Bitcoin Return Prediction: Is It Possible via Stock-to-Flow, Metcalfe’s Law, Technical Analysis, or Market Sentiment?

Abstract

Popular methods to value Bitcoin include the stock-to-flow model, Metcalfe’s Law, technical analysis, and sentiment-related measures. Within this paper, I test whether such models and variables are predictive of Bitcoin’s returns. I find that the stock-to-flow model predictions and Metcalfe’s Law help to explain Bitcoin’s returns in-sample but have limited to no ability to predict Bitcoin’s returns out-of-sample. In contrast, Bitcoin market sentiment and technical analysis measures are generally unrelated to Bitcoin’s returns in-sample and are poor predictors of Bitcoin’s returns out-of-sample. Despite the poor performance of Bitcoin return predictors within out-of-sample regressions, I demonstrate that a very successful out-of-sample Bitcoin tactical allocation or “market timing” strategy is formed via blending out-of-sample univariate model predictions. This OOS-blended model trading strategy, which algorithmically allocates between Bitcoin and cash (USD), significantly outperforms buying-and-holding or “HODL”ing Bitcoin, boosting CAPM alpha by almost 1300 basis points while also increasing portfolio Sharpe Ratio and Sortino Ratio and dramatically reducing portfolio maximum drawdown relative to buying-and-holding Bitcoin.

1. Introduction

Multiple popular models have been proposed in an effort to value Bitcoin. Within this work, I examine the predictive ability of such Bitcoin valuation models and other popular predictors of Bitcoin’s returns. Unlike other studies examining Bitcoin valuation models or potential Bitcoin predictors, I test whether Bitcoin valuation models and other popular predictors of Bitcoin’s returns are able to not only explain Bitcoin’s returns in-sample but also whether such measures are able to predict Bitcoin’s returns out-of-sample. Thus, the findings of this study are particularly extant to Bitcoin investors and asset allocators.

Before proceeding further, it is necessary to quickly introduce and define the popular proposed valuation models and predictors of Bitcoin tested herein. These come both from the academic literature and contemporary quantitative analysts who are extremely popular within the Bitcoin community. The first, and perhaps most important, Bitcoin valuation model to discuss is the Bitcoin stock-to-flow model.

1.1. The Stock-to-Flow Model

Likely, the most well-known and popular of all Bitcoin pricing models is that of a pseudonymous Dutch blogger known only as “Plan B”. “Plan B’s” stock-to-flow model states that Bitcoin’s price at any point in time is a function of the Bitcoin stock, or total supply, over Bitcoin’s flow, or its newly minted supply over the next year (Anonymous (“Plan B”) 2019). Thus, “Plan B” argues that Bitcoin can be effectively priced as a traditional commodity or hard asset, such as gold, silver, diamonds, or real estate, as stock-to-flow models are extremely popular valuation measures for scarce commodities.

The model was made public by “Plan B” in 2019 and quickly became popular to “Bitcoiners” for a variety of reasons. However, the primary reason is that the model was remarkably accurate in projecting Bitcoin’s price from its introduction to the public via a Medium article authored by “Plan B” in 22nd March 2019 through the end of November 2021.1

While “Plan B’s” model has provided a guiding paradigm to many Bitcoin investors, it has serious shortcomings if used in isolation. The first potential shortcoming is that “Plan B’s” stock-to-flow model is focused on predicting Bitcoin’s price or log-price, not Bitcoin’s return or log-return, as the stock-to-flow model is written as either a logarithmic regression of BTC’s log-price or an exponential regression of BTC’s price. However, “Plan B’s” stock-to-flow model is easily transformed into a “Stock-to-Flow Deflection” model that predicts Bitcoin’s returns rather than Bitcoin’s price, thereby removing some of the large statistical problems inherent in time-series regressions of prices, rather than returns. Thus, within this research I examine the in-sample and out-of-sample accuracy of “Stock-to-Flow Deflection” estimates.

The second large shortcoming of the stock-to-flow model is that Bitcoin’s stock and flow at any point in time are both completely dependent on time since the Genesis Block of Bitcoin; thus, there is a very strong argument that any stock-to-flow model estimate is spurious. In fact, over the timeframe of this study (June 2014–February 2024) there is an 80.57% Pearson correlation between the Bitcoin stock-to-flow model estimate and the log of time since Bitcoin’s genesis block. Adding credence to this argument, I find that in-sample stock-to-flow model regression estimates, which appear statistically significant, become statistically insignificant once time fixed-effects are introduced.

