# Stylus Capital — Public Research Corpus --- # Is Bitcoin the Ultimate Momentum Asset? Published: 2026-07-22 Authors: Burak Yenigun, Robert Carver Topics: Bitcoin, Ethereum, momentum, managed futures Canonical: https://stylus.digital/is-bitcoin-the-ultimate-momentum-asset PDF: https://stylus.digital/research-pdfs/Is-Bitcoin-the-Ultimate-Momentum-Asset.pdf Eight years ago, our co-founder Burak Yenigun called Bitcoin the ultimate momentum asset: the only liquid asset with no fundamentals to anchor its price. In this research note, Burak and Robert Carver revisit that claim. Does the evidence support it? RESEARCH  ·  Q3 2026 Is Bitcoin the Ultimate Momentum Asset? BY BURAK YENIGUN & ROBERT CARVER Eight years ago, our co-founder Burak Yenigun called Bitcoin the ultimate momentum asset: the only liquid asset with no fundamentals to anchor its price. In this research note, Burak and Robert Carver revisit that claim. Does the evidence support it? DOWNLOAD AS PDF ↓︎ This piece was co-written by our co-founder, Burak Yenigun, and research advisor Rob Carver. We knew well in advance that they would not agree on the subject, so we present it as a debate between the two authors. Burak CO-FOUNDER, STYLUS CAPITAL I have long maintained that Bitcoin is the ultimate momentum asset. Eight years have now passed since I first articulated this view, long enough perhaps to revisit it and see whether there’s any empirical evidence supporting the claim. But first, let me explain why I believe this to be the case. In short: Bitcoin is the only liquid asset with absolutely no fundamentals — nothing to act as a center of gravity to stabilize the price. All other liquid assets we can think of have something that can act as an anchor around price. To see why, consider equities, bonds, commodities, and currencies. For equities, you have earnings. Business prospects and expectations about future earnings may fluctuate over time, but the fundamentals ultimately matter, often with a vengeance. AMC Entertainment, a meme stock favorite, surged 10x within weeks. It has since fallen more than 99% from its peak1. The fundamentals killed the party, once and for all. Even meme stocks must eventually face the cold hard business realities. For bonds, it’s even easier to see the price anchor: bonds promise a stream of payments, subject to credit risk. Investors can calculate a fair value depending on their view on interest rates and default probability, which anchors the price. For commodities, there are the extraction costs. What it takes to mine an ounce of gold or pull a barrel of oil out of the ground matters — when fracking transformed supply, oil prices collapsed despite rising demand. Speculative manias cannot last too long when physical reality can “cap” prices or drag them around. For currencies, you have central banks actively trying to stabilize the price of the currency against a basket of goods and services, using a variety of policy tools like interest rates. Sometimes they fail, but more often than not, especially in developed countries, they are successful in keeping the currency stable. When central banks do fail — usually by signaling that they no longer care about price stability — their currencies present speculative opportunities, not unlike cryptocurrencies. So, looking at our typical menu of liquid assets, each one of them has some anchor, some center of gravity around price. Now, to be fair, there are some assets as devoid of fundamentals as bitcoin. The problem is they are illiquid, so you cannot easily trade them. Take collectibles: an Honus Wagner baseball card sold for $2.8 million in 2007, more than 100 times its price 30 years prior. Then, in 2022, another (apparently lower quality) Honus Wagner sold for $7.5 million. What’s the fundamental value of a baseball card? Impossible to calculate. Its utility is limited: you could hold it, admire it, maybe brag about it, and hopefully sell it later at a higher price. As Ken Goldin colorfully noted, “No Wagner card has ever sold for less than it was previously purchased for.” Note how “number go up” appears to be a core appeal of baseball cards, which should sound familiar. A common objection to this line of reasoning is that bitcoin has “mining”, like gold. You need specialized chips and a lot of electricity to mine bitcoin. On the surface, this seems conceptually similar to commodities, but there is a critical difference people often miss: unlike commodities, bitcoin’s supply is totally inelastic to price. Annual gold production went up from 2,299 tonnes in 1995 to 3,556 tonnes in 2018, responding to higher prices. Bitcoin is up two-hundred-fold in the past ten years, yet the “mining” reward has fallen from 25 to 3.125 coins every ten minutes — an eight-fold reduction, exactly as scheduled by the network’s algorithm. Higher prices cannot, and did not, unlock more supply2. Therefore, thinking of bitcoin in mining terms is a distraction. What matters is: there will only ever be 21 million bitcoins3, just as there will only ever be fewer than 200 Honus Wagner baseball cards (some of which have been lost — again, not unlike bitcoin). The combination of these factors means bitcoin is the first asset that completely lacks fundamentals, like art and collectibles, but is liquid, unlike art and collectibles. It is also just different enough from every other asset to generate seemingly endless waves of narratives. It started out as a peer-to-peer, permissionless payments tool, then became a store of value, then an inflation hedge, then digital gold. It is a confusing enough asset that many people are fooled by these narratives. My favorite example is Nassim Taleb first hailing bitcoin as insurance against central banks’ mistakes, and then dismissing it as “worth exactly zero” a few years later. He was wrong in both cases. That someone with so much experience in financial markets can be so wrong about bitcoin — not once but twice — illustrates how easily bitcoin confuses people. The constant flicker of a volatile price ticker, perfect scarcity, susceptibility to false narratives, internet-scale access… If someone had asked me to design the perfect momentum asset, I wouldn’t have been imaginative enough to come up with Bitcoin — not in a hundred years. So, the question is: am I right? Now that eight years have passed since my original claim, let’s check if we can find statistical evidence that bitcoin is, indeed, the ultimate momentum asset. Over to Rob. Rob RESEARCH ADVISOR Burak makes an interesting case. But what makes a good momentum asset more generally? We want something that will go up, and carry on going up; and for which a reversal in price will be followed by further bad news for those with long positions. The attributes that would make assets more or less suited to momentum trading strategies are not obvious. Explanations from the world of academia mostly focus on delayed reaction to news, or investor preferences to sell assets at a small profit and hang on to losers; a phenomenon dressed up by economists as a “risk premia”. It is unclear why certain assets would be more susceptible to purchase by people who are particularly slow to react, or who are vulnerable to the cognitive biases that create behavioural risk premia. Instead it is easier to think about what would make a good mean reverting asset, and hence a terrible momentum asset. Let’s imagine an asset where there is a fundamental value; an equilibrium price. We shall also pretend that there is widespread agreement on the precise level of this equilibrium. Furthermore, we imagine there are no “limits to arbitrage”; no significant costs or restrictions which would prevent us from buying or selling if the price wandered too far from its fundamentals. Such assets are rare in the world of outright prices, but are common in cross asset relationships. For example, the value of the calendar spread between two adjacent delivery months in the gold futures contract is driven by numbers that are fairly easy to estimate, and can be plugged into a well-known formula. There are occasionally limits to arbitrage, due to the complexities of deliverability and warehouses, but the calendar spread price will usually revert to its fundamental value. Trading momentum here is unlikely to be a profitable exercise, except perhaps for extremely short time frames. Reversing this argument, what are the likely characteristics of a good momentum asset? Clearly it must be something where there is no fundamental value, or where that value is not generally agreed, or where there are substantial limits to arbitrage. Burak’s argument that bitcoin ticks all of these boxes is compelling. But is it borne out by the data? A cursory look at the evidence seems to support his case. Here are the returns from trading bitcoin and ethereum using a particular momentum signal4: FIG. 1Cumulative returns from trading Bitcoin and Ethereum with a momentum strategy. It looks5 fantastic. We see the classic “up the escalator, down the stairs” positive skew of a momentum account curve, with infrequent big profits interspersed by longer periods of modest losses whilst waiting for trends to occur. The Sharpe Ratios come in at 0.98 and 0.90 for BTC and ETH respectively. Case closed? Well, no, Burak’s thesis is about relative performance. I could claim to be the ultimate chess player, but nobody would believe me until I’d played a few matches against Magnus Carlsen. We need to look at the performance of other assets before we can decide who the winner is. The easiest way to trade momentum across different asset classes, as any CTA will tell you, is via the futures market. In my futures data set I have the following asset classes, where the number in brackets is the quantity of instruments6: Equity indices e.g. S&P 500 (25) Bonds and interest rate futures, e.g. US 10 year (18) Energies e.g. WTI Crude oil (6) Agricultural products e.g. Corn (13) Metals e.g. Gold (9) FX, e.g. USD/EUR (17) If my maths is correct that is 88 instruments. We can also trade a couple of crypto coins in the traditional futures market, but I can get data for a wider range of instruments by using the spot market. If I also include the 40 most liquid crypto coins in my database of spot prices, I get a total universe of 128 instruments. If I run a momentum strategy on each of the instruments in this universe I get the following, where the y-axis is the Sharpe Ratio7 of each: FIG. 2Sharpe Ratio of momentum performance since 1972 across instruments. To avoid creating a plot with an unreadably small font I’m only showing the top and bottom 20 instruments. I’ve also highlighted each asset class in a different colour; grey is crypto. On the extreme right hand side we have seven crypto coins in grey which are amongst the most profitable including bitcoin and ether; though they cede the top spot to Korean 10 year bond futures. But there are also a couple of cryptocurrencies with far worse performance; as you can see from the hint of grey on the left. What happens if we take the average of the Sharpe Ratios in the plot above for each asset class? FIG. 3Average Sharpe Ratio per asset class of momentum performance since 1972. The average performance for crypto isn’t the crème de la crème with the top spot held by Metals; actual Gold seems to have done better than digital gold. But at Stylus we’ve only been trading bitcoin since 2018, whereas I have price data going back much further for most futures contracts. It’s a well-known phenomenon that the performance of trend