Monday, April 30, 2007

Value investing is arbitrage

The other day, I talked about the reverse-split arbitrage I've been been engaged in for the past year. Thinking about the methods I use to evaluate the opportunities, I started to wonder if they could be applied to other investments. Certainly the concept of arbitrage can be extended to other realms such as sports betting. The key element is that there must be multiple markets for the arbitrageur to exploit. In the case of a reverse-split, the two markets are the open market where one normally purchases the shares, and the company market where the company buys the shares. The reason this arbitrage is profitable is that the second market is only available to those who hold a small number of shares. In mergers and tender offers open to unlimited amounts, the market adjusts almost immediately to the offered price.

Value investors do something similar when we attempt to profit on discrepancies between the price and the value of a stock. Of course, the value market is a theoretical one, at least in the short term. But the purpose of buying an "undervalued" company is the hope that eventually the market will change in such a way to properly value the position.

Let's take a look at Berkshire Hathaway, the classic value stock. First, we need an estimate of the payout if a bet on Berkshire is successful. The Berkshire Hathaway Intrisivaluator is as good a place to start as any. Currently, the "Cost of Capital" estimate puts BRK.B shares at $4754. This estimate assumes a healthy growth rate discounted at Berkshire's cost of capital. For an estimate of the minimum value, we'll use the "Liquidation" scenario of $3114 a share. Here the assumption is Berkshire sells off all its assets, settles all its debts, and distributes what's left to shareholders. There are other choices offered by the model, but for the sake of argument, let's assume that these are the payouts for success and failure.

The market values BRK.B at $3628 as of today's close. Using the method I described last week, that implies the market thinks there is roughly a 45% chance Berkshire will perform well enough in the future for "B" shares to be worth $4754 today. By elimination, that means there's a 55% chance Berkshire will stall out and only pay out $3114. Obviously any rational view of a company's future will be more nuanced and complicated than a simply success/failure trial. But it does provide a dead-simple method of calculating the odds of a stock investment. In this case, the market seems to think Berkshire doesn't have much gas left in the tank.

One issue with thinking this way for ordinary stocks is that there is no finite termination date. It's as if the coin keeps spinning and never comes down—or maybe the coin is flipped over and over again as shares are traded. But that's not a bad thing from a practical standpoint, since the company's value doesn't stop moving either. Each quarter there is new input into the value calculation, which often makes a good deal look even better. If you flip back in the Intrinsivaluator to 1981 ("B" shares, if they existed, were valued at $40), the value keeps climbing as you step through the years. Even in 1995, when Berkshire seemed most overvalued, a long-term investor would probably regret selling.

Thursday, April 26, 2007

Select Comfort's new ad direction

I've just had a chance to review two Select Comfort commercials from its new "Cure Tired" campaign. As I mentioned in the past, the most recent advertisements seemed more like they were hawking drugs not beds. The new ads are much better and get back to the key elements of the original ads: humor and product focused. True to form, McKinney produced one spot aimed at women and another aimed at men.

"Bright Eyed", the weaker of the two in my opinion, begins with scenes of women trying to cover up baggy eyes in the morning with the familiar "What the world needs now..." tune in the background. A voiceover suggests, "The world doesn't need a better way to fake a good night's sleep... It needs a better way to sleep." The payoff is a 5-second explanation of the Sleep Number bed followed by the new tag: "You Can Cure Tired." Since I'm not the target audience, I don't know if my judgment can be relied on, but the makeup and cucumber scenes seem less humorous and more pathetic than I'd like.

On the other hand, "Staying Awake" seems to hit just the right notes. The opening scenes this time represent over-the-top caffeine/energy drink/stimulant attempts to stay awake under the same music. The voiceover this time says, "The world doesn't need a better way to stay awake... It needs a better way to sleep." The spot is a full minute instead of 30-seconds and it uses the time to establish a bit more clearly that the first part is about covering up the real problem: being tired. It also introduces a protagonist who buys a moderate-sized cup of coffee and rejects the "moster caf 72" coffee mug. As he walks down the street, he observes in disbelief the Ka-Blowie stimulant-smoothie stand, Wakey'z Drugmall, a dog lapping up coffee abandoned by a napping newspaper seller, and so on. Finally, the man notices a helpful Select Comfort salesman waving to him from in front of his store. The ad ends with the same explanation and tagline.

"Cure Tired" is a pretty good tag, especially since the beds actually work. Every time I'm forced to sleep in some other bed, even a relatively comfortable bed, I'm quite happy to go home and rest in a bed that adjusts to fit me.

SCSS has just released their first quarter earnings which were fairly well described on the Fool. Obviously I'd prefer if comparable sales were better and it makes me nervous to have management back-load earnings so much. But I think there is a good chance advertising will make a difference.

