense, the WFC warrants are under 6% (5.75%?), wouldn't that make it an even better choice?

 

2. What if we use the leftover cash to leverage again and buy another warrant instead of buying the common?

 

3. Some brokers allow the purchase of TARP warrants in non-margin accounts.

[ERICOPOLY]

 

Ericopoly,

 

1. You mentioned that you also prefer the AIG warrants which come at a lower cost (~8%)? In this sense, the WFC warrants are under 6% (5.75%?), wouldn't that make it an even better choice?

 

2. What if we use the leftover cash to leverage again and buy another warrant instead of buying the common?

 

3. Some brokers allow the purchase of TARP warrants in non-margin accounts.

 

1.  I own the AIG warrants -- 8% seems reasonable cost for non-recourse leverage.  I look at the notional value of my total portfolio and would rather take on the leverage where it's cheaper.  So if I wanted to hold both AIG and BAC, and I wanted leverage, I'd juggle it so the leverage lies in the warrants that have lower cost.  What matters in the end is total portfolio leverage, so use the leverage where it's cheaper.  You mention WFC warrants being cheaper still, but I'm not invested in WFC.  Thing is, WFC is cheaper leverage because it has less (market believes) upside.  Same reason why I'm saying the BAC borrowing costs embedded within the warrant will drop like a stone as BAC approaches $20.  This will happen when the earnings normalize and uncertainty is lifted.  So why fight that headwind!!!  Today BAC is just below tangible book and they might earn 13%-15% on tangible book, as well as a premium to tangible book based on that coming out to 10x P/E.  So people are willing to pay a higher price for leverage.  Once it's at P/E of 10x normalized earnings and potential gains above 10% annualized in the common are difficult, then nobody (I assume) will want to leverage at 13% cost.  The people who pay 13% annualized today for all 6 years will be pissing fire when they realize they paid 13% annualized for years 3,4,5, and 6 but the market only wants to pay 10%, or maybe only 8% -- all because the stock went up which is what they were hoping for.  Be careful what you wish for, I guess.

 

2.  The break-even point is still $25 -- so it still costs you 13% annualized for the leverage.  Only... now you have more leverage.  What happens if I buy two calls for $2 apiece for a total outlay of $4?  Same story...  the leverage in the calls still costs me 10% annualized no matter how much I leverage it (same with the warrants).  You can't change the cost of the loan by borrowing more!  You just have more risk for more potential gain.  Works great if the stock (dividends included) compounds more than 13% annualized... otherwise, maybe not so good.

 

3.  Yes.  A RothIRA is a non-margin account and I currently hold AIG warrants there (and just sold my BAC warrants there).  But I also hold my BAC calls there.  Why did you raise this point?  Were you not realizing that you can hold options in cash-only accounts?

 

 

 

[meiroy]

 

1. Do you recall what was the cost of the BAC warrants when you first bought them?

 

3. Right, sorry. Meant cash-only no-options-allowed accounts. 

 

 

[ERICOPOLY]

 

1. Do you recall what was the cost of the BAC warrants when you first bought them?

 

 

Stock was $9.30, warrants were $3.70.

 

9.30 - 3.70 = 5.60

 

13.30 / 5.60 = 2.375

 

So about 13.7% annualized over 6.25 years.

 

 

[ERICOPOLY]

And at a price of $9.30, the normalized earnings yield ($1.60 earnings at 13% ROTE) was 17.2%.  I was borrowing at 13.7% to get a normalized earnings yield of 17.2% -- a spread of 3.9%.

 

Today (at $12 stock price) that same yield is 13.3%, but cost of leverage is 13%.  So spread is now only 0.3%.

 

Prospects are nowhere near as good. 

 

And who, I ask again, will keep paying 13% when the earnings yield is only 10% (at $16 stock price)?  Hmm?  This is not even to mention that by this time much of the speculative gains will have been realized (going from $9.30 or from $12 to $16 is a great tailwind).  What tailwind will be left?

 

Yes, we could do this argument with a higher ROTE (like 15% or 18%), but the same story remains -- at some point the stock hits a point where it trades at normalized earnings and you won't be able to sell your leverage at 13% cost anymore.