following in most asset classes hasn’t been as good recently as it was in the past. So, we’re comparing bitcoin for the last ten years, where trend following hasn’t done so well overall, with the likes of Corn with over 50 years of performance; of which the first few decades were pretty good. To get a fairer comparison then, let’s exclude the period before 2018 from our results: FIG. 4Sharpe Ratio of momentum performance since 2018 across instruments. Well the good news is with everyone else pushed down, bitcoin and ethereum have slid neatly into the top two places. What about the sector averages? FIG. 5Average Sharpe Ratio per asset class of momentum performance since 2018. Overall, this makes for a more depressing picture than the full sample, but crypto is now flying high and running a close second to Bonds. However, by restricting ourselves to post 2018 data we have also made it harder to draw firm statistically grounded conclusions. In particular, it’s much easier to look like a genius if you’re trend following an asset that has gone upwards in a straight line for several years. We need to measure the alpha from our raw momentum performance; the extra juice that isn’t attributable to just being long the market. We can do this with the standard CAPM regression, where the returns of our momentum strategy are on the left hand side, and the market returns on the right. For “the market” I use a long only strategy on the relevant instrument, but with the same volatility scaled position sizing rule as for trend following. Here are the average alphas by asset class, focusing on the period since 2018: FIG. 6Average alpha per asset class of momentum performance since 2018. The relative ranking hasn’t changed much from when we just used Sharpe Ratios: bonds and crypto are still in first and second place, and we can see that their relative performance hasn’t been harmed after we factor out its excellent long only performance. Incidentally, were I to plot the instrument by instrument figures, you’d see ethereum in 6th place and bitcoin just above it in 5th. Those are respectable numbers in a field of 128 contenders, but they are not what you would expect from the “ultimate” momentum assets. This result may not bother you too much; if you think that crypto will continue to be in a secular bull market of the same magnitude as that seen post 2018, then you can ignore the alphas and just look at the Sharpe Ratios. And you may also believe that there is something special about bitcoin (and maybe ethereum) — the results in figure 4 do look pretty compelling. But is this result statistically significant? Or could it be just down to luck? After all, just over eight years of data isn’t very long to evaluate the performance of a relatively low Sharpe Ratio strategy like momentum. To find out, we need to look at the distribution of return statistics. I construct these in the following way. As I’m going to focus on the post 2018 period, which is just about eight years, I’m going to create a series of synthetic eight year returns for trend following in each instrument. I do this by resampling with replacement eight years’ worth of return history, drawn from the actual performance achieved by momentum in the available time period. For each eight year price history I measure the Sharpe Ratio. We can then look at the distribution of these Sharpe Ratios, rather than just the average. FIG. 7Box plot with distribution of Sharpe Ratio estimates for each instrument, data since 2018. The resulting chart is very similar to figure 4 but instead of just a bar chart showing the Sharpe Ratio (SR) for each instrument, we have a box plot with the distribution of SR. Whilst bitcoin, ethereum are still top of the tree, we can see that the uncertainty of historic SR estimates, illustrated by the relatively wide width of each bar, means they’re not necessarily significantly better. We can check this result by running a type of statistical test known as a T-test. This compares the return series for two instruments and calculates a p-value. The p-value is the probability that the results are just a fluke. A p-value below a predetermined critical value, often 1% or 5%, implies that it’s very likely that one set of returns really is better than the other; and not just a statistical coincidence. FIG. 8p-value from T-test of performance since 2018 compared to bitcoin. Lower numbers mean bitcoin is better. Red line is 5% critical value. Only instruments with a p-value above the critical value are shown. Figure 8 shows only the markets where the p-value is greater than 0.05, and where we can’t be confident that bitcoin has a superior post 2018 Sharpe Ratio. The red line shows the 5% critical value; anything with a p-value below that has a 95% chance of being inferior to bitcoin. As there are 90 instruments in the plot, we know that only around 27 fall into the category of having an inferior Sharpe Ratio confirmed by a low p-value. Eight years just isn’t long enough to gather statistically significant evidence about performance. To summarise then, there is no evidence that crypto as an asset class is the ultimate momentum asset. However it does look as though bitcoin and ethereum can lay some claim to that title, at least if we exclude the performance of traditional assets prior to 2018 when trend following seemed to work better, and if we ignore the tailwind provided by the secular upward trend in crypto prices over the last eight years. On that basis bitcoin and ethereum have the highest Sharpe Ratio, although it’s too soon to say if we have enough statistical evidence to be confident. In the interests of fairness I will let Burak have the last word. I am particularly interested in his reasoning on what makes Bitcoin, and perhaps