Tesla: A Checklist Of Bearish And Bullish Points

The Euphoria of Growth Stocks

The last 3 years have been a very good time for the growth stocks. For many of the star companies, the old conservative valuation models based on book value and earnings yield are being replaced by the growth rate and future potential. The high P/S (Price to Sales) ratio shows that investors have many optimistic projections of the future growth.

As the history shows, investors tend to have very short memory about the financial history, and the euphoria of growth stocks often signals the end of a bull market.

Among all the growth stories, the story of Tesla (NASDAQ:TSLA) is one of my favorites, since I truly believe Tesla is likely to be a successful disruptor and may eventually take over the world. This is partly because there were no disruptors in the automobile industry in the past decades, and the existing players got too big and too slow on innovations.

However, investors often confuse the ultimate success of the company with a successful investment. Due to competition, the history shows many, many times that glamour companies often turn out to be bad investments, simply because the good story, if well known, will bring in even higher bids than its intrinsic value. Also, things rarely happen in the same way as expected.

The human brain has limited capacity, and it tends to focus on a couple of things at a time. The manic depression symptoms found in Mr. Market and the investors are understandable because our mind tends to focus on the recent news or a narrow perspective of the fundamentals at different times. When a story appears and focuses on the good side, people tend to be bullish and bid the price up. But when the recent news turns bad, they suddenly turn to the bearish side and take a loss quickly in order to sleep better.

That said, it is not a simple accusation to the other investors, because I am one of them. I have been guilty of swinging between the two extremes myself. For this reason, it has been important for me to keep a checklist of the high level bullish and bearish points, something I can check on at any time before I make a purchase/sale decision.

The Good Side

Let’s start with the good news first:

1. Take over the world.

As I mentioned above, I truly believe Tesla will likely “take over the world”. Although this doesn’t mean that Tesla will become the largest car company in the world, I do think it is likely to have the most loved car and the company will eventually get to the size of BMW, with about $100 billion revenue.

The innovative ideas and enthusiasm in the model design and all the advanced technologies, the innovative direct sales model, the efficiency in the manufacturing process, and the laser focus on user experience all give Tesla a huge competitive advantage. Other companies can be copy-cats, but it is very hard for them to match Tesla. This is mostly because the automobile industry is full of old players who are usually very slow on moving forward.

This industry has significant economies of scale too, in terms of the R&D needed and the brand name recognition required. It is also a capital intensive industry, as we have seen in the poor ROA (return on assets) of the industry. Ford, GM and BMW only have 3% – 5% ROA. Their ROE may reach 10% or more for now, but that is based on a good economy, low interest rate, stable revenue and loose credit. When these conditions no longer hold, we may find the growth of these mighty car companies are only destroying shareholder value. The more they grow, the more value they destroy.

All these mean that it is very hard for new entrants to enter. In fact, the only reason Tesla exists today is because it was not profit-seeking when it was founded! (Elon Musk estimated that there was only 10% chance of success when Tesla was founded.)

One relatively new player and close competitor is BYD in China. I have been a shareholder of BYD in the past too. The CEO of BYD (Chuanfu Wang) is very smart and had some great achievements too. However, in my own opinion, BYD is still not a match to Tesla in terms of innovation and model design. It is great in its own way, and it has easy access to the cheap human capital in China, but so far it doesn’t seem to be a threat to Tesla yet.

2. Direct Sales Model and Low Working Capital.

Tesla’s innovation goes to the sales model too. The direct sales model not only saves the distribution cost, but also reduces the working capital. The whole system also becomes much more efficient. In the US, I believe the regular consumer experience with car dealerships can be ranged from poor to awful. So it actually helps on improving the customer experience too.

Dell’s success mainly came from the direct sales model, and it actually had negative working capital because of this. This advantage may not reflect on earnings, but small investors usually don’t know that in terms of investment returns, this difference is huge. In other words, the cost of any capital (whether it is current assets or fixed assets) is not to be ignored.

3. New innovations and ventures.

When Apple first announced the iPod, people who liked it would use iPod and Mac sales to value the company. In hindsight, we know that valuation would have greatly undervalued the company because they should have considered the possibility of further new product releases, such as the huge successes we have later witnessed in iphone and ipad.

Similarly, Tesla may not stop at EV. The opportunity at autonomous cars, batteries, and who knows what other technology could be some pleasant surprises to investors later.

4. No demand problem in the long term.

Despite the fact that Elon Musk continuously said Tesla has no demand problem, many speculators always worry about the potential demand saturation. In my opinion, Tesla doesn’t have a demand problem right now, since it still has a lot of tools it hasn’t used to boost demand, such as advertisement. Also, the hesitation of the wealthy is related to the lack of charging stations which are being built up gradually. The information diffusion also takes some time to reach its peaks (this translate to Tesla not yet being seen as a “fashion” product in many areas.)

Eventually, the luxury car sales will saturate at some point, but by that time, we may have the 3rd generation model coming out. The price/value ratio with that model will be hugely attractive to the average consumers, and it would be a time for Tesla to really take over the world.

Right now, Tesla only have two hurdles: price and charging. The 3rd generation model will address the first problem, and the charging network are gradually being built up. This is a classic “network effect” problem, as more charging stations will allow more EVs and more EVs will bring in more charging stations. The adoption of EVs are already picking up in the US. We may soon reach the tipping point of that network effect.

Saying “no demand problem” doesn’t mean the demand will always keep up with the pace of the production growth, or there will be no short term demand problems at all. From time to time, we may see the demand doesn’t keep up with the expectation or production, but in the long term, it is likely that the peak demand is large enough to allow Tesla to reach the $100 billion revenue mark.

5. Better Economies Of Scale.

While Tesla has already reached a certain scale, as it increases the scale even further, there may be additional cost savings and possible margin expansion. It is hard to provide an accurate analysis on this, but a couple percentage points of margin expansion could cause a big change in the valuation.

