To evaluate the risk/reward of owning the 2019 Series A and 2018 Series B Bank of America (NYSE:BAC) warrants, I built a simple Black-Scholes-Merton option pricing model, which allowed me to estimate the expected return profile of the warrants under various scenarios. While different investors have different risk tolerances, I believe that owning the stock outright offers far and away the best risk/reward profile (in excess of a 5:1 ratio of upside to downside pay-off). The report below is broken up into the following sections:
- Results
- Warrant Detail
- Methodology
- Assumptions
- Sensitivity
RESULTS--Just Go Long The Stock, Forget The Warrants
In the table below, I show my expected IRR in both my base case and my downside scenario across a range of holding periods for the stock, the Series A warrants, and the Series B warrants. For the stock, I calculate an expected return-to-downside ratio of 5.2x, this compares to 0.9x for the Series A warrants and 0.5x for the Series B warrants. Anything below 1.0x implies the expected return is less than the loss in the downside scenario. Or said another way, a ratio less than 1.0x is a less compelling trade.
While the Series B warrants do offer a higher IRR in my base case scenario in the short-term, given their very high loss rates in my downside scenario, I don't find the risk/reward trade-off to be compelling. Warren Buffet once said, "The first rule of investing is don't lose money; the second rule of investing is don't forget Rule 1." As I see it, investing in either the Series A or Series B warrants ignores both rules.
WARRANT DETAIL
Series A Warrants (chart)
- Yahoo! Tkr: BAC-WTA
- Strike: $13.30
- Expiry: 1/16/2019
- Price: $3.60
- Implied Vol: 67%
- Dividend Adjustment: Strike price will be adjusted downward for dividends in excess of $0.01. The language around this in the prospectus is a nightmare, but for those of you looking to dig in page S-28 has the details here.
Series B Warrants (chart)
- Yahoo! Tkr: BAC-WTB
- Strike: $30.79
- Expiry: 10/28/2018
- Price: $0.76
- Implied Vol: 44%
- Dividend Adjustment: Strike price will be adjusted downward for dividends in excess of $0.01. The language around this in the prospectus is a nightmare, but for those of you looking to dig in page S-28 has the details here.
METHODOLOGY--Project Future TBVs By Forecasting ROEs Then Estimate Price Using A Series Of P/TBV Multiples
For those of you who read my most recent article, Why You Need To Own BAC--20% Expected IRR With A Sufficient Margin Of Safety, a good chunk of this section will be a rehash from my methodology section in that article, but there is some additional information on the pricing of warrants.
I began by building a very simple model, available for download here, to forecast the bank's tangible common equity per share (TCE or TBV) by making assumptions for:
- Return on tangible common equity (ROTCE)
- Dividend payout
- Additional unanticipated losses (e.g. settlement & GSE put-back costs)
- Additional dilutive capital raises
My base case forecast model is shown below and my assumptions are explained in more detail in the next section:
Once I have my TBV estimates for all future periods, I can calculate the expected future stock price by multiplying my TBV estimate by a P/TBV multiple.
However, given that I don't actually know what the future multiple for the stock will be, I forecast a range of possible P/TBV multiples (0.3x - 2.0x) and then layer on my own expectation for the probability distribution of these P/TBV multiples (basically this is my view of the likelihood of each of these multiples being the right multiple in the future). I have forecast a separate probability distribution for each holding period as shown below:
My expectation is that as the bank puts its legacy issues behind it, BAC is likely to trade at or above 1.0x TBV as I believe the firm's return on tangible common equity will begin to approach or even exceed the firm's cost of capital. If they are able to do this, a multiple at or above 1.0x TBV will be justified. I realize this view isn't shared by all, so please feel free to tweak my model with estimates you find more appropriate.
Now as I mentioned above, I calculate my price by multiplying the previous year's TBV by a P/TBV multiple. So for example, if I expect the firm 2 years forward (in May 2014) to trade at a 0.8x P/TBV multiple, I will calculate my expected price by multiplying the 2013 year-end TBV estimate of $13.34 by 0.8x to arrive at an expected price of $10.67. Below, I show my expected price 2 years forward across a range of P/TBV multiples:
While not shown, I have created similar tables to the one above for all holding periods. Next, I layer on my probability distribution across those P/TBV multiples to generate my weighted average probability adjusted target price for the stock (basically, my base case target price). Additionally, to calculate my downside scenario, I try and estimate the P/TBV in the bottom 10% of my probability distribution. So for example, using the table below a P/TBV of about 0.43x represents a good estimate for the P/TBV in the bottom decile. In the table below, I show my base case target price and my estimated downside target price along with the calculated IRR assuming a 2 year holding period.
Now that I've created a series of stock prices across a range of P/TBV for each holding period, I can use the stock price as an input into my Black-Scholes-Merton options pricing model. That model takes the following inputs to estimate a price for the warrants in the future:
- Stock price
- Strike price (may have been adjusted for dividends)
- Time to expiry
- Dividend yield
- Implied volatility
- Risk-free rate
In the next section, I'll go into more detail on how I estimate the forward implied volatility and forward risk-free rates.