Despite the above statistical flaws inherent in the stock-to-flow model, there is extensive economic rationale and prior empirical evidence to indicate that Plan B’s stock-to-flow model may provide explanatory power in describing Bitcoin’s returns. In fact, stock-to-flow models have been extremely popular to value scarce commodities, traditionally considered a store of value, including precious metals such as gold (Merkaš and Roška 2021). The higher the stock-to-flow of a scarce store of value asset, the more scarce the asset is, and thus the higher the price should be, given a fixed demand curve. Furthermore, Merkaš and Roška (2021) demonstrate that there appears to be an in-sample relationship between the Bitcoin stock-to-flow model estimate and Bitcoin’s price. Perhaps the most popular narrative surrounding Bitcoin today is that it is “digital gold” as it cannot be confiscated, has a fixed supply, is a monetary hedge, and is considered a scarce store of value asset and thus the same economic rationale and factors that have traditionally been applied to gold’s price are also well applied to Bitcoin (Dyhrberg 2016). Given this narrative and prior studies examining stock-to-flow models and precious metals, it is straightforward to hypothesize that Plan B’s stock-to-flow model estimate is likely to be linked to Bitcoin’s in-sample and out-of-sample return performance. While Merkaš and Roška (2021) demonstrate a link between Bitcoin’s in-sample price performance and the Bitcoin stock-to-flow model estimate, I examine the in-sample and out-of-sample relationship between the Bitcoin stock-to-flow model and Bitcoin’s returns in order to test whether there is actually a predictive link between the stock-to-flow model estimate and Bitcoin’s returns.

While “Plan B” has introduced different modifications to his model, including a stock-to-flow cross asset model, his base Bitcoin stock-to-flow model published within Medium in 2019 states that:

$$Bitcoin Price in USD=e^a\ast Stock-to-flo{w}^b.$$

(1)

Plan B estimates the $a$ parameter to equal −1.84 and the $b$ parameter to equal 3.36, using pre-2019 data to train the model and the lagged 463 days to estimate flow.

Based on both the economic rationale of Plan B’s stock-to-flow model and the prior findings of Merkaš and Roška (2021), I expect that the stock-to-flow model estimate will be positively associated with Bitcoin’s in-sample returns. This prediction implies that when Bitcoin’s scarcity is higher its contemporaneous returns will also be higher.

Furthermore, while Merkaš and Roška (2021) and others do not test the out-of-sample performance of the stock-to-flow model, I expect that Bitcoin’s out-of-sample returns will also be higher when the stock-to-flow model estimate is higher. In essence, this prediction is hinged upon the notion that the Bitcoin market is not perfectly efficient and that the increase in Bitcoin’s stock-to-flow mechanically induced via Bitcoin halvings will not be perfectly priced into the Bitcoin market contemporaneous with, or even prior to, Bitcoin halvings. Instead, I posit that the reduction in newly minted Bitcoin supply and increase in stock-to-flow due to halvings will slowly be priced into the Bitcoin market over a period of several months. Thus, I expect an out-of-sample link between the stock-to-flow model prediction and Bitcoin’s returns to be found, in which Bitcoin’s out-of-sample returns are somewhat predictable based on the stock-to-flow model implied returns.

Following the stock-to-flow model, the second most popular Bitcoin valuation model is arguably Metcalfe’s Law proposed by Robert Metcalfe in the early 1980s. Metcalfe’s Law is a popular model of value accretion within network theory and has been successfully applied to various technologies since the 1980s, most recently Bitcoin and cryptocurrencies.

1.2. Metcalfe’s Law

In addition to the stock-to-flow model, Metcalfe’s Law is used as one of the most popular Bitcoin valuation models. Metcalfe’ Law was proposed by Robert Metcalfe in the early 1980s as Metcalfe argues that the value of any network is proportional to the square of its nodes, as this represents the total number of available peer-to-peer connections within the network. Thus, Metcalfe’s Law states that:

$$Network Value \alpha N^2$$

(2)

where $N$ is the number of network nodes. Intuitively, this basic yet brilliant claim is very sensible. Within any network, there exists $NxN$ possible peer-to-peer connections given that the network has $N$ participants, and thus each unique peer-to-peer network connection may naturally be represented as a pairwise, row–column combination within an $NxN$ matrix. Looking at percentage changes in value or returns to a network, Metcalfe’s Law implies that:

$$(\% \mathsf{\Delta }Network Value) \alpha (\% {\mathsf{\Delta }N}^2 )$$

(3)

or that the percentage change in network value over a given time period is proportionate to the percentage change in the number of users squared over that given time period.