 

 

[ERICOPOLY]

History lesson.

 

When the stock was $5 in December 2011, the warrants sold for $2.

 

When I purchased the warrants for $3.70 in October 2012, the stock was $9.30.

 

So the stock had risen 86% since the $5 bottom, but the warrants had only risen 85%.

 

No advantage whatsoever from the warrants during those first 10 months if you held and didn't trade them up to that point.  This is because the cost of leverage tanked over that period.

 

Then when I bought the warrants at $3.70 I made a 52% gain during my holding period during a period when the common went up only 29%. 

 

Better lucky than good I suppose.

 

 

[ERICOPOLY]

Also, it seems funny that some people won't buy BAC because they question whether the bank can earn 13% ROTE.  I find this funny because of the following:

 

A shareholder can earn 13% annualized for 6 years if they put on the following trade:

1) Purchase BAC common

2)  Short the A warrant

 

That's a trade:

A)  gives you max downside of owning the common stock at roughly $6.60 cost

B)  Earns you 13% annualized yield for the next 6 years.

 

You only need the stock to trade above $13.30 in six years in order to get your full 13% annualized.  You'll make less if the stock is below $13.30 in 2019.

 

Anyways, BAC at $6.60 cost isn't risk-free, but I'm still surprised it's worth 13% annualized.

 

Translation:  you can lend money at 13% rate for 6 years (fixed rate and fixed term) -- your downside risk is if BAC tanks below a cost of $6.60 and you only get paid in full if the stock is above $13.30 in six years.

 

 

(ahhh... didn't check the cost of borrowing a warrant, whatever that may be).

 

[meiroy]

 

 

If you're expecting a rising interest environment, isn't it an advantage to pay that "fixed interest" in advance for the next 6 years (even better for the AIG warrants)?  For the options, were you to roll them, wouldn't the cost rise with higher interest?

 

 

[ERICOPOLY]

 

 

If you're expecting a rising interest environment, isn't it an advantage to pay that "fixed interest" in advance for the next 6 years (even better for the AIG warrants)?  For the options, were you to roll them, wouldn't the cost rise with higher interest?

 

So you want to leverage at a 13% fixed rate into market that could be spooked by rising rates?  Takes balls.  No thanks for me.

 

This is why I'm saying just take a "wait and see" approach.  Go with a 2 year term and be flexible.

 

Maybe we do in fact have a wicked recession matched with rising rates -- the company might be boosting loan loss provisions, taking hits from sudden rise in interest rates, and maybe... more legal reserve increases.

 

Yet people have the balls to presume that none of that matters... let's just lockup the leverage for 6 years because nothing can go wrong.

 

Again, wait and see.  Caution.  Fools rush in (no, I"m not calling you guys fools, it's just a saying).

 

 

[meiroy]

 

Well, I'm starting to think all these TARP warrants are worthless considering the risk. Why not just use 2 year LEAPS and roll them forward every year? What is the advantage of the AIG warrants for example?

 

[ERICOPOLY]

So, question:

 

Can you lend out your warrant to short sellers for lending income?  You can do this with common stock, but can you do it with warrants?

 

See my comment above about purchasing the common stock and shorting the warrant for 13% annualized yield but only $6.60 per share downside.  Only works out that way if:

A)  no lending fees for borrowing the warrant

B)  stock above $13.30 in six years.

[ERICOPOLY]

 

Well, I'm starting to think all these TARP warrants are worthless considering the risk. Why not just use 2 year LEAPS and roll them forward every year? What is the advantage of the AIG warrants for example?

 

I'm thinking about it regarding the AIG warrants as well.  I have the warrants in my RothIRA but the LEAPS might possibly be better (haven't yet done the math though).

 

[actuary]

Sorry if this is beating a dead horse at this point.

 

Maybe I'm missing something, but I'm surprised no one has mentioned borrowing constraints when talking about the cost of leverage.

 

Eric, I understand how you're calculating the financing cost figure. Said one way: Suppose I have enough cash to buy one warrant. I could alternatively buy a synthetic warrant by purchasing one share and one put option with a $13.30 strike using my cash and a margin loan with FV equal to the strike. Ignoring margin calls and taxes, these two will have the same ultimate payoff assuming you reinvest dividends in the synthetic version.