Once I have estimated a price for the warrants given the above inputs, I can perform the same basic math I did to calculate my base case and downside target prices for each holding period. In the table below, I show the expected price and IRR for the Series A warrants assuming a 2 year holding period:
ASSUMPTIONS--Use Conservative Assumptions To Build In A Margin of Safety
Below I walk through the assumptions embedded in my forecast and pricing models discussed above. I'll keep this section brief as it's a bit of a rehash from my previous BAC article:
- ROTCE - For 2012-2014, I start with consensus GAAP EPS estimates from Bloomberg. I then adjust those estimates downward to incorporate $10b of additional losses and the net effect of small slightly dilutive capital raise of about $2b at $6.50/share. So essentially for the first 3 years, ROTCE is an output, not an input. However, for 2015-2018, I forecast that the firm can generate an ROTCE of between 9.5% to 11%. For those of you who are interested, in my previous article, I go into a fair bit of detail explaining why I believe the firm will be able to generate an ROTCE north of 10%.
- Dividend - I forecast that the bank's dividend will remain fixed at $0.04/yr through 2013. Starting in 2014, I anticipate the bank will receive regulatory approval to increase its dividend payout slightly to a 10% payout ratio (or $0.13/yr). Over the next four years, I forecast that the firm will slowly increase its payout ratio to about 30% (or a $0.63/yr in 2018). Additionally, once the firm increases its dividend above $0.04/yr, I assume a 0% dividend yield for the stock for the purposes of calculating the warrant price because the warrant strikes are dividend adjusted.
- Additional Losses - I estimate that analyst estimates fail to capture about $10b of additional losses that Bank of America will realize as it settles outstanding lawsuits and other legacy issues. If you feel my $10b estimate understates future losses, please feel free to tweak my model as you see fit.
- Additional Capital Raises - I have assumed that the bank needs to do a small dilutive capital raise of about $2b at about $6.50 per share. Again, if you feel my estimate is not harsh enough, please feel free to tweak my model.
- Implied Volatility - Estimating future implied volatility is certainly challenging, but here's how I've approached it. I first calculate the current implied vol based on the warrant's current price. I then look at my probability weighted average stock price 6yrs out and compare it to the adjusted strike price of the warrants. As an example, for the series A warrants, in May 2018, I expect the stock to trade around $18.50 in my base case and I expect the warrants to have an adjusted strike price of around $12. This means that I expect the strike to be about 35% below the spot price. Additionally, I calculate that the time to expiry will be about 8mths in May 2018. Next, I look for current options that roughly matches that criteria (i.e. a strike about 35% below the current spot rate with about 8mths to expiry). The $5.00 Jan '13 calls roughly match this criteria. I then look up the implied vol for these options, which as of 5/14/12 is 57%. Next, I assume that vol will linearly move towards that future implied vol to calculate implied vol for the intermit holding periods. This is all a bit confusing, so I provide a table below with my assumptions to help clarify things a bit.
- Forward Risk-Free Rate - Another tricky variable to estimate for options is the future risk-free rate. Fortunately, Bloomberg provides a nice little matrix showing the expected forward rate curves (FWCM <GO>). Below I provide a screen shot of this table. Using this table, I can interpolate what the implied forward rates will be for each period. Additionally, my assumptions for the risk-free rate used for each holding period are shown below. While I'm well aware that forward rate curves don't have a great history of predicting actual future rates, it's the best I can do right now.
SENSITIVITY--What If My Assumptions Are Wrong?
To help other analysts gauge my model's sensitivity to various assumptions, I walk through the impact of tweaking a few of the big ones. Again, for anyone who is interested, you can download my model here and make additional changes as you see fit.
Raise Unanticipated Loss to $20b (vs $10b currently) - My risk/reward ratio falls to 3.4x, 0.7x, and 0.4x for the stock, the Series A warrants, and the Series B warrants, respectively (vs 4.9x, 0.9x, and 0.5x, previously).
Increase Cap Raise to $10b, Sold At $5.00 (vs $2b @ $6.50) - My risk/reward ratio falls to 2.9x, 0.6x, and 0.3x for the stock, the Series A warrants, and the Series B warrants, respectively (vs 4.9x, 0.9x, and 0.5x, previously).
Cap ROTCE At 8% (vs 11% currently) - My risk/reward ratio falls to 4.6x, 0.8x, and 0.5x for the stock, the Series A warrants, and the Series B warrants, respectively (vs 4.9x, 0.9x, and 0.5x, previously).
Increase Implied Volatility 10% Across All Holding Periods - My risk/reward ratio increases to 1.7x and 2.3x for the Series A and the Series B warrants, respectively (vs 0.9x and 0.5x, previously). The stock risk/reward is unchanged by changes in implied vol assumptions. I also show the updated implied vol table below for comparison purposes.
Increase the Risk-free Rate 100bps Across All Holding Period - My risk/reward ratio increases to 1.0x and 0.6x for the Series A and the Series B warrants, respectively (vs 0.9x and 0.5x, previously). The stock risk/reward is unchanged by changes in forward rate assumptions. I also show the updated risk-free rate table below for comparison purposes.
BOTTOM LINE
Owning BAC stock outright offers a superior risk/reward profile to owning warrants for investors with a the long-term time horizon and a general aversion to putting too much capital at risk. For investors that have confidence that BAC will head higher within the next two years and aren't concerned about downside risk (that's not me), the Series B warrants can provide a more leveraged return than the stock itself. The Series A warrants are just way too expensive and offer limited upside vs the stock and plenty of additional downside.
Disclosure: I am currently long BAC and was previously long the Series A warrants, but have exited that position following completion of this analysis.
As always your comments and questions below are appreciated.