Tuesday, April 24, 2007

How I added to Canon's results

There's a pretty good summary of Canon's Q1 at the Motley Fool. As it happens, I feel partially responsible. You see, earlier this year I bought my wife a Canon Rebel XT . It was intended to replace the A85 I bought her a few years ago and the Rebel 2000 I gave her a few years before. For at least this consumer, Canon has been able to sell higher margin products as the years go by.

The financial statements support this. In 1999, the year the Rebel 2000 was first introduced in Japan, Canon converted ¥3 of every ¥100 in sales to profit. In 2006, it converted ¥11. There are lots of reasons for this, such as the move from film to digital, point & shoot to SLRs, black and white to color copiers and printers, currency benefits, and operating efficiencies. Meanwhile, Canon has taken a hit in asset turnover, which has fallen from ¥98 to ¥92 of revenue per ¥100 of assets. This is to be expected since higher margins usually imply lower sales. Fortunately, the overall effect has been positive as measured by ROA, which went from 2.71% to 10.07%.

Meanwhile, Canon has been de-leveraging over that same time-frame. Its equity to asset ratio dropped from 2.15 to 1.51 thanks to decreases in long-term debt and capital leases. Normally this has a negative effect on return on equity, but because of Canon's stellar margins, ROE has improved from 5.84% to 15.25%. Mathematically, it doesn't much matter which of the ROE component ratios improve, but financially its nice to "front-load" the ratios. In general, it is easier to improve asset turnover through discounting or leverage through borrowing than it is to increase margins. This is especially true in a highly competitive business like digital cameras and printers.

I don't imagine margins will improve much from here on out, but there is hope for further growth in new products. Currently the company is working on launching SED TVs and have announced a medical device initiative. I'm a bit worried about the plan to develop (and I'm not making this up) intelligent robots. Whatever that means. I'm confident that Canon's R&D investments will pay off over time, but it's nice to have such strong operations while we wait.

The business of beauty

It's been a while since I wrote about Sally Beauty, but there were two stories that I thought were worth reading. First is a story from Forbes on starting a salon business. Sally got a mention as a supplier of salons, but what was more interesting to me was the advice to adopt a Whole Foods approach to employees. "In the salon world, the most precious resources are stylists, so keeping them around and happy is critical." The article suggested emulating Whole Foods' training program.

On a related note, Regis is dropping out of the beauty school business by merging most of its schools with Empire Education Group. The press release has more information including the suggestion that the need for IT investment was the reason for the merger. As you might recall, Regis was initially interested in buying Sally Beauty, but was rejected at the last moment because of operating weakness.

It seems to me that while the beauty salon industry as a whole resists consolidation, the supporting industries are successfully consolidating. Beauty schools and salon product distributors benefit from economies of scale, but salons themselves rely to a large extent on the services of talented stylists. Since talented stylists know they are an important part of the success of a salon, they demand a larger slice of the profits. There are dozens of professions with this dynamic including chefs, athletes, programmers, artists of all types, and so on. But unlike other professions, it's difficult for individual stylists to scale their work—they can only cut one head of hair at a time.

Monday, April 23, 2007

Arbitrage odds

One of the ways I've been evaluating going-private and other arbitrage opportunities is to look at the market's implied probability of success. Like gambling situations and unlike most investment situations, arbitrage is essentially a binary, win-loss event. That makes it relatively easy to apply the Kelly Criterion.

To show how it works, let's take my first going-private transaction, Major Automotive. On October 14, 2005, the company announced plans to implement a reverse split that would pay $1.90 to shareholders of less then 1000 shares. On March 29, 2006, I bought 999 shares at $1.75 a share. After the $19.95 commission charged by my broker at the time, I hoped to make $129.90 when the reverse split was resolved. I guess that there was at least a 95% chance the split would succeed from that point since insiders owned 49.4% of the company. I don't like the idea of assigning higher odds because of Murphy's Law.

If the split failed to happen, what would my position have been worth? The most pessimistic choice would be to assign no value. It isn't unreasonable either, since I'd done basically zero research into the underlying value of the company. In that case, I'd have lost the entire $1,768.20 that the position had cost. The expected payout would be $129.90*0.95 + (0-$1,768.20)*(1-0.95) = $34.995, which isn't half bad for a zero-research investment. A slightly more realistic value would be the price of the shares just before the reverse split was announced. On October 13, 2005, Major Automotive was priced at $1.40 a share. Using that price as a floor, the expected payout was $103.93. If you are following along don't forget to include an extra commission as an added cost of failure.