 

I believe your previous cost of leverage numbers have assumed the put option mentioned above costs nothing. Okay, let's just go with that for now. Then using $12 stock price, $13.30 strike, 6 years till exp, etc: Assuming we can borrow at 13% would imply a $5.60 warrant price, assuming 10% gives $4.50, etc. That matches your numbers. But, Eric, what if we can borrow at 1%?? Using the same approach, that would imply a negative warrant price!

 

So it seems like this measure of cost of leverage is really mischaracterizing something. Well, as SJ pointed out, there's the cost of the put option that we ignored. But, even if we accept hand-waiving there (i.e. both accounts are bankrupt if the stock ends lower than the strike, so there's no need to buy a put in the synthetic version), we also need to consider borrowing constraints for the synthetic version. Namely, suppose I have $3 and that's where the warrant trades. The typical broker is not going to let me borrow $9 to buy 1 share. So there's a constraint that would prevent me from even creating the full synthetic warrant in that case.

 

To calculate an implied margin rate, we now need to make assumptions about the borrowing constraint and the underlying price distribution at expiration. I've attached a simple spreadsheet to illustrate. The bottom line is that it looks like the simpler approach severely overestimates the premium that would come out of the warrants due to a much lower implied borrowing cost... even before considering the embedded put.

 

I own a mix of common and warrants and don't intend to pay short term cap gains on any of it. Would agree with swapping warrants for common at this point in tax-free accounts, but you really run into borrowing constraints there. Looks like you've gotten around that with options, though.

 

Not trying to be confrontational, just enjoyed thinking about this yesterday. Please poke holes if you're not tired of the subject. I always appreciate your posts. Following you has made me a lot of money.

doodle_wt.xlsx

[ERICOPOLY]

Sorry if this is beating a dead horse at this point.

 

Maybe I'm missing something, but I'm surprised no one has mentioned borrowing constraints when talking about the cost of leverage.

 

Eric, I understand how you're calculating the financing cost figure. Said one way: Suppose I have enough cash to buy one warrant. I could alternatively buy a synthetic warrant by purchasing one share and one put option with a $13.30 strike using my cash and a margin loan with FV equal to the strike. Ignoring margin calls and taxes, these two will have the same ultimate payoff assuming you reinvest dividends in the synthetic version.

 

I believe your previous cost of leverage numbers have assumed the put option mentioned above costs nothing. Okay, let's just go with that for now. Then using $12 stock price, $13.30 strike, 6 years till exp, etc: Assuming we can borrow at 13% would imply a $5.60 warrant price, assuming 10% gives $4.50, etc. That matches your numbers. But, Eric, what if we can borrow at 1%?? Using the same approach, that would imply a negative warrant price!

 

So it seems like this measure of cost of leverage is really mischaracterizing something. Well, as SJ pointed out, there's the cost of the put option that we ignored. But, even if we accept hand-waiving there (i.e. both accounts are bankrupt if the stock ends lower than the strike, so there's no need to buy a put in the synthetic version), we also need to consider borrowing constraints for the synthetic version. Namely, suppose I have $3 and that's where the warrant trades. The typical broker is not going to let me borrow $9 to buy 1 share. So there's a constraint that would prevent me from even creating the full synthetic warrant in that case.

 

To calculate an implied margin rate, we now need to make assumptions about the borrowing constraint and the underlying price distribution at expiration. I've attached a simple spreadsheet to illustrate. The bottom line is that it looks like the simpler approach severely overestimates the premium that would come out of the warrants due to a much lower implied borrowing cost... even before considering the embedded put.

 

I own a mix of common and warrants and don't intend to pay short term cap gains on any of it. Would agree with swapping warrants for common at this point in tax-free accounts, but you really run into borrowing constraints there. Looks like you've gotten around that with options, though.

 

Not trying to be confrontational, just enjoyed thinking about this yesterday. Please poke holes if you're not tired of the subject. I always appreciate your posts. Following you has made me a lot of money.

