Now that financials are tanking around the world, I thought it might be interesting to take a quick look at some of these warrants. I was going to set up a table with all the listed warrants, their fair values and implied volatilities, but I'm too lazy to do that now so let's just look at a couple of them.

It makes sense to first look at the JPM warrants since I am a fan of the stock at this level, and am a fan of the bank itself. The JPM warrants (listed under ticker JPM-WT) has a strike price of $42.42 and expires on October 28, 2018. JPM's current stock price is $30.30, and the warrants are trading at $9.80. For interest rates, I will use the treasury rate of 1.36% and for dividends I will use 4.0%. I actually have no idea how to think about forward dividend yields as most banks are not paying dividends so as to preserve capital.

Plugging in the above figures and using a fair volatility of 20% shows the warrants to be worth $1.35. With a 30% volatility, the warrants are still worth only $3.52 versus the current warrant price of $9.80. If you back in the current price of the warrants to get an implied volatility figure, that comes to around 56.5%! That is very high. Yes, financial stocks have been volatile in the recent past, but it is highly, highly unlikely that the stock price can maintain a volatility level of 56.5% for seven years.

So from a conventional option model point of view, JPM warrants are trading way off any sense of fair value. You can tweak the interest rates and dividends and get different figures, but I don't think the general conclusion will change.

Looking at WFC, Buffett's favorite big bank, we have a current stock price of $24.31, warrant price of $7.90. This warrant expires on October 28, 2018. Using similar figures as above, the fair value of these warrants at 20% volatility is $1.07, and at 30% volatility it is $2.80 versus the current trading price of $7.90. The implied volatility at $7.90 is around 57%

So these warrants too, from a conventional options model point of view is way off fair value.

Bank of America (BAC) too has warrants out in two series; the class A and class B warrants. They give the same sort of conclusion. The valuations are way off and too expensive. Implied volatilities on those come to 57% for the B and 85% for the As.

Here is a summary of the above:

Stock Warrant Strike Fair values Implied

__Price__

__price__

__price__

__Expiration__

__@20% vol__

__@30% vol__

__volatility__

JPM-WT $30.30 $9.80 $42.42 10/28/18 $1.35 $3.52 57%

WFC-WT $24.31 $7.90 $34.01 10/28/18 $1.07 $2.80 57%

BAC-WTA $ 6.42 $2.98 $13.39 1/16/19 $0.07 $0.37 85%

BAC-WTB $ 6.42 $0.91 $30.79 10/28/18 $0.06 $0.04 57%

As you can see, based on a standard option model, these warrants are trading way out there.

However, this does not mean that these warrants are no good. There is a flaw in the standard options model. A standard option model is very good at calculating fair values over the short term, but for the long term it can get pretty inaccurate.

Why?

Because of the concept of forward prices. Over the short term, stock prices are pretty random; they will go up and down in something that looks like a normal distribution, maybe with some fat tails. The Black-Scholes option model is very good at capturing that.

However, when the option gets longer and longer term, like out to seven years, the model fails to account for the growth in a company. I suppose in a Chicagoesque efficient market world, the long term interest rate is supposed to represent 'growth'. Of course the interest rate represents the cost of carry in replicating the option position.

But it (the forward price calculated with the interest rate) is also the neutral estimate of where the stock price will be in the future. This forward price is the base price where the normal distribution is applied to calculate the likely range of stock prices at the future date. The forward price is simply the spot price times (1+ interest rate minus dividend yield).

Why can this lead to wild inaccuracies? If the company pays no dividends and the interest rate is 1.4%, but the company grows it's book value at 10% per year and the stock usually trades at around book value, then a long term option model is going to be way off.

Of course, the option model's job is not to incorporate such things. It's only input is to calculate the value without such 'forecasts'. Input can only be dividends and interest rates and some volatility figure, figures that are observable now. And as far as hedging the position is concerned, absent market disruption, in normal markets the hedge costs calculated by these models tend to be accurate. (actually future volatility is not observable in advance, of course, but volatility does tend to be mean reverting over time)

In other words, option models do not incorporate this growth factor, so if a company does grow, long term options models will be more inaccurate the higher growth the company is and the longer term the options are. (Efficient market folks will tell us that we can't predict who will be the winners tommorow, who will grow more etc... So in that sense, the option model is perfectly fine.).

So what is the other way to look at these warrants? Instead of looking at it from a conventional options model point of view, you can look at these things as binary bets, or all or nothing bets. You can of course create any number of different scenarios and plug in your own numbers; it doesn't have to be binary.

But for simplicity, I will use a binary approach. One scenario is for things to totally melt down and the U.S./world won't recover in the next seven years and bank stocks will either go under or stay below the respective strike prices. In this scenario, the warrants are obviously worthless.