As it turns out, you can calculate the odds the market is assigning to an arbitrage situation with a little bit of math. This is the equation for expected payout:

S*p + F*(1-p) = E

S = price if split succeeds
F = price if split fails
p = split probablity
E = expected price
If the market is rational, you'd expect the market price to match the expected price. I used the Mathomatic Computer Algebra System to solve for p:
$ mathomatic
Mathomatic version 12.6.10 (
Copyright (C) 1987-2006 George Gesslein II.
50 equation spaces available, 960KB per equation space.

1-> S*p + F*(1-p) = E

#1: (S*p) + (F*(1 - p)) = E

1-> solve p

        (E - F)
#1: p = -------
        (S - F)

Now if you plug in the values for Major Automotive when I bought it, you get a 70% probability that the split would happen.

Since my probability estimate (95%) was much greater than the market's, my expected payout was correspondingly higher. Given enough of these situations profits would be astronomical for anyone who could identify them. According to the Kelly Criterion, the optimum allocation for even the pessimistic case is 27%. (This can be calculated by taking the expected payout and dividing by the maximum payout or $34.99/$129.90. The more optimistic case calls for a whopping 80% allocation.) Unfortunately, these situations are rare. The only reason reverse splits are so wildly mis-priced is that arbitrage positions are limited to a small number of shares. Unless you have a portfolio of only a few thousand dollars, it's impossible to allocate the optimal amount even under the pessimistic case.

Monday, April 16, 2007

First Marblehead gets cheaper and I couldn't be happier

First Marblehead has lost 23.67% since I bought it in March (-98.36% annualized). Obviously, I would be happier if I had waited to buy, but getting cheaper is a good thing overall. Consider the Four Factors. The only one that has really changed since I bought is equity valuation, which has improved to 24¢ of equity per dollar of price. Other investors might have lowered their estimates of asset value and future earnings based on potential defaults or the potential acquisition of Sallie Mae. But I don't think those fears are warranted and I haven't changed my estimates.

Having already bought shares, how can the lower price help me? For one thing, I could buy more shares (double down). But as I'm short of investable cash, that isn't an option. If the price doesn't recover before First Marblehead distributes its next dividend, I'll be able to reinvest it at a lower cost. A more likely scenario is that First Marblehead will repurchase on the open market over the next few days.

There are potential disadvantages to a lower prices. For instance, if I needed to sell today, I would realize a substantial loss. Or a third party might attempt to takeover First Marblehead. Or if First Marblehead were to issue shares (perhaps as a part of executive compensation), it will get less value per share than it would have a few months ago. But as long as those things don't occur, lower prices can only be good for shareholders.

As for the "news" that has been driving down FMD's price, I'm not too worried. The default scare seems totally bogus. First Marblehead's estimate of residual value seems very solid.

The issue with the SLM buyout seems to be that two potential purchasers, JP Morgan Chase and Bank of America, are also two of First Marblehead's clients and might direct private student loan business to Sallie Mae. FMD's CEO has said that there will be no impact on his company. I don't see how there could be an immediate impact since neither company would control SLM. Two private equity investment companies, J.C. Flowers & Co. and Friedman Fleischer & Lowe LLC, hold majority stakes and I doubt they would be willing to give away Sallie Mae's competitive advantages to the giant banks. A scenario that seems more probably is that the banks will outsource their student loans to SLM over time. But they could have done that even before this buyout was proposed, so I don't see what the big deal is.

Tuesday, April 03, 2007

Four Factors of value creation

Dean Oliver (the Bill James of basketball), describes the Four Factors of Basketball Success. They are shooting, taking care of the ball, offensive rebounding, and getting to to foul line. There are hundreds of other statistics that are of interest, but unless they measure aspects of these factors, they aren't all that important to actual basketball success. Think of the Four Factors as a framework for interpretation.

I believe that there are Four Factors for value creation as well. Obviously there are even more statistics that may be important to understanding a company, but these four represent a complete path from customer to shareholder. I'm going to use my new favorite investment, First Marblehead, to illustrate the concepts.

Most public companies derive their value from sales. (The exception are companies like biotechnology firms that hope to turn ideas or other assets into sales at a later date.) But not all sales are created equal. Companies need to charge more than the goods and services cost to produce. And there are other costs such as overhead and taxes that need to be considered. From a shareholders perspective, those costs add little to the value of the company. So the first factor is Net Profit Margin:

-------- = Net Profit Margin

In it's most recent 10-K, from June 2006, First Marblehead reported revenue of $563.572 million and, after subtracting costs, earnings of $235.960 million. Divide earnings by sales and the profit margin works out to 41.87%. In other words, 42¢ of each dollar in sales is profit to First Marblehead owners. Compared to the Consumer Financial Services industry average of 13.77%1, FMD must be doing something right.