Ethereum, in particular so special. Surely all crypto shares the property of lacking an equilibrium value to which prices will mean revert? Burak CO-FOUNDER, STYLUS CAPITAL Rob’s question is fair. If Bitcoin has no fundamentals, neither does Dogecoin. So why treat them any differently? Back in 2018, having declared bitcoin the “ultimate momentum asset”, we chose to trend-follow the top ten coins by market value, with half the risk going towards bitcoin and ethereum. The idea was simple: trend-following is known to work better on indices like the S&P 500 than on single stocks, so we figured the largest coins would behave more like an index and trend better — and they did8. It also helped that most major coins back then were broadly bitcoin-like — supply completely inelastic to price — so we didn’t have to worry about coins with a potential “fair value” slipping into the trading universe9. But none of the decisions above were driven by explicit reasoning about Rob’s question. So let’s do that now: why stop at the top ten coins and not the top hundred, or even the top thousand? Is there really a difference between Bitcoin and Dogecoin? How about Dogecoin and “Baby Doge Coin”? I think there is, for two reasons. The first is liquidity. When a coin trades thinly, a single large order can knock the price around, causing short-lived dislocations that quickly mean-revert and hurt trend-following. This argument is compelling, and research does suggest a strong effect in crypto, but annoyingly (for me) it barely shows up as an effect in the major futures markets (maybe illiquidity begins to hurt trend only beyond a certain threshold?). Still, I would argue the strength of this effect in crypto alone justifies leaving the less liquid coins out of the evaluation. Plus, deeper research in traditional finance might yet reveal similar phenomena — maybe we just have to look further along the illiquidity curve. The second reason is legitimacy. If a few friends come together, mint a random coin, and get it listed on a decentralized exchange, does it automatically deserve a spot in our evaluation universe? Again, I would argue not. We should demand, for lack of a better word, some legitimacy. Traditional assets do not quite have this problem since their legitimacy is established through other means long before they have liquid futures markets to trade — more on this later. The problem, of course, is that bitcoin started out as an obscure project among a few online friends too, so where do we draw the line on legitimacy? Vitalik Buterin, Ethereum’s creator, has an excellent essay on this. His argument is that legitimacy is fundamentally a social process: something becomes legitimate when enough people believe that enough other people will treat it as legitimate10. This belief is reinforced and sustained through signals like continuity and track record. Bitcoin was launched with serious objectives and got adopted, becoming increasingly legitimate over time as its central claims — digital scarcity above all — held up over the years. Dogecoin did the opposite: it started out as a joke with no serious premise at all, but got increasingly legitimate over time through little more than the mindshare it built with memes. Despite its “unserious” origins11, I’d have no qualms about including Dogecoin in our evaluation universe. Conversely, hundreds of cryptocurrencies were launched with perfectly “serious” grand objectives and narratives (appeals to legitimacy? One is reminded of the art market again), and yet most were forgotten within months. Some continue to trade thinly, but I’d vote against including them in our universe. Interesting to note how we never have to pose these legitimacy questions about commodities. “Is oil legitimate?” is self-answering in a way that makes the question amusing. “Is gold legitimate?” is perhaps a bit less self-answering, which hints at some social machinery at work there as well, but we’ll leave that aside — that discussion has been had many times elsewhere. In short, I’d argue we should only consider coins that are both legitimate and liquid. Conveniently, there’s a single metric that captures both: market capitalization. A coin with a larger valuation is, almost by definition, both more liquid and more widely perceived as legitimate — people have revealed a preference for holding it over the alternatives. So here’s how I’d extend my original “Bitcoin is the ultimate momentum asset” claim to the whole asset class, to future-proof things: Crypto is the ultimate momentum asset class — where “crypto” means a market cap weighted index of coins that share Bitcoin’s defining trait: there’s no way to calculate a fundamental value for them. For now, for the 2018-to-date period, sticking to Bitcoin (or Bitcoin plus Ethereum) as a proxy for a market cap weighted index of cryptocurrencies would suffice. Considering their dominant market cap over the period, expanding the list further would barely change the results12. In either case, I would call this a mildly encouraging start for the “ultimate momentum asset” thesis, but as we saw from Rob’s analysis we need years, if not decades, to get meaningful results. Such is life when dealing with financial data. Still, if I’m right, the statistical evidence should get stronger over time. So let’s revisit this idea in another five years. FOOTNOTES GameStop, however, has fared surprisingly well. Down “just” 74% from its peak, perhaps because the company took advantage of the bubble to improve its financial position. An interesting case that shows how price can sometimes influence fundamentals! A similar story applies to Tesla. Similarly, no amount of money in the world can create a new original Da Vinci painting, beyond the ones that are already