The Bad Side

1. Capital intensive industry.

I have seen arguments like Tesla should be classified as a high-tech company because it mainly focuses on R&D. While this argument is not completely unreasonable, we have to be aware that the high tech companies could have quite different economics.

The key difference between the high-tech world and traditional industries is the difference on variable cost and capital needed for fixed assets.

Traditional industry (manufacturing industry) produces goods with raw materials. So the gross margin is low, and variable cost is high. It also tends to require significant up-front investment in fixed assets, such as factories and distribution infrastructure.

On the other hand, for the high-tech industries like the software industry, the variable cost is low: selling one more software license or installation CD costs almost nothing. The up-front investment is mainly on R&D in the software industry, which is certainly a significant cost, but both the gross margin and the profit margin are very high, once the company has reached a certain scale.

Comparing to the software industry, the high-tech hardware companies such as Apple tend to have lower gross margins, but Apple outsources much of the manufacturing to the third party suppliers. Therefore it doesn’t need a lot of investment on factories, which makes it easy to scale up and scale down.

On the other hand, if the hardware company is producing regular PCs like HP or Dell, once the product becomes a commodity, it looks more like a traditional industry than a high tech industry.

In this sense, although Tesla’s success mainly comes from its focus on R&D, the capital intensive nature and low margin nature do not change much. It requires huge fixed asset investments on manufacturing facilities, battery factories, and charging stations. Therefore, although Tesla is quite different from the other car companies, it should still be classified as in the traditional auto industry.

So far, Tesla has $2.6 billion in fixed assets, mainly in factories, charging stations, service and retail centers. Based on what I have seen from BMW, the fixed assets are close to its annual sales. If so, a 10% profit margin means the return on assets is roughly 10% too. This is certainly much less attractive than the most companies in the high tech industries.

To be fair, Tesla may be more efficient than BMW in terms of the manufacturing process, so maybe it can achieve better ROA and ROIC (Return On Invested Capital), but it may not be a lot better.

In fact, we have to assume its ROA is better than 10%, because otherwise, the growth will not provide any economic value at all, assuming the average cost of capital is 10%.

The following question would be: where will the capital come from? If it is growing fast at 30% – 40% a year, the profit generated internally will not be enough. If it is from the share issuance, it will have a dilution effect. As long as the shares are traded at the current level, it is not very damaging, but a company usually has a hard time to find money when it needs it most. There is no assurance that the company can get the same valuation on its stocks when it needs the money to fund its future growth.

If it finances mainly by debt, it is certainly possible, as other auto companies already did it, but it puts the company into a greater risk.

In terms of working capital, it may be close to zero right now. (Although there appears to be about $1 billion working capital on the balance sheet, much of it may be just some reserve cash for the future capex.) I am not sure if this will continue though. If it has to rely on dealers later, it may need to increase the working capital.

2. Past fast growth in an overvalued market.

Yes, you didn’t hear me wrong. The past fast growth in the last 3 years could be a bad thing!

Of course, just by itself, the fast growth in the past is always a good thing. However, when the market is overvalued, a fast growing company with great awareness among small investors can get highly overvalued.

The only possible relief is the high short ratio. So it is possible that shorts are keeping the pressure on the share price. This force balances the potential over-optimistic valuation, and becomes a good thing instead.

Of course, it is unfair to say a company may be overvalued without giving a valuation first (I will give a valuation under various assumptions later), but at least it is a warning sign.

In fact, that optimism has already affected the CEO Elon Musk himself. As he mentioned recently, he thinks Tesla could pass Apple in market cap by 2025.

Even if we assume Tesla can continue to grow 50% a year for 11 years by the end of 2025, reaching a revenue more than double what GM has this year, for a 10% net profit margin, it requires a P/E of over 20 to pass Apple’s $700 billion market cap. At least for me, a P/E in that range for such a big company is pretty hard to imagine. Even Apple, with much better ROIC, a lot of cash, and a short term earnings boost could not reach that P/E in this overvalued market.

Now, growing 50% a year for 11 years is also going to be extremely difficult to achieve. It may be OK to grow 50% in 2014 or 2015, but this kind of exponential growth has to face a much bigger base later. If Tesla can’t deliver model X and 3rd generation EV on schedule, why would investors believe it will deliver 50% growth without any interruption for the next 11 years? Even if production can grow that fast, we don’t know if the demand will keep up the pace. Unlike solving an engineering problem, economic forecast is very hard to be accurate. There are simply too many moving parts in play to be fairly confident to bet on something in the next 11 years.

Since Musk got a lot of fans right now, a lot of admirers really trust his words. Given the so-believed potential of getting to the size of Apple without significant dilution, it could be particularly damaging if these people are willing to pay whatever the high price for the stock, and eventually get really disappointed by a reality check. I don’t think Musk had realized this, but he may have unintentionally reinforced the confirmatory bias of the shareholders.

Frankly, this kind of over-optimism can be very damaging based on what we have seen in the history, and even a great person like Musk would not be an exception.

3. Competition.

Yes, I just mentioned that competitors are no match for Tesla. However, it is simply not right to ignore competition completely. After all, there are so many auto companies in this world, many of them are good copy-cats and some of them are fairly good at innovation too.

Of course, the success of any competitor doesn’t mean the failure of Tesla, since the potential EV market is huge. In fact, since the networking effect of charging stations is obvious, the success of other EVs may actually help Tesla at the early stage.

Still, it is important to keep competition in mind and remember that things may not be really smooth over the next 5 – 10 years.

4. Non-Profit-Seeking.

Tesla is a for-profit company, but Elon Musk is not a for-profit leader.

It is kind of ironic to me that investors have worried so much about all those managers seeking profits for themselves at the investors’ expense, but now they have to worry about managers not so interested in profits at all.

This is certainly a “new” problem to investors, with not many precedents in history!