Specifically, what companies with high profit margins have done is a combination of raising prices and lowering costs. The risk is that customers don't like higher prices and that lower costs might mean lower quality products, which also don't go over well with customers. So if you've got two companies and one has a higher profit margin than the other, you would also expect it to have lower sales. But just as we compared earnings to sales, we need to compare sales to something else. If one company has two stores, you'd expect it to sell twice as much as a company with just one store. A company that sells to customers all over the world probably has more sales than a similar company that just operates in one city. So you have to compare sales to the company's size or potential.

Asset Turnover is the second factor:

------ = Asset Turnover
Every company has assets such as offices, factories, stores, patent portfolios, and so on, which it can use to generate sales. First Marblehead had $770.346 million worth of assets as of June, 2006. The bulk of those assets are residuals in its securitization trusts, which have the potential to contribute to future income as the underlying loans are paid off. For fiscal 2006, every dollar of assets produced 73¢ of sales. Since the industry average is about 21¢, First Marblehead looks even better.

How much better? Well if you multiply the first two factors, you get another ratio called Return on Assets:

Earnings   Sales
-------- X ------ = Return on Assets
Sales      Assets
This number measures how well management has balanced price, costs, quality and demand. Higher prices tend to depress demand, and lower costs tend to lower quality which lowers demand. But First Marblehead seems to be able to defy those tendencies since it has a ROA of 30.63% compared to the industry at 2.91%.2 Given the first two factors, you might wonder how other financial service companies could compete with First Marblehead. There are several answers including some peculiarities in the way GAAP requires it to report earnings that affect the ratios. But the biggest difference is the third factor, which is Leverage:
------ = Leverage

Companies, especially financial companies, use debt an other liabilities to buy more assets that can in turn be used to generate sales. If you have one store and you've maximized its ROA, you can borrow money to open a second store. The result on the balance sheet is that you've increased you assets, but your equity has stayed the same. One the second store is operating as efficiently as the first, you will be generating twice as many sales and twice the earnings as well. As an equity investor, I don't really care how much debt a company takes on as long as there is a reasonable chance the company can pay it off with out hurting earnings.

First Marblehead's leverage is 1.34, which is wimpy compared to the industry average of 7.54. Sally Mae, a competitor, is leveraged at $26.6 of assets for each dollar of equity. This is serious leverage which can lead to serious returns. At this point, there is a possibility FMD is leaving money on the table by not taking on debt to increase leverage. In order to decide, we can calculate Return on Equity:

Earnings   Sales    Assets
-------- X ------ X ------ = Return on Equity
Sales      Assets   Equity

First Marblehead's ROE is 40.95% compared to 22.01% for its industry. Imagine a rich uncle offered to give you a fixed amount of equity in any company in the world. You pick the company and your uncle will give you enough shares so that the equity you own equals the fixed amount. It's obvious that you'd look for a company that has the best ROE and seems likely to continue to do well in the future. If you were limited to student loan companies First Marblehead looks a lot better than My Rich Uncle which has a ROE of -253.53%3. If this were the way you acquired shares, we could stop the analysis right here. But normally you have to buy them on the stock market. The final factor doesn't have a standard name, but I'm going to call it Equity Valuation:

------ = Equity Valuation

In theory, if a company closed shop, sold off all its assets, paid off all its creditors, and distributed the proceeds to investors, shareholder equity would be the value of the company. But some assets (such as newly purchased manufacturing equipment) are overvalued on the books and other assets (such as goodwill from profitable acquisitions) are undervalued. Further, some assets like brand names don't show up on the books at all. So Equity Valuation is rarely equal to one. For First Marblehead on June 30, 2006 the market paid one dollar for just 16¢ of shareholder equity. The industry average is 28¢, so the market rightly considers First Marblehead to be a better than average company.

When you put together all of the factors, you get a familiar measure:

Earnings   Sales    Assets   Equity
-------- X ------ X ------ X ------ = Earnings Yield
Sales      Assets   Equity   Price
Earnings Yield is P/E ratio inverted. First Marblehead's earnings yield was 6.46% compared to 6.88% for the industry. Now you might argue the relative quality of FMD to industry earnings or the relative growth rates or relative risks that make the final numbers better or worse than they appear, but that's missing the point. When I really need to find a companies value, I'm better off running a discount cash flow model. This exercise is more about the way earning yields can be composed and what companies can do to increase their value.


  1. Reuters uses a different method to calculate these ratios, so we have to take these numbers with a grain of salt.
  2. Remember, other methods of calculation give different results. The important thing to understand is what the ratios mean and to try to be consistent. In this case, the 5-year average assets that Reuters uses overstates First Marblehead's ROA, since it is growing so quickly.
  3. MRU holdings seems an unbelievably bad investment. I suppose the thesis is that eventually it will grow its way into profitability.