 

The borrowing constraints are something I thought about before I swapped in my taxable account.  Here is my thinking:

 

First the obvious scenario:

1)  Initially, the leverage starts out as a $12 call for first two years (years 1 and 2)

2)  For year 3 perhaps I don't want to leverage the stock anymore (price is at $20)

 

Second scenario:

1)  Stock is still in the dumps ($14.10 or less will be tax-free roll of the calls).  Purchase another at-the-money call

 

Third scenario:

1)  Take delivery of the stock using margin hedged with a put.

 

So it's the third scenario you are concerned with -- borrowing capacity.  Here's what I have to say about that....

A)  you are saying that brokers won't give you that much borrowing capacity, but really you only have slightly more than 2x notional upside with the warrant at maximum. 

B)  In two years time when the calls mature you can take delivery on a partial amount of the shares hedged with put, but rollover perhaps 1/2 into the calls.  Keep in mind this will trigger some long-term capital gains on only the calls that get rolled over, and those capital gains will need to be paid in year 3. 

C)  Because those capital gains would have been due anyway eventually upon selling the warrants and/or stock, it's not quite so bad as it looks.  Just put a bit more money into the calls (financing the tax bill at the rate of borrow in the calls)

D)  On the brighter side from a tax perspective, in years 5 and 6 there will be capital losses to utilize from those puts expiring worthless if this is a process worth repeating.

 

 

Needless to repeat, but you don't need as much leverage in the first place if your borrowing cost is significantly below 13%.  Like for example that 1% borrowing cost from margin.  However I was always assuming that if you were using margin you would hedge a good portion with $12 puts.  That raises the costs significantly unless the stock is much higher than today in year 3 or in year 5 -- in that case the $12 puts will be cheaper.

[LC]

Eric, this is some bloody brilliant analysis. Very good job illustrating how all leveraged securities have an embedded cost of leverage, and part of their value is that cost of leverage versus the ROE of the security (or underlying). Good on you (and thanks for the free education)!

[ERICOPOLY]

Here is another one we didn't talk about:

 

In year 3 if we do in fact want to keep invested in BAC with leverage, we can do so by either purchasing new calls at-the-money or by exercising shares on margin and hedging the loan with at-the-money puts.

 

What if the shares are $18 at the time?

 

Okay, we'll you'll be hedging at $18.  Yes, you'll be locking in your gains to date.  Yes, the cost of the at-the-money calls and puts will likely be roughly the same as today, about 10% annualized, but the dividend rate will also still likely be 3% (on a higher stock price). 

 

So instead of paying 13% annualized for the low strike puts embedded in the warrants upfront, in year 3 and 4 you will be getting a high-strike put if you go my preferred route that I've undertaken.

 

So this way, the leverage comes at the same price but you get much higher strike priced puts.

 

The put strike in the warrants never adjusts upwards (so you never have the chance to lock in the cumulative gains to date as the stock rises).

[ERICOPOLY]

Eric, this is some bloody brilliant analysis. Very good job illustrating how all leveraged securities have an embedded cost of leverage, and part of their value is that cost of leverage versus the ROE of the security (or underlying). Good on you (and thanks for the free education)!

 

That was too kind, but thank you.

 

As for talking about options in terms of Theta, Gamma, Alpha -- is that a sorority full of hotties or something?  Because that seems to be where the party is going on!  I'm over here all by myself.

 

(I can't talk about options in those terms because I haven't learned the terms)

 

 

[Olmsted]

I may be looking at this the wrong way - but I am getting a 2-year option leverage cost that is a bit above the warrants. 

 

25 is the warrant-common break-even - ignoring the dividend readjustment but also ignoring dividends on the common - which is probably the right way to look at it (the readjustments should cancel each other out).  That implies an annualized cost of leverage of about 13%.

 

The two-year option at $2.10, ignoring dividends, gives you a 10% cost of leverage.  But the two-year options don't benefit from the dividend adjustment.  So the leverage cost of the options is 10% plus lost dividends over the next two years.