Although I am a big fan of Musk and fully admire his intention to help mankind, objectively as an investor, the non-profit-seeking nature could bring in a conflict of interests later. So far, we haven’t seen this as a big problem yet. The patents he gave up may not be that critical, plus it may bring in more goodwill and enthusiasm.

Just as an example, if Musk later finds that demand is not as strong as he expected, he might still choose to push on and invest in capex aggressively, simply because he is not concerned much about the risk. Also, since he said he would personally bet on getting to Apple’s market cap in 10 years, he may have more “commitment bias” and gets more aggressive on growth.

5. Key personnel risk

Elon Musk has showed his intention to leave the company once the 3rd generation car is ramped up to a certain point. Certainly, his contribution has been critical to the company. No other person will likely be an equal replacement.

6. The decline of oil price

Since shale oil has been growing fast and comes at a lower cost than the other non-conventional oil, and the demand has not been growing very fast recently, OPEC has decided to keep production volume without controlling the oil price any more.

While some people may think this is declaring war to US Shale Oil, we have to keep in mind that OPEC’s historical price manipulation was an anomaly in the commodities industry.

If their market share has not been enough to allow them to keep doing that, it will be a fundamental shift in the industry.

While $45 oil may not last long, it is also likely that oil price may just stay in the $60 – $70 range for the long term, which is just enough to keep Shale oil from growing too fast.

This certainly changes some of the economics of EVs. However, I don’t think this is a big problem in the next few years for Tesla, since I believe many more people bought Tesla because of its other innovations and features, rather than to save money on gas. (Those who just want to save money would not buy a much more expensive Model S.)

For the 3rd generation model, the low oil price may reduce the peak demand though. If the 3rd generation EV can save $1500 per year on gas price, this saving is going to be reduced by $400. This may translate to 10% higher cost for a $35,000 car. For regular folks who care about the features and the bills at the same time, it will reduce the eventual peak demand.

7. Short term challenges.

There are many short term challenges. Although they sound very serious, they don’t seem to be big problems in the big picture to me:

I. Strong USD.

The strong dollar has put pressure on all the export companies. It will do the same for Tesla. However, this is not a huge problem in the long term. In this race of currency devaluation, nobody knows what will happen later, and the force balances itself too (more trade imbalance will devalue US dollar).

II. Delay of Model X.

This should have been expected to happen. A delay of a project schedule happens a lot more often than delivering a project on time.

III. Demand from China was not as big as Musk expected.

This is not a long term problem either. It may take some time to get visibility and become another “fashion” product in China, but the ultimate demand is determined by the value of the product. Also, as mentioned above, since the two hurdles are “price” and “charging”, it is expected to get more early adoptors in a rich and small country. Places like HongKong seems to be the ideal target.


One thing that is common for the stock market is that the variation of the valuation is much more significant than the change of the fundamental.

Investors tend to buy/sell based on the mood of the day, rather than trying to quantify everything based on the facts.

So it is important to do a reality check by putting everything into numbers with reasonable and clearly documented assumptions.

Below you will find the basic assumptions of my valuation:

1. Tesla will not get serious challenges from its competitors.

2. Tesla will not have long term problems with demand.

3. Tesla will not have serious long term problems with scaling up the production. However, the speed of scaling up may vary.

4. Tesla may work on newer technology not related to EV, but this potential will not be included in the valuation, since it is hard to stay objective with fantasies or day dreams. It is also hard to quantify the potential in those areas.

5. Once reaching a certain scale, Tesla’s growth will slow down, so that we can use a constant P/E model to estimate its terminal value.

6. We assume the capital needs will be mainly financed by internal profits and external debts. We assume there will be 10 million shares dilution (about $2 billion capital in today’s price), and 4 million shares of stock options.

7. We will use a discount rate of 10% per year.

I certainly don’t claim these assumptions are right or safe, but any valuation has to be based on some assumptions. It is important to clearly document these assumptions and check whether the assumptions are still sensible from time to time.

Variable assumptions:

1. Growth rate and years of growth.

This factor will have the most effect on value. We will try two growth rates: 30% or 40%, and years of constant growth at that rate for 7 years or 10 years. If the company grows 40% for 10 years, its sales will be $89 billion, which is 10% more than BMW’s sales.

2. Profit margin.

Considering that BMW has 20% gross margin and 7.5% profit margin, since Tesla has 26% gross margin right now, we assume the profit margin will be 10%.

Although better economies of scale may improve the margin, we also have to keep in mind that the 3rd generation models will be in higher volume and may have a lower gross margin than the luxury models. The EV credits may not last forever either (currently it is 4% of gross margin).

Also, since we assumed that it will rely mainly on debt financing for its capital needs, the high debt ratio will give higher risk, which also justifies a lower P/E ratio.

3. Terminal P/E multiple.

As I mentioned before, the variation on valuation is often the main source of capital gains/losses. Even if we assume the company has fairly stable earnings and growth, what P/E should we use for the valuation?

The long term return rate of an investment is usually somewhere between the current earnings yield and the ROIC, assuming the company doesn’t invest more capital than its earnings. Whether it is closer to the current earnings yield or ROIC, it depends on the potential market capacity, whether it can constantly win that market over its competitors, and how much it reinvests its earnings. Since we have assumed that Tesla will enter a slow growth phase after 7-10 years, a P/E of 15 makes sense given its large size, high debt ratio and slower long term growth.

Given the current sales of $3.1 billion, if we assume 40% growth for 10 years, 10% profit margin, a P/E of 15, 10% discount rate, 125 million shares outstanding and 12% shares dilution, the fair value is:

3.1 * 1.4^10 * 0.1 * 15 / (1.1 ^ 10) / (0.125 * 1.12) = $370 per share.