out there. Perhaps this is why many artworks get more valuable after the artist passes away. Assuming, of course, the network’s design stands the test of time. That’s a separate discussion, but it is a reasonable assumption both generally and for the purposes of this piece. An equal blend of exponentially weighted moving average crossovers on daily prices, with look backs of 2,8 days; 4,16 days; 8,32 days; 16,64 days; 32,128 days; and 64,256 days, on the fast and slow crossover respectively. Positions are adjusted each day for the strength of the trend and the volatility of the price. A few important notes about this and subsequent graphs; the y-axis is for an arbitrary amount of capital, but the returns shown are cumulative summed daily percentage returns. This means they are not compounded, and are equivalent to plotting the log of the account value. Returns are shown before costs, but these will be minimal at the speed we are trading at. This does not represent all the possible instruments we could trade, but is a selection of those that are both liquid and have substantial trading history. For simplicity I haven’t deducted a risk free rate from these figures, as is the norm for Sharpe Ratios. For futures contracts the risk free rate is already implicit in the price. But this will slightly favour the results for crypto, which will be a few basis points lower once the risk free rate is deducted. Years later, both internal and external research showed that larger coins indeed trend better in a statistically meaningful way. Increasingly, some coins are acquiring “revenue models” or “token buyback mechanisms”. I don’t think these are the slam-dunk valuation bases many believe they are, but they do threaten the “no valuation basis” claim for the coins in question, so I’d exclude them in future analysis just in case. The similarities to the art market just keep piling up. Importantly, the underlying technology ensures that both Bitcoin and Dogecoin remain scarce. None of these serious or unserious claims would have mattered if this key feature, digital scarcity, had failed to hold up. If anything, it would strengthen the results in favor of the thesis. Other large-cap coins like Solana have also trended well. IMPORTANT DISCLOSURES This material has been prepared by Stylus Capital Partners, LLC (“Stylus”) and is provided for informational and educational purposes only. It is not intended to provide investment advice, nor does it take into account the specific investment objectives, financial situation, or needs of any particular investor. Before making any investment decision, recipients are urged to consult with their own financial, legal, tax, and other professional advisors. This material does not constitute an offer to sell, or a solicitation of an offer to buy, any securities or financial instruments. Any such offering will be made only pursuant to a confidential offering memorandum and subject to the terms and conditions set forth therein. No investment decision should be made based solely on this material, which is illustrative in nature and may include assumptions that are subject to change without notice. Stylus’s actual investment strategies and positions may differ materially from any views or models presented herein, and are subject to change based on client mandates, risk considerations, transaction costs, market conditions, and other factors. Nothing in this document should be construed as a recommendation to buy or sell any particular security or investment. The securities or companies mentioned herein are for illustrative purposes only and do not represent actual portfolio holdings or future intent. All investments involve risk, including the risk of a complete loss of capital. The value of investments and the income derived from them can go down as well as up, and there is no assurance that any investment strategy will achieve its objectives. Investments involving leverage, derivatives, short selling, or other complex instruments may carry higher degrees of risk and may not be suitable for all investors. Past performance is not indicative of future results, and forward-looking statements should not be relied upon as guarantees of future outcomes. This material may reference data and analysis derived from both internal and external sources, including public and subscription-based databases. While we believe such information to be reliable, Stylus does not guarantee its accuracy, completeness, or timeliness, and disclaims any liability for reliance on it. The views and opinions expressed are those of Stylus as of the date indicated and are subject to change without notice. This material is not directed at or intended for distribution to any person in any jurisdiction where such distribution would be unlawful or where Stylus would be subject to additional regulatory requirements. --- # A Strategy for (Micro)Strategy Published: 2025-04-25 Authors: Robert Carver Topics: Bitcoin, MicroStrategy, systematic investing, relative value Canonical: https://stylus.digital/a-strategy-for-microstrategy PDF: https://stylus.digital/research-pdfs/Stylus-Capital-A-Strategy-for-MicroStrategy.pdf MicroStrategy trades at a premium to its bitcoin holdings, but buying bitcoin and shorting MSTR is not a free lunch. In this first research note, Robert Carver explores an alternative strategy, and walks through the real-world examples and frictions. RESEARCH  ·  Q2 2025 A Strategy for (Micro)​Strategy BY ROBERT CARVER  ·  FOR STYLUS CAPITAL MicroStrategy trades at a large premium to its bitcoin holdings, but buying bitcoin and shorting MSTR is not a free lunch. Robert Carver explores an alternative strategy, and walks through the real-world examples and frictions. DOWNLOAD AS PDF ↓︎ 01Introduction