The other scenario is that things normalize over time, and the banks do return to 12% return on equity and their book values grow around 8%/year from now until these warrants mature. Book value per share (BPS) growth of 8% is a number I just picked assuming a 12% return-on-equity for the large banks and a 33%-ish dividend payout ratio. I don't take into account potential for share repurchases. Jamie Dimon has stated he wants to get dividends back up to 30-40% payout ratio.

For now, I will just look at what these warrants might be worth in this 'normalization' scenario.

JPM's book value per share is $44.79 (according to Yahoo Finance). Assuming 8% growth in BPS over the next seven years gives us $76 in BPS. If JPM trades at BPS, then the JPM warrants would be worth $33.58 by maturity. If JPM trades at 1.5x book then, that would give a warrant value of $71.58 by 2018. This is versus the current warrant price of $9.80. Is that a stretch? What do you think?

For WFC, the BPS is $23.86. In seven years, that grows to $40.80, and if WFC trades at book, the warrants are worth $6.80 versus the current warrant price of $7.90. If WFC trades at 1.5x book at that point, the stock would be at $61.20 and warrants would be worth $27.20.

What about BAC? BAC gives some insane figures due to it's huge discount to book value now. I have no idea how big future losses will be, but let's just go through the excercise. The BPS of BAC now is $20.30. I can hear the laughter of people reading this. I know, I know. BAC has a bunch of problems. But let's just keep going. BAC BPS would grow to $34.71, and if it just trades at this book value, then the A-warrants would be worth $21.41 (versus the current price of $2.98) and the B-warrants would be worth $3.92 versus the current $0.91. If BAC trades up to 1.5x book, that would be $38.77 in value for the A-warrants and $21.97 for the B-warrants in value.

These are what these warrants can be worth if banks can return 12% on ROE over the next seven years and pays out 33% or so in dividends. To discount this scenario you can give these prices a haircut, say, 20% or 30% by assuming that there is a 20% or 30% chance that this 'normalization' will not happen.

Of course, many people will say that this is much higher; I'm sure many people will tell you that the possibility of a bad scenario is more like 80%.

In that scenario, of course, these warrants would not be attractive.

At this point, I don't own any of these warrants, but I will keep an eye on them. You can't really look at them from an option model point of view. I find it highly unlikely these things will trade at a low implied volatility.

In any case, these warrants will be worth absolutely ZERO in seven years if banks don't recover, so these are obviously highly speculative. If anyone wants to play with these, they should only play it with the speculative portion of their portfolio.

I understood the strike price of these warrants would be lowered by each dividend paid since the warrants were issued. True?

ReplyDeleteHi,

DeleteYes, if you google TARP warrant adjustments, you will see it discussed. I don't have the link to the actual filings that explain it off hand, but you can find it and read it there.

Thanks for reading.

Hi Brooklyn Investor,

DeleteI love your blog- thanks for your efforts. I was wondering what you think of TARP warrants today?

Do you own any and what % of portfolio would you feel comfortable with?

Cheers,

Matt

Hi, I haven't looked closely recently, but I think the TARP warrants are good. I tended to play banks with the LEAPS as I like a little bit shorter maturities.

DeleteAs for percentage of portfolio, I don't know. That really depends. Banks have run up quite a bit in the past few years, so it's not as cheap as they used to be even thought they're still attractive.

Hi Brooklyn Investor,

DeleteI love your analysis and I was wondering if you had any thoughts on COF warrants. At a price of 32, with a strike price of 42 and COF at 74, there doesn't seem to be any time value at all in the warrants. This seems like a bit of anomaly, Is there something I am missing here.

Thanks

Drew

No, I don't think you are missing anything. The deeper in the money these things go, the closer to parity it will trade at, and even a discount if you consider dividends. Imagine a warrant with a zero strike price. The only difference would be that the stock holder gets dividends and the warrant holder doesn't. If there are dividends, then the warrants would trade at a discount to reflect that.

DeleteThe TARP warrants have a dividend adjustment, but for COF, that's $0.375/share or something, which comes to around 2% yield (if that is actually paid) that the warrant holders wouldn't get (adjustments is for amounts above that). So you are effectively 'borrowing' 60% of purchase amount and the cost of financing that is the dividend you would get if you owned the stock but don't if you owned the warrants.

So it sort of looks like an anomaly here but isn't.

I might have got some detail wrong here, but that's basically how it works; the dividends you don't get as a warrant holder is the cost of financing you incur to get the benefit of the leverage.

Thanks that is very helpful.

DeleteCheers

Drew