Here, we have all numbers in billions, and the formula is the following:

sales * (1+growth rate)^period * margin * PE / (1 + discount rate)^period / (number of shares * (1 + dilution)) = value per share

If we change it to be 30% growth for 10 years, it becomes:

3.1 * 1.3^10 * 0.1 * 15 / (1.1 ^ 10) / (0.125 * 1.12) = $177

Under the assumption of 40% growth for 7 years, it is:

3.1 * 1.4^7 * 0.1 * 15 / (1.1 ^ 7) / (0.125 * 1.12) = $180

Under the assumption of 30% growth for 7 years, it is:

3.1 * 1.3^7 * 0.1 * 15 / (1.1 ^ 7) / (0.125 * 1.12) = $107


Although the valuations I did above show more upside ($370) than the downside ($107), we have to keep in mind that the valuation is based on the optimistic basic assumptions, and those assumptions may simply be wrong.

The bulls may argue that Tesla deserves a higher terminal P/E after 7 or 10 years since it may maintain higher growth for a much longer time, and may even pass GM in sales. That is certainly possible, but it is more like a speculation than the current optimistic assumptions I have already made. For BMW, even in a bull market, it is still being traded at P/E 13 right now.

Clearly, the fair value for high growth stocks is a very wide range. This is mainly because of the difficulty of forecasting the potential growth rates for many years. In the past, not many people have been good forecasters, so it is always better to be on the cautious side.

So what does this article say? Is Tesla a good buy at the current price?

Investors tend to reach conclusions too fast. And value investors tend to assign a fair value to everything.

For high growth stocks like Tesla, the fair value is such a wide range that it is not easy to say what price gives a reasonable entry point. From all the points above, I believe a conservative entry point is around $130. That said, it may be OK to build a very small starting position at a price below $200.

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New Federal Fund Rate Projection and Its Implications

The New Projections

A rising short term interest rate is not any news to the market. The only thing people don’t know is when and how fast it would happen. To the surprise of many market participants, the schedule of the potential Federal Fund Rate hike is accelerated in today’s release compared to the last meeting’s projections.

Screen Shot 2014-09-17 at 2.57.31 PM

As we can see in the projections above, although there are widely different opinions among FOMC members, the average interest rate projections have been increased compared to the release in June, 2014. In average, the interest rate is roughly 1.375% for 2015, 2.75% for 2016, and 3.75% for 2017.

Also, in the last two meetings, there were no projections for year 2017. We only knew that the interest rate for the long term is expected to be stabilized around 3.75%. However, today’s projection shows that the majority of the FOMC members expect the interest rate to go beyond 3% in 2017, or 3 years from now.

Some Implications On Stock Investments

In history, we can find that the yield curve tends to be flattened when the short term interest rate goes up. This will severely impact those companies that “borrowed short and invested long” (borrowed short term loans like credit facilities and invested in long term assets, while getting profits from the yield spread between the long term interest rate and the short term interest rate). Certainly, anyone can do this without much experience and still make a lot of money. In fact, a lot of companies have been doing this for quite long now. Obviously, there is no free lunch in this world. The catch here is that once the short term interest rate goes up, their profit will vaporize or even turn to a big loss. By definition, the long term assets are not flexible since they are long term commitments. Once the short term rate goes up, these companies will be forced to pay a higher interest expense, but still obligated to accept the same long term interest income as before.

For example, a REIT company can borrow short term loans through credit facilities, leveraging up 6-8 times, and invest on long term mortgages (such as 30 years Mortgage Backed Securities). Because there is a 3% interest rate spread and it is leveraged up 7 times, they could easily earn 20% over equity in this way. Also, in the past few years, when interest rate decreased, the fair value of the long term MBS increased and boosted the book value. So on surface, we have seen these companies with increasing book value, very attractive earnings and generous dividends, but once the short term interest rate starts to go up, it will be a completely different or even entirely opposite scenario.

For professionals, all these are not big news. However, I still see a lot of headline news around saying the insurance companies will be benefited by the rising short term interest rates. That statement alone is correct, in the long term. However, in the short term, you will see their book value and comprehensive income getting reduced significantly, since a higher interest rate means lower bond value on their books. Therefore, people who valued insurance companies based on their book value or comprehensive income may actually see a decline in share price in the short term. That said, in general, I do agree a rising interest rate is a good thing for insurance companies, especially when they have shorter maturity bonds in the assets. So essentially, after we balance the effects of a declining book value and a potentially higher future income, a fast rising short term interest rate will benefit the insurance companies with shorter duration assets a lot more than those with longer duration assets.

Another thing investors need to pay attention to is the leverage of their invested companies. For those companies heavily on debt, and financed primarily on short term loans like credit facilities, a higher interest rate means less profit. It may even get to a point of turning profits into losses. Also, some people were talking about coverage ratios calculated from the interest payments on short term loans. Obviously, that can be very misleading. While the long term interest rate could double in a bad scenario, the interest rate on short term loans could go up more than 5 times from here. Therefore, even a good coverage ratio of 5 is not that good if it is calculated from the short term loan’s interest payments in the past few years.

In addition, since many unsophisticated investors primarily focused only on P/E, these high leverage companies’ stocks have enjoyed much on lower capital cost on short term debts in the past. This is unlikely to continue for long.

Take Advantage of The Low Rates for Personal Finance

For personal finance, if one is buying a home, he/she could still enjoy good mortgage rates for now, but perhaps not for long. I have been recommending many of my friends to get mortgages even if they can afford to pay down more mortgages by cash. Many of them felt it is hard to understand, especially when the stock market is inflated, and we suffer from the lack of good alternative investment options at the moment. There are 4 reasons behind this recommendation:

1. Additional liquidity is handy during bad times and we should be prepared. The liquidity also offers flexibility when good opportunities in real estate or stock market come along.
2. In the long term, buying many big cap value stocks right now would still give a return much higher than the current mortgage rates. Also, in 3 years, even the 1 year bank CD has a good chance to give a yield higher than today’s 30 year mortgage rate. There could also be many other good long term corporate bonds that would offer much better yields 2-3 years later.
3. Since interest rate is much more likely to go down than up, some people might consider shorting long term bonds right now. Essentially, getting a mortgage is like shorting a long term bond. However, shorting bond requires capital to support the leverage and also subjects to margin calls. On the other hand, there is no margin call to borrow a mortgage; it requires no equity to support the leverage; its interest payment is often tax deductible, and it reduces the potential maximum liabilities for unforeseen disasters like major earthquakes.
4. Inflation still remains one big threat for the financial market and personal investments. While some people may suggest to hold gold or commodity assets as a hedge against inflation, borrowing a mortgage is a good or maybe better hedge too.

