Summary The Kelly criterion offers a balanced Bitcoin investment strategy, providing downside protection while maintaining risk-adjusted performance. The strategy generates positive alpha and outperforms traditional investments, despite lower performance compared to a pure buy-and-hold Bitcoin approach. The Kelly strategy is ideal for conservative investors seeking crypto exposure with manageable risk, protecting against sudden market crashes. INTRODUCTION In investor circles, Bitcoin USD (BTC-USD) ha s become an asset of growing importance and controversy. While some believe this cryptocurrency will soon reach the $1 million mark, others claim it is worthless and will go to $0. Because of this, the question remains if there is no safer way to invest in Bitcoin that, on the one hand, gives investors downside protection in a sudden crash but, on the other hand, does not sacrifice risk-adjusted performance. The Kelly criterion is one way to accomplish this task. THE KELLY CRITERION The Kelly criterion was developed by John L. Kelly Jr. and was originally used as a system to maximize gambling returns. This means that it is mostly based on given odds. However, as there are no given odds in the stock market, one has to estimate them using historical data. Kelly formula (Investopedia) WHAT DOES THE KELLY CRITERION DO IN PRACTICE? In practice, the Kelly criterion rebalances your portfolio to a fixed asset allocation at the end of every predetermined period. Once the Kelly criterion is calculated, the percentage of capital that has to be allocated to the asset is known. The remaining money is normally considered to be kept in cash. This means that one's exposure to the asset (here BTC/USD) reduces when the price rises and increases when the price falls. EXAMPLE - USING THE KELLY CRITERION FOR BITCOIN I am using the period between 2015 and the end of 2018 to estimate the Kelly criterion for 3 months. Each investor can choose the period, however, a too-high period has insufficient data, while a too-low period will inflict high transaction costs. If one would take 1-month periods, for example, one would have to rebalance the portfolio three times as much, leading to approximately three times the transaction costs. Also, the data has to contain multiple up and down periods, which is why a 3-month period is recommendable. Using BTC/USD price from Yahoo Finance, one gets: W = 0.5625 R = 3.4277 Kelly % = 0.4349 This means that at the end of every 3-month period, 43.49% of the available cash should be invested in BTC/USD while 56.51% is supposed to be in cash equivalents. As seen in Table 1, the strategy produces positive alpha in comparison to BTC/USD (data from 01.02.2019 to 04.02.2025) as well as to traditional investments such as SPY (SPDR S&P 500 ETF). Additionally, the R^2 to both BTC/USD and SPY is very low. While the performance of the strategy (Table 2) is lower than that of BTC/USD, it is still above 40%, by far beating any other asset class (such as stocks and long-term bonds) but investing in crypto without any strategy in absolute terms. These lower returns, however, come as a trade-off to a far lower risk. When looking at traditional risk measurements (Table 2), one can see that the standard deviation has more than halved when using the strategy. Further on, the maximum drawdown of the strategy is better than that of TLT (iShares 20+ Year Treasury Bond ETF) and 34% less than traditional BTC/USD investments. Table 1 - Alpha and Beta (Composer) Table 2 - Performance Metrics (Composer) During the 2018 crash, the strategy outperformed BTC/USD by 34.3%, showing a far lower standard deviation and drawdown (Table 3). The same holds for the 2022 crash, where the strategy's drawdown was less than half of that of a buy-and-hold BTC/USD strategy. Table 3 - Performance during 2018 (Composer) Table 4 - Performance during 2022 (Composer) Overall, the strategy shows positive returns during periods where BTC/USD is falling but fails to beat the strategy due to its lower exposure. However, in times when BTC/USD is falling, the strategy strongly outperforms but still shows negative returns. ADVANTAGES AND DISADVANTAGES OF USING THE KELLY STRATEGY The Kelly strategy has mainly two advantages. The first, undeniable strength, is that it produces alpha. The second factor is the far easier risk management. As I have already mentioned at the beginning of this article, there are many opinions about BTC/USD. However, nobody can claim with 100% certainty that BTC/USD will not go to $0. The Kelly strategy protects investors against a sudden crash, by having less than 50% exposure to BTC/USD. Additionally, it is easier to manage risk in general when using this strategy. While risk numbers such as VaR only give a chance of what the maximum loss might be (which often proves to be wrong), one can easily treat the maximum loss of the Kelly strategy in a given quarter as the money exposed to the asset, leading to more certainty. The main disadvantage of the strategy is naturally the lower exposure, and therefore performance, in contrast to opting for a buy-and-hold strategy. An additional point of critique could be that the Kelly % might be wrongly calculated, as one can only use past data. Since the data of BTC/USD is very volatile, one crash could strongly influence the calculated Kelly %. This point, although valid, does not make a big difference as the function of the Kelly % to expected return is usually parabolic, meaning that miscalculations still yield returns close to that of the maximum. If one would miscalculate the Kelly % with a negative bias, the strategy will yield lower returns but also have lower risk. Further on, should the bias be that Kelly % is higher than intended, the risk will still be lower than a buy-and-hold investment. Additionally, the risk-return trade-off would only minimally change. CONCLUSION In conclusion, one can say that the Kelly strategy is an interesting alternative to the classic buy-and-hold strategies in the crypto sector. It is especially attractive for investors afraid of the risk of a big crash in crypto assets and can be seen as a more conservative way to get exposure to the crypto sector. This especially holds true as the strategy drastically reduces the risk (in terms of drawdown) of holding crypto to the level of traditional investments such as long-term bonds (Table 3) while yielding a very high return, fitting it to the risk profile of stock or long-term bond investors.