Would you like the chance to buy $1 for 50 cents? That isn’t easy, but there are people out there willing to pay a dollar and receive 50 cents in return. Of course I’m talking about MicroStrategy. A firm consisting mostly of a pile of Bitcoins (that’s the 50 cents) with a money losing software business thrown in, whose market cap is significantly greater than the sum of these parts (that’s the dollar). (I will refer to the firm by its ticker, MSTR, so I don’t get confused in talking about Strategy, the firm, and a trading strategy which involves trading Strategy). If we can sit on the other side of this trade, we can make some apparently risk free profits. Sadly, it’s not as easy as that. 02A Brief History of Capital Component Trades The efficient markets theory purists would be very surprised that anyone would want to pay a dollar for 50 cents, or that you could buy a dollar for a couple of quarters. But it happens. The purest example of this would be something like a closed end fund / UK investment trust. In the UK many of these funds have traded at a discount over the last few years. If you were able to short the underlying assets and buy the fund, you would make a profit when/if the discount closes1. Please indulge me in a brief history lesson. In the late 1990s an electronics retailer called Dixons (now subsumed into Currys plc) owned one of the early UK-based internet ISPs2, Freeserve. This was subsequently listed with Dixons retaining most of their shares. Because of the internet boom, the Freeserve stake alone ended up being worth many times the market cap of Dixons, implying that the quite profitable Dixons shops had a massive negative value3. An apparently straightforward trade would have been buying Dixons shares and shorting the overvalued Freeserve stock. But it wasn’t easy. Why not? Well, principally because the stock borrow fee on Freeserve was substantial. Because most of the shares were owned by Dixons, getting hold of shares to short was extremely difficult. These trades are the living embodiment of the Keynes quote: “Markets can remain irrational longer than you can remain solvent.” Just because something trades at a relative discount or premium doesn’t mean the gap cannot widen before gravity brings it down4. With these dark warnings from history in mind, let us look at MSTR in more detail. 03A Brief History of MSTR Microstrategy (as was) was founded in 1989 by Michael Saylor, listed in 1998, and for most of its existence was a boring software company with a market cap that rarely exceeded $1bn. Even now, their website’s front page is mostly about “AI” (artificial intelligence) and “BI” (business intelligence, apparently – an oxymoron?), “the cloud”, “enterprise scale” and the buzzwords go on, and on… The software business currently has a modest revenue of about $450m a year. But they aren’t very good at software since they appear to be losing quite a bit of money on operating expenses. However, on their website there is a tell-tale menu option: “Bitcoin”. Click on that, and there is a blizzard of figures, none of which have anything to do with “AI” or “BI”, and everything to do with “BIT”, and “COIN”. Moreover, if you click on their latest financial presentation, there is not a single mention of their software business until you get to the appendices! It’s all mostly about Bitcoin, with a few slides on their convertible bonds, their new website, and … their new merchandise store. This isn’t a company – it’s a cult! This all began in August 2020 when MSTR bought $250m of BTC as a “treasury reserve”. Corporate treasuries are where you keep your corporate war chest of cash. Often it’s cash that will be needed in the fairly short term for working capital or meeting payroll, so usually it’s kept in fairly safe assets like treasury bills. Sometimes firms will get a bit racy, and push into stuff that’s higher yielding. Usually that goes badly. Putting your corporate treasury into a highly volatile asset like Bitcoin with no natural yield seems…. well frankly it’s highly irresponsible. It really ought to be against the law. Anyway, rant over: that brings us to the present day, when the MSTR numbers look like this as I write this (from strategy.com, menu option Bitcoin, though the numbers will be different when you check it yourself): MSTR BY THE NUMBERS MSTR market cap $71.6bn Debt and preferred $8.9bn Enterprise value $80.5bn Bitcoins owned 500k Bitcoin price $88.6k Value of BTC $44.2bn Cost of BTC5 $32.6bn Cost of BTC is not on the website; derived from the Q4 report and other information. If you were to buy all the equity and the debt, costing just over $80bn you would end up with around $44bn worth of Bitcoins and a money-losing software business. That’s about 55 cents for each dollar, which still doesn’t seem like fantastic value. There are a few different ways we could try and profit from this apparent stupidity. A very simple way would be to short MSTR and buy BTC, unless the premium reverses in which case we would go long MSTR and short BTC. As Keynes pointed out, the problem with such simple mean reversion trades is that the premium or discount can persist for a…. long…. time. Consider the market cap of MSTR (blue) and the value of BTC owned (orange): FIG. 1MSTR market cap (blue) vs mark-to-market value of BTC held (orange), USD. Although there was some nice mean reversion from 2021 to 2023, this would have been a money losing strategy from 2024 onwards as the premium exploded. This is even clearer if we plot the ratio of market cap to BTC held: FIG. 2Ratio of MSTR market cap to the value of BTC held. Can we do better? A common trick when operating mean reversion is to use something like a moving average to estimate “fair value” for the premium. Rather than assuming the premium will always shrink to zero (which would be a ratio of 1 in the second graph), we assume it will revert to the moving average. But moving averages always lag, so we still end up playing catch up in a strong secular trend. The flaw with both of these ideas is that we are naively assuming that the MSTR “investors” are, like us, rational people. Clearly they are not! Let us try and model that irrationality. 