When being asked recently on what can still be a good investment in today’s market, Buffett mentioned that if he is a small investor, he might try to find a real estate property in a still distressed area and borrow 30 years mortgage to invest on it.


Certainly I can not accurate predict what will happen to the interest rates, and everything above is not very meaningful if the interest rates don’t go up or only go up very slowly, but given the obvious trend and the official projections, we should be prepared to avoid the potential risks and seize the opportunity while it still lasts.

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Thinking as a business owner – part II

As I said in my previous post, in theory, we, as long term investors, should all think as business owners. As the teaching of Ben Graham and Warren Buffett, it is right to think we own a piece of a business, instead of own a piece of paper with a price that crawls up and down on the wall street stock chart.

However, I would also argue there are reasons for regular investor who can’t think a business owner. And there are mainly two reasons: lack of information, and lack of control.

First, only a small part of information was disclosed. Sometimes it is to prevent a leak of business secrets and giving advantages to competitors, but more often it is to avoid scaring the investors. However, without complete information, investors are becoming more scared, as we all know the most scary thing is always the “unknown”. Once you get complete knowledge, you can handle it.

Managers often blame wall street analysts (representatives of investors) care quarter-to-quarter results too much. Why do they care so much about quarter-to-quarter fluctuations? Did they know that the business is never meant to have stable straight-line growth every 3 months? It is only because investors are constantly live in fear (generally), and they are prepared to run if things don’t feel right and hopefully they can run faster/earlier than the other longs.

If their knowledge level is comparable to insiders, they wouldn’t be so scared. Sometimes, even after the management told the investors about certain facts, they still get scared, because they don’t fully trust the words of management, since they get cheated from time to time.

Lack of information is one thing, but even if they have all the information, they are not in charge. Can they really stop management from doing stupid or selfish things when the board is on the side of management? (They often have relationships with management, and plus they are getting paid by management.)

So what is the answer to these questions? I think this brings something not many long term investors have carefully thought about. Although these are fundamental issues, we do have ways to mitigate the risks.

1. We have to trust the management before we invest.

If you don’t know the management, or don’t have confidence in management, then you probably shouldn’t invest in that company at all, at least not a big investment. Or we may call it speculation, not investment.

It is hard to really know the management, especially for a small company. But we can always find as much information as we can. Check what the management said and did. If they rewarded investors, cautious on making predictions, not afraid of talking negative things and stay with their words, you can trust them.

With a good management, there will be plenty of pleasant surprises since the managers were cautious to begin with and didn’t set up too much false expectations. On the other hand, with a bad management, it is like sleeping with a bunch of rats, you never know what is going to get left afterwards. (Just think about Bank Of America in 2008)

Buffett said a good business works well even with a bad management, so many people only pay attention to the business, not the management. I think at least half of the bet should be on the management, since good business may survive an incompetent management, but it will not survive a management without integrity, always thinking about stealing from shareholders for their own benefits.

Although I like management to talk about the negative views or their mistakes in public, we shouldn’t take it too far and make it a mandatory requirement before invest in a company. Not everyone wants to directly admit their mistakes, and management’s public statement often has a material impact on the business. For the sake of business reputation, sometimes they are required to stay bullish. This is not intended to fool investors. However, if there are signs of too much hype, or too many failed promises, we should stay away.

One example is Sears’ Lampert. Investors all have to guess what he really wanted to do. Did he really want to turn around this hard-bleeding retailer? Or he wants to slowly liquidate the company? Or he wants to split it to parts, so he can reward the investors in some degree, and yet keep the main company afloat as long as he can, so he don’t have to be irresponsible for 250,000 employees. Maybe he wants to tell investors, but he can’t because that is too much impact to the business, the morale and to the partners/suppliers. In that case, I can understand him not being so straight forward, and I don’t doubt his integrity just because he wasn’t entirely open.

Still, if management is very honest, not shy to admit his/her mistakes, and very conservatives on promises and accounting, that is a huge plus! A P/E of 30 from an honest and conservative management might be equivalent to a P/E of 10 from an all-hype management.

If the management is competent, honest and conservative, you really don’t need to have control and full information on the company. All you need to do is to listen to what management says and act accordingly.

Unfortunately, that is probably asking too much. If we have to invest on a company with mediocre integrity, we have to spend a lot of time to monitor everything, verify what management says against facts, and adjust the expectation accordingly. The whole process is tiring and risk is significantly higher, but may still be worth doing if the value is very appealing. For bad management, you may need to require 4 times more value and still only able to commit a small speculative position.

In a private investment, we wouldn’t entrust a big trunk of money with a friend who is not completely trustable, perhaps we should do the same with stocks too.

2. Make sure the company has a board that represents shareholders’ interest.

If the manager owns a lot of shares, that is a very good sign. If not, at least the board directors should own a lot of shares, or they represent the people who own a big stake. In this way, managers will be monitored and influenced by shareholders.

3. Have enough due-diligent research.

Although a lot of information is not released to public, there is still a lot that is. From 10-K, internet reviews, forums, youtube, investor presentations, and information from competitors, you can find a lot of information that is not easily noticeable by other investors. Without a thorough understanding of the business, certainly there is no way to think like a business owner.