 

If you wanted to make an apples-apples comparison, one could use the post-adjustment strike and shares/warrant and compare that to the options.  Guessing at an $11 strike and 1.2 shares/warrant I get a break-even at $19 versus the common stock - implying a leverage cost of 8% plus lost dividends over the next 6 years (stock price at 12.06, warrant price at 5.54 as write).

 

Now of course we don't expect the bulk of the capital return in the next two years - so the 2015 options look ok in that regard.  But unless I am way off, the warrants look a little cheaper than the options.

 

EDIT: since you're paying for dividend protection up front, options could be cheaper over the next two years since serious dividends won't kick in until later.

 

Is this totally wrong?

 

 

Put it this way...

 

If $2.10 is the cost of the 2015 $12 strike call at a cost of leverage rate of 10% annualized, then at a 13% rate it would cost what... roughly 60 cents more (I'm not being exact, just winging it after 4 drinks in Death Valley and no calculator).

 

I have 60 cents of cash still in my pocket from paying a 10% rate instead of a 13% rate.

 

So I decide to invest that 60 cents in the stock at $12 per share.

 

Call it... a certain dividend that I get paid upfront.

 

Meanwhile, other people buying the warrants are implicitly speculating that the dividend over the next two years will exceed 60 cents.  So confident are they that they are paying the 60 cents upfront, hoping to get a dividend that exceeds 60 cents.  They'll lose money on that if it comes in below 60 cents (cumulatively over two years).

 

But it's better.  My way, I'm investing my 60 cents into the stock at $12 per share.

 

The warrant holder?  Maybe a some of the dividend gets invested at $12, maybe some at $15, maybe a good chunk of the 2nd year dividend gets invested at $18.

 

Hmm...  a 45 cent dividend invested at $18 is no better than a 30 cent dividend at $12.

 

Does anyone really want to throw away a certain 60 cents dividend reinvested at $12 today just to gamble on a bigger dividend that will probably get invested at a much higher price? 

 

So yes, the warrants ostensibly have "dividend protection" -- me, since I have the calls at 10% cost of leverage I have that approximate 60 cent dividend already invested in the stock at $12.

 

Fair enough - makes sense.  Another issue with what I wrote above is you are paying for all 6 years of "interest" up front, where with the option you're only paying for two years at a time.  If it reprices, you benefit when you roll the options over.  If the warrant "interest" reprices, you lose.  You mentioned this in one of the posts.

[mhdousa]

This discussion has been way beyond my level of understanding.  However, I'm curious how the discussion has quickly changed from essentially that the TARP warrants are the greatest thing ever to the common is now considered a much better deal.  Or am I misinterpreting things?

The common has actually done better over the last year.

[stahleyp]

eric, I want to just thank you again for all that you do. You're a good man (though still a dirty, immoral atheist).  ;)

[enoch01]

This discussion has been way beyond my level of understanding.  However, I'm curious how the discussion has quickly changed from essentially that the TARP warrants are the greatest thing ever to the common is now considered a much better deal.  Or am I misinterpreting things?

The common has actually done better over the last year.

 

There is a time element involved in the price of the warrants.  So that means that you must re-evaluate as time passes.  They've both gone up a lot in the last year, but there is one year less left in the life of the warrants.

 

Maybe some day they'll become a better deal again relative to the common (they still are not an awful deal relative to lots of other stuff).

[Liberty]

Eric (and others), what are your thoughts about the TARP warrants vs. the common without any extra leverage?

 

I understand that your new strategy optimizes returns and lowers risk vs the warrant (at least at current prices), though not being a math/options wizard I'm not getting all the subtleties of what you are saying (though I think I get the general idea).

 

But did the warrant just go from the bee's knees to total dirt, or is it just sub-optimal compared to this new approach (common + LEAPS, etc)? Or is even the unleveraged common a better deal in your opinion? In other words, if you could only own the common or only the warrant, which would you take?

 

One additional consideration for me is that I'm in a taxable account in Canada, so dividends from US companies are taxed pretty heavily. With the warrant, I feel that div-equivalent is getting reinvested mostly tax-free thanks to the adjustment mechanism. This makes the break-even point between the common and warrant lower than 25 for me, unless I'm mistaken.