04A Simple Model of MSTR Value To model MSTR properly from an accounting perspective would be quite complicated. It has some funky convertible debt, so we’d need an option pricing model6. There are also some triggers and covenants in their debt, resulting in nonlinear sensitivity to BTC price. But all of this is pretty second order; BTC would have to fall quite a lot before MSTR would have issues with its debt. They also have a relatively low debt servicing cost, thanks to those cheap convertibles. So the sensitivity of its “accounting value” to BTC is pretty close to 1$ = $1. But we don’t care about any of that! We can’t trade “accounting value”, only equity value. Let’s begin from first principles: Enterprise value = Equity market cap + Debt = MSTR core business value + BTC value owned + vibes value BTC value owned = BTC coins held × BTC price … where “vibes value” is the enterprise value of MSTR which can’t be explained by its core business, or by the mark to market value of the Bitcoin it holds. It seems reasonable that this will depend on the price of Bitcoin; probably the higher BTC is, the more “vibes”. Rearranging: Market cap = (MSTR core business value − debt) + BTC value owned + V(BTC value owned) V is the “vibes” function; it gives us the responsiveness of the market valuation of MSTR to BTC above and beyond what the actual balance sheet value is. We allow V to be time varying. If we assume that V is a linear function7, we can write this as a function to estimate: Market cap = α + β × BTC value owned + ε Where: α, β are to be estimated; and we allow them to be time varying. α includes the MSTR core business, debt, and any fixed part of the “vibes” function. I currently estimate this at $2.8bn, suggesting the MSTR core business is worth negative several billion dollars. β incorporates the accounting value of BTC, and the linear part of the “vibes” function. My current estimate for this is 1.71; this is 71% higher than if the market value of MSTR had a 1:1 sensitivity to the mark to market account value of BTC. We have quantitative proof that “vibes” exist, and are positive! ε is the error term, which we assume to be mean reverting. This is what we will use to construct our positions. 05Fitting the Model As we know vibes “shift” and we don’t want to estimate parameters in sample, let’s use a rolling 12 month window for our estimation (refitting daily). Here is the fitted (blue) and actual (orange) market cap, with the fitting done using backward looking parameter estimates: FIG. 3Fitted (blue) vs actual (orange) MSTR market cap, $bn, rolling 12-month regression refit daily. Now for the error term (market cap – fitted market cap): FIG. 4Error term: actual minus fitted market cap, $bn. A positive error term means the market cap is too high (and we should sell MSTR / buy Bitcoin); a negative error term means it is too low (buy MSTR / sell Bitcoin). The strategy will be profitable if the error term mean reverts. It looks like this is happening. This is easier to see if we normalise the error term, dividing by the current market cap: FIG. 5Error term normalised by current market cap. That certainly looks like a vaguely mean reverting time series. We can see that errors of up to 50% of market cap have been available at times in the last couple of years; with even larger differences prior to that. 06Trading the Model Let’s now dive into the weeds and see how this model can be traded in practice. Recall: Market cap = α + β × BTC value owned If we include all the individual components: MSTR price × MSTR shares outstanding = α + β × BTC price × BTC coins held This gives us the following: MSTR price = (α / MSTR shares outstanding) + (β × BTC coins held / MSTR shares outstanding) × BTC price Hence we have a hedge ratio of (β × BTC coins held / MSTR shares outstanding) when trading MSTR against BTC. Here is the hedge ratio over time: FIG. 6Hedge ratio: β × BTC coins held / MSTR shares outstanding. The tenfold drop in August 2024 is the 10:1 share split. This climbs as more BTC coins are purchased, but as our estimate of β falls in recent years this causes it to flatten off. The tenfold drop in August 2024 is caused by a 10:1 share split. Here is the synthetic price of the artificial instrument we are trading: Bitcoin price × hedge ratio — MSTR price FIG. 7Synthetic price of the traded instrument: Bitcoin price × hedge ratio − MSTR price. How big should our positions be? Generally it’s better to have larger positions if there is more opportunity in a trade. In this case, that would be a larger error term. To scale positions in my trading strategies, I use forecasts scaled so that 10 is an average sized position. A forecast of +10 indicates an average long position; -10 is an average short, -20 would be double the average short, +5 would be half the average long and so on. We can construct a forecast by taking the error term from before, divided by the market cap, and then multiply by 20. Thus an error term of 50% would give us an average sized position of +10 or -10. If you think the smaller errors of recent years are more likely in future, you might want to be more aggressive. FIG. 8Forecast over time. Positive = long BTC / short MSTR; negative = the reverse. The plot above shows the forecast over time. A positive number means we would be long BTC/short MSTR; a negative number implies the reverse. Unlike a simple “premium reverts to zero” model, we have a more balanced series of longs and shorts. 