4. Don’t deal with companies that are too hard to understand.

If you feel the company is too hard to understand, or its financial statements are too complex, or its 10-K didn’t disclose a very important piece of information, you may need to stay away from it, or at least mark it as a big risk and give it a big discount. However, if you really trust the management, and strong believe their integrity and their words, you may give complete control to them, and let them take it over from you. In another word, invest solely based on their words and projections.


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A simple derivation of Kelly Bet

While I have searched online quite a bit, I didn’t find a satisfying simple derivation of Kelly Bet formula. So I have worked on it by my own, and it turns out the derivation can be quite simple

Assume X is the distribution of potential investment return (a random variable), and d is the percentage of capital investment (what percentage of net worth you want to put in), assume we bet N times,

Each bet gives return: 1 + d*X

Total return (multiply all individual returns) after N times is:

product(1 + d*X)

Apply a monotone log function on this: log(product(1+d*X)) = sum(log(1+d*X))

So our goal is to maximize this sum, in order to maximize total return.

If we apply taylor expansion on log(1+d*X) and take the first two terms (assuming d*X is not too big, we don’t need the third order term):

sum(log(1+d*X)) = sum(d*X – d*d*X*X/2) = d*sum(X) – d*d*sum(X*X)/2

= d*m*N – d*d*(V + m*m)*N/2

(Here m is the mean of X, and V is the variance of X. And we used the fact that m = sum(X)/N, V = sum(X*X)/N – m*m  ==> sum(X*X) = (V+m*m)*N )

To maximize this value, we need to set the first derivative relative to d to zero:

first derivative = m*N – d*(V+m*m)*N = 0

==> d = m/(V+m*m)  

When m*m << V, this can be simplified to d = m/V  (mean/variance)

Here we can see that d = m/(V+m*m) is another simple yet more accurate formula for Kelly Bet. Many articles uses d = m/V, where V is variance or second central moment, but it really should be second non-central moment, as shown in the Wiki: http://en.wikipedia.org/wiki/Kelly_criterion


A binary game has 60% chance winning, and 40% chance losing. The expected return forms a Bernoulli distribution. Mean is 0.6 – 0.4 = 0.2, variance = 1 – 0.2*0.2 = 0.96.

From the formula d = m/(V+m*m),  d is 0.2/(0.96 + 0.04) = 0.2. Numerical test shows that this is a correct formula, and more accurate than d = m/V formula.

What are the assumptions we have used?

1.  We assumed the distribution is known and doesn’t change.

2. We assumed there are a large of number bets we can do within our interested time frame. (Otherwise, sum(X) is a distribution itself, and is not same as mean *N). For trading, it is not a problem. For long term investment, this might be a problem, but with enough diversification and fairly long term horizon (10-20 years), it should be OK (if we have 7 positions at any time, and each position’s average hold time is 1 year, total we have 70 bets in 10 years, not ideal, but still close to normal distributions, still for long term fundamental investing, we have to be more cautious to use Kelly Bet as it is, since fluctuation within 2-3 years could still be pretty big, human psychology may not sustain such big fluctuations).

3. We assumed d*X is small, so we can ignore the 3rd term in Tayler Expansion. So what small it has to be? If the third term is 5% to 10% of the second term, it may be small enough, and that requires d*X < 0.15 to 0.3.  Normally for fundamental investment or short term trading, this should be closely satisfied, since trading has small returns, and fundamental investment has small capital percentage per-position. However, this condition is very important, if it is not satisfied, the final conclusion is often completely wrong (such like more upside may result in less capital allocation).

So the real questionable assumption here is the #1: distribution unknown. We don’t know the distribution, not even the mean or variance. This means to claim Kelly Bet as the optimal bet size, we have to be very conservative on estimating the mean and variance. Any mistake on the aggressive side is much more devastating than being on the conservative side. In another word, it is “better safe than sorry”.

For stocks, the distribution is certainly not a Bernoulli distribution, the returns are more like a log-normal distribution, although the formula above didn’t use any assumption of a particular distribution, we only need to know mean and variance.


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Kelly Bet explained

There are two reasons for being risk aversion.

The first reason is about “Utility Theory”. If you only have $1000, losing $100 is a big deal, but if you have $1,000,000, losing $100 is nothing. So the same amount of money is less valuable when you have more money. So gaining 10% always gives less value than losing 10%, because the bigger the asset, the less the value of the same amount of incremental asset.

The second reason is the asymmetry of gain and loss. If you lose 50%, you have to gain 100% to get back to even. This is because the returns are multiplicative, not additive. In another word, we want to maximize the expected log-asset, not expected asset.

The basic Kelly bet formula is just  capital_allocation_percentage = mean/variance. (“Mean” is expected excess return)

However, we can’t simply use it as is for the following reasons:

1. Kelly bet only gives you an “upper bound”, and that upper bound is very big. 

Example: If you are playing a binary game (double or lose everything), and you have 60% chance win and 40% chance lose, your expected return is 0.6 – 0.4 = 0.2. Then your variance is 0.6*1*1 + 0.4 *(-1) * (-1) – 0.2*0.2 = 0.96, and the percentage of capital allocation is 0.2 / 0.96 = 19%. In another word, you should bet 20% of all your money in one single bet. That is really aggressive.

This number is still valuable though, since it tells you no matter how aggressive you are, more than this number will only bring you worse result, not better. It also tells you if you have a very large number of bets at the same odds, this is the optimal bet size. Less than this bet size will NOT make it safer for you, only give you less returns.

Now what it means for stocks? Assume BRKB is much undervalued, and there is 50% upside. The mean return is 50%. Now assume BRKB is so safe that the standard deviation is only 35% of stock price. The kelly bet is 0.5 / (0.35 * 0.35) = 4  or 400% of your capital!!

This means no only you should put all your money into it. You should also borrow 3 times of your capital to bet on it. That is assuming there is no liquidation calls when it goes down.

Apparently this number is too big. We can’t use this number in practical case, and almost nobody uses it except in high frequency trading.

That said, it does give a general sense about how the capital should be allocated. For example, if a stock is twice more risky, then we should only put 25% of the position size.

For example, if BRKB is $130 right now, and we think its eventual share price in a year is likely to be in $100 to $180 (assume equal chance in this range), kelly bet gives about 25% of capital size. Some people choose to use half kelly bet, or 12.5%. For an value investor, this size is still too much, since the mean is $140, so only 7.6% upside. Nobody should put 12% of capital into a stock with only 7.6% upside right? Especially when the likely downside is 12% (half of the maximum drop).

Even though Kelly bet is too big for practical cases, the math here remains true. Meaning we should use a bet that is inversely proportional to the square of risk, and proportional to the mean return.

2. Kelly bet assumes you get large number of opportunities within a reasonable time frame, plus with known fixed odds.

3. We have to be careful about using leverage and the maximum downside.

If it can ever get to complete loss (due to leverage usually), then since anything times zero is zero, the eventual result is zero. This is certainly not the optimal result. So whatever the distribution we use, we must make sure it can never gets to zero.  Even the distribution we use doesn’t lead to a zero, in real life, the distribution is never fixed, so it is always possible to lead to a zero when distribution changes temporarily.

In math, when it gets to zero or negative number, the log function applied on it will be undefined.

The beauty of Kelly Formula is that it gives an optimal bet no matter how much risk appetite a person has. So it is irrelevant to risk aversion factor or utility function.

However, if it could ever gets to zero (no matter how small the chance is), the final result is zero. Apparently, in this case, it does matter to be more risk averse.

In another word, in the classic Kelly Setup, you take “no risk” if you play the game long enough, since final result is almost a given. But if it could end up with a zero at any point, it will have a chance to be zero, the final result is not a given. In fact, if you play infinite number of times, the final result is always zero!

Another way to think this, Kelly is try to maximize the expected log-asset, once that number is zero, log(0) is undefined.

So the question is why do we have such a big difference between Kelly bet and realistic bet we should use? Didn’t I just say less than Kelly bet will not make it safer, only reduce overall returns?

Here are the reasons:

a. Kelly bet assumes you can bet many times (> 100 or at least > 40) within a reasonable time frame, and each bet has same known odds. This is OK for casino case, but not for long term investing. For trading, you can do many times, but still each time it may have different odds since market is always changing. If you can’t bet many times, lets say you bet only 3 times within 10 years, you will not have “the law of large numbers” to help you, and then the fluctuations caused by bad luck will be really damaging to you. So in that case, you would need to be much more cautious. In real life, we don’t know the odds and we could be overly optimistic especially when it is fundamental investing, not technical trading, as there is no historical data to backup our estimate. Even if we know the odds, the odds will be different for different stocks at different times. However, among all the three factors (unknown odds/variance, small number of available bets, different odds over time), the unknown odds and its variance is the most significant factor usually, that means we better use a pretty conservative odds/variance estimation before we can apply Kelly Bet!


b. The mean/variance formula is not a precise formula, it is approximate, but usually it is a good enough approximate number. However, during high leverage case, it may get more complicated. Since the kelly bet is optimizing the expected log asset, if asset gets to zero or negative, it is undefined!! So anytime when we apply leverage, there is a chance for asset to go to zero, and therefore kelly bet may not apply. That is why using kelly formula can be risky or conceptually wrong when used in high leverage bet.

c. The psychological challenge is too big if the fluctuation is too big.

d. As mentioned above, we have to care about the possibility of changed distribution and that may cause a wipe-out event. Any possibility of wipe-out event will break the promise of optimal result given by Kelly Bet.

What about for multiple stocks in a portfolio? The good news is that kelly bet is additive. So if for BRKB, kelly bet says you should put in 20%, and for UBNT, kelly bet says you need to put in 10%, you should just do so. This is assuming the sum of both proportion ratio is less than 100%. In this case, the sum is 20% + 10% = 30%.

What if Kelly bet says to put 80% to BRKB, and 70% to UBNT? If the sum goes beyond 100% and you don’t want to use leverage, you can scale it down accordingly. So use 80% / 1.5 = 53% for BRKB and 47% for UBNT. However, this is not really optimal in long term growth. For optimal long term growth, usually we need to put more into the one that gives higher expected excess return, and in this case, we may need to put more into UBNT since it gives higher return. But this would certainly increase risk. Linearly scale-down usually gives better/optimal risk profile within single period, but sacrifices the long term growth.

The above is assuming there is no correlations between stocks, if you have strongly correlated stocks such as two banks in the same industry, the correct formula is to multiply the expected return vector by an inverse of covariance matrix. That math is getting a bit more complicated.

Another word of truth unrelated to this: since the average correlation between stocks is about 15%, math shows that over-diversification will not help. Having a portfolio of 7 stocks is not much different from having a portfolio of 700 stocks, in terms of risk diversification, assuming these 7 stocks have average correlation (15%), and equal sized positions.


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How Engineers do Business

After studying a lot of Elon Musk and Robert Pera, I found they have a lot of similarities.

First, they are both engineers and later started to do business.

The way they do business is quite different from traditional business schools.

Why would Tesla choose to not make money on car service, and gives supercharging for free? Why would Ubiquiti prices something that can easily sell for $1500 – $2000 (still a lot cheaper than competitors) for $1000?

Why would Tesla sell their luxury car at the same price in China as US? Didn’t Musk know that China’s demand is already so high, and reducing the price of a luxury goods won’t necessarily boost the demand? Plus all the other luxury brands are often selling twice more expensive in China.

Why would Ubiquiti give out software for free? Is it not nice to have a steady revenue stream by charging the annual license fees like other big companies did?

Instead of milking every penny out of their consumer, they pass on the value to consumer.