07A Trade Example Let’s look at how we would construct this trade today (7th April 2025). Note that most of these figures are handily available from the (Micro)Strategy website, apart from the α and β. CURRENT ESTIMATES — 7 APRIL 2025 β 1.71 α 2.82 MSTR price $268.44 Market cap $71.453 billion Shares outstanding 266 million Bitcoin price $78,565 Bitcoin held 528,155 Value of bitcoin held $41.5 billion Hedge Ratio Calculation We define the hedge ratio as: Hedge ratio = (β × BTC coins held) / MSTR shares outstanding = (1.71 × 528,155) / 266,000,000 ≈ 0.003392 Thus, to hedge 1 BTC, we should hold: 1 / 0.003392 ≈ 294.72 MSTR shares At a price of $268.44 per share, this equates to: 294.72 × $268.44 ≈ $79,117 This is slightly more than 1 BTC ($78,565), so this is close to being an equal notional hedge. Error Calculation Error = actual market cap − (α + β × BTC value held) = 71.453 − (2.82 + 1.71 × 41.5) = 71.453 − 73.785 = −2.332 billion Normalising the error by dividing by market cap = -2.332 / 71.453 = -0.033 The market cap is lower than the fitted value, so we should buy MSTR and short BTC. In this case the error is quite small at just 3.3% of market cap. Multiply by approximate forecast scalar of 20 = -0.033 × 20 = 0.66 Currently then the forecast is pretty weak and we’d have a position of less than one-tenth of the average. Concretely, assuming we had $10m of capital with an annualised standard deviation target of 20%, which comes out to $2m a year, here is how we would calculate our average position: Daily standard deviation of synthetic price (Bitcoin price × hedge ratio – MSTR price) = $20 Annual standard deviation = 20 × 16 = $320 Ignoring the forecast for the moment, we want to hold $2m / $320 = 6250 units of the spread, which is long 6250 MSTR shares versus short 0.003393 × 6250 = 21.2 Bitcoin. Note that both legs have a notional value of around $1.7m, and the total position size is about $3.4m. However, because the forecast is only 0.66 in practice we multiply all these numbers by (0.66 / 10): giving us short 1.4 bitcoin vs long 412 MSTR. 08Accounting Example I probably wouldn’t bother putting on such a small position, on a weak forecast which is unlikely to overcome costs, but what kind of profit could we hope for if we had a larger error, of say -50%? In that case we’d have the full sized position of short 21.2 BTC and long 6,250 shares of MSTR. Let’s assume the error goes to zero, and for simplicity does it entirely on the MSTR price. If the error was 50%, this implies that the MSTR market cap – and price – would have doubled. That gives us a gross profit of $1.68mn, or 16.8% of our notional capital. Even if that reversion took a year, which is slow by historical standards, that isn’t a bad return. In Sharpe Ratio terms, the profit comes out to 0.84. Rolldown losses on the short futures position would be roughly equal to the risk free rate, but we’d have to pay a spread above risk free on borrowing to buy the MSTR shares. Even if we had to pay base + 1% in margin, we’d still be ahead here. 09Simulated Returns Let’s find out how this strategy performs, with all the usual caveats about a back-tested simulation definitely not representing what might happen in the future. Here is a simple account curve, with no costs or borrowing costs: FIG. 9Simulated account curve, before costs and borrowing costs. It’s a pretty wild ride in the early years; but in the last couple of years we see quite a nice standard mean reversion profitability (periods of steady returns, followed by sharp drawdowns which are quickly reversed). More recent forecasts are quite small, so there is less risk. What doesn’t this include: stock borrowing costs for MSTR (currently quite low at around 0.5% annualised) futures rolldown on Bitcoin (pretty close to risk free, about 6% a year), net interest/funding costs 10Conclusion Vibes exist, and we have managed to quantify them. The maths in this model makes it superficially safer than a simple “let us assume that the NAV premium closes to zero” strategy. But all the caveats mentioned earlier apply. History may repeat itself, and the ghost of Freeserve may come to haunt us. And mean reversion trades tend to suffer in periods of high uncertainty... FOOTNOTES It isn’t that easy, which is why a lot of people just buy trusts with big discounts to NAV and hope. People like Saba Capital. And people like me, whose ISA consists mostly of investment trusts currently showing a mark to market loss of about 30%. Note for Millennials and Gen-Z; an ISP was an ‘internet service provider’ whose services were required to get dial-up access to the internet. As an impoverished student I bought into that Freeserve IPO (due to massive oversubscription each investor was allocated about £80 of shares), and I later did an analysis of this trade as a case study which I used in my interview with the Barclays Capital equity research team. I didn’t get that job, but I did get hired by the trading desk. Please draw your own conclusions from this anecdote. This would have ended up being a very profitable trade; Freeserve fell 85% in the dot com crash of 2000, whilst Dixons merely halved. I note in passing that these guys are not great traders. They started buying when BTC was $10k, and yet they’ve only made a 35% MTM profit. As far as I know, MSTR is the only publicly listed firm that is proud of, and advertises, its realised and implied volatility. Because, naturally, that is what makes its convertible debt so cheap. Initially I allowed V to be quadratic but the squared terms were not significant, so I dropped them. 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