Instead of playing all kinds of tricks and put hidden charges, they put everything straight forward with just one price tag.

Instead of just getting excited by the profit growth, they also get excited by the value they create.

Instead of getting the best margin possible, they focus on getting the best efficiency possible.

Instead of following everyone else on conducting business, they have their own business model.

What happens then? Is that a good choice or a bad one?

With Tesla and Ubiquiti, we see trust from customer, fans all around the world, efficient corporate structure and production, and amazing growing speed that is rocketing way above expectations or even imaginations.

The disruption they brought to their industry is profound, which goes much beyond a particular industry. It brings a new perspective on how we conduct businesses, and it is what the engineering mind brings to the business world.


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The flaw of traditional valuation model

The traditional valuation model, whether it is the model from DCF or wall street’s popular P/E multiple method, requires estimating a fair value of a stock, and either use that value to see the upside potential (potential return of investment), or apply a discount as “margin of safety”.

This model, if used simply as it is, is inherently flawed. The reason is that it doesn’t consider the possible variations of the fair value. Or using the language of statistics, it doesn’t consider the “variance” of the expected mean value.

Some people may argue that the “riskiness” of the investment is already compensated when we change the discount rate (or cost of capital) for different situations. If it is a highly leveraged company, we will use higher cost of capital rate, or high discount rate, or lower P/E multiple.

However, this kind of “compensating” method is pretty ambiguous. Because the compensated higher margin of safety really consists of two parts:

1. The lower expected mean value:

If a company has high financial leverage or operating leverage, it may have 20% chance to go bankrupt in the next 5 years, so 80% chance we have $100 share price, and 20% chance we have $0 share price, the expected mean value is $80 share price. In this case, the additional discount required is 20%

2. The additional return required to compensate the additional risk observed:

This is also a part of the high discount we needed, but it is hard to quantify this either from intuition or from math, since it really depends on personal risk tolerance and the position size.

So if a company has debt to equity ratio of 2 to 1, should we use 12% discount rate? or 10%? or 15%?

What is the justification for that percentage? And how much of that percentage is the part 1 of the premium, or the part 2 of the premium?

If a company has a clearly bad CEO who is very likely to make a very expensive acquisition to waste all the cash on the balance sheet, how much discount should you apply to that fair value?

That is why I call the traditional method very “ambiguous”.

In the modern finance (quant finance), the situation is much clearer, at least in the theory. We just estimate a mean value with different scenarios assuming a probability for each scenario, and then estimate the variance of that mean value given those scenarios. Then we will apply a discount based on the variance.

Despite the additional clarity, there are still two challenges:

1. How much additional discount we need for a given variance still depends on personal risk tolerance.

This problem is not really an issue in two cases:

a. If the position size is very small, and the individual company’s risk can be fully diversified away, we can simply ignore the variance completely. In practical cases though, manual selection of stocks requires a lot of research and follow-up, plus best opportunity is very rare, so this kind of massive diversification is not practical. Still, if position is smaller, variance is not that bad any more, therefore we can require less discount on the risky stock.

b. There is a well defined upper bound of max position size for each stock given its variance and expected return.

The beauty here is that this upper bound (as defined in “Kelly bet”) does not depend on individual’s risk tolerance. No matter how aggressive you are, once you risk more than this limit, you are simply wrong!

“Kelly bet” defines the upper bound, but it doesn’t tell you the “right” bet size, since practical situation is quite different from a theoretical setup, where you don’t have a large number of identical bets waiting for you, and you don’t know the predefined risk-reward ratio. So the “right” bet size still depends on personal risk appetite, but at least we have some theoretical ground work here, and some people just choose “half kelly bet” as their choice.

In Kelly bet, the right position size should be inversely proportional to variance, and proportional to expected return. Remember variance is square of standard deviation, this means if a stock is twice risker, we need to put 25% of position size, or for the same position size we have to require 4 times more expected return.

For example, if buying BRKB has 15% standard deviation, and buying sears has 60% standard deviation, and I am willing to put 60% of my net worth in BRKB if it is 33% discounted (50% expected return), it means I can only put 60% / (4 ^2) = 4% of my net worth to sears if it is expected return is also 50%. Or I have to require 50% * (4 ^ 2)  = 800% expected return to put 60% of my net worth into sears.

This is why I found it wrong when many value investors estimated sears’ real estate asset value and bet big on it. Yes, it does have a lot of asset value, but given its deeply troubled retailed business, the uncertainty of how many years of continued bleeding, the cost of liquidation, and the illiquid nature of real estate asset (it is hard to sell a lot of them in short term), the variance is very big. Therefore, applying 33% discount or even 50% discount may be not enough, especially when someone tries to bet big on it.

2. It is already very hard to estimate fair value, it would be even harder to estimate variance.

This is true, but a general sense would still help here. Plus, if we can list out a few scenarios and its probability, we can have a very rough estimate on the variance.

For quite some time, I was always puzzled about how much certainty I would need before making an investment. Since “certainty” is what Buffett cares most about. If I require too much certainty, it will bring very few opportunities. Too less, I am risking too much.

Later I figured out that, the certainty is important, but we can’t expect too much. There is always risk in an investment. What we should do is to adjust the position size and/or the margin of safety to compensate it.

A word of caution is that impact of risk goes quadratically, not linearly. So twice of risk (standard deviation) would require 4 times more potential return or 4 times less position size. Since it is very unlikely to get that much potential return, what usually ends up is a much smaller position size.

Apparently, this makes a very risky investment not worthwhile at some point, since we don’t want to diversify too much and we have limited time to do the research and follow-ups.

In conclusion, I think we should not neglect “variance” when we evaluate a stock, as it is as critical for evaluation. We should also remember, higher variance doesn’t always require a much higher expected return or higher discount, it really depends on how diversified we are. This concept of quant finance can help to refine the traditional valuation model.

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