While Metcalfe’s Law was developed with telecommunications (ethernet) networks in mind, the most rigorous and accurate tests of Metcalfe’s law to date have actually been undertaken in recent years with more modern networks in mind. Metcalfe (2013) himself, evaluates the growth in value of Facebook’s market capitalization as a function of its squared user base, $N^2$, and finds that Facebook’s historical market capitalization is, in fact, highly related to the square of its user base. Furthermore, Zhang et al. (2015) reevaluate this proposition using a large Chinese competitor to Facebook, Tencent, and again find support for Metcalfe’s Law, as Tencent’s historical growth in market capitalization has been roughly proportional to the square of its user base.

The Bitcoin network is a very natural fit for the application of Metcalfe’s Law. First, the premise of Bitcoin is described by Nakamoto within the title of his infamous Bitcoin whitepaper as a “peer-to-peer electronic cash system” (Nakamoto 2008). Second, any layer 1 blockchain (including Bitcoin), is simply a computer network of $N$ nodes in which each of the $N$ nodes may transact or in some way communicate with any other node. As such, it is quite natural to believe Metcalfe’s Law would aid in explaining the market capitalization of Bitcoin and other layer 1 cryptocurrencies.

In fact, the premise that Metcalfe’s Law may explain Bitcoin’s network value has been investigated within several published papers and the findings are generally favorable. The most comprehensive and highly cited work is Alabi (2017), fittingly titled Digital Blockchain Networks appear to be following Metcalfe’s Law. Alabi (2017) analyzes the Bitcoin, Ethereum, and Dash blockchains and finds that Metcalfe’s Law is helpful in explaining the historical market capitalization of each.

Clearly, Metcalfe’s Law posits a positive link between network user growth and the value of the underlying network and, based on this and the findings of Alabi (2017), I expect an unambiguous, positive link between Bitcoin’s returns and the percentage change in the squared number of Bitcoin network users. However, what is again less clear, is whether the percentage change in the squared number of Bitcoin network users may actually be predictive of Bitcoin’s returns out-of-sample. Again, this relationship would be assumed to be positive if one believes that there is a high degree of market inefficiency within the Bitcoin market and would be posited to be closer to zero if the Bitcoin market is perfectly efficient or at least has become sufficiently efficient over time. Since I believe that the features of the Bitcoin market, which include extreme market volatility, the lack of an obvious fundamental value anchor, and extreme market cycles, are naturally associated with greater marker inefficiency, I expect there to be an out-of-sample predictive link between the percentage change in the squared number of Bitcoin’s network users and Bitcoin’s monthly returns.

Although many longer-term investors attempt to price Bitcoin via the two leading valuation models of Bitcoin, the stock-to-flow model and Metcalfe’s Law, many Bitcoin speculators and shorter-term traders primarily trade Bitcoin based on technical analysis.

1.3. Technical Analysis

While so-called “chartists” deeply believe in TA, more quantitatively oriented or fundamentally oriented value investors oftentimes consider TA a form of voodoo. But, while most academics and fundamental investors alike downplay the role of technical analysis within traditional markets, several key prior studies indicate that technical patterns do seem to have at least some importance in predicting the price of US stocks (for a leading example see Lo et al. 2000).

One may expect that such factors have much more importance within cryptocurrency markets, as a vast amount, if not the majority, of cryptocurrency traders tend to be chartists and many may be relatively uninformed or perhaps just altogether uninterested in fundamental factors. In fact, in a working paper, Detzel et al. (2018) demonstrate that the lagged 1-to-20 week moving averages of daily Bitcoin prices are highly predictive of Bitcoin’s current daily price and return movement in-sample.

Within this work, I test whether intermediate- and longer-term-lagged simple moving averages are predictive of Bitcoin’s monthly returns. In addition, I also test whether a very popular technical analysis measure, the Relative Strength Index (RSI), is predictive of Bitcoin’s monthly returns.

Due to the findings of Detzel et al. (2018), I expect a positive in-sample link between simple-lagged moving averages and Bitcoin’s returns. However, out-of-sample prediction of Bitcoin’s returns using only Bitcoin’s lagged moving averages seems dubious, as many Bitcoin traders closely examine Bitcoin’s lagged moving averages and thus it would seem contradictory that outperformance within the Bitcoin market could be gained via using such an obvious and widely used measure. While I believe that the Bitcoin market is far from perfectly efficient, I also expect it to not violate weak form market efficiency in a manner such that simple lagged moving averages successfully predict Bitcoin’s out-of-sample returns.

In addition to closely watching lagged moving averages of price, technical analysts often examine short-term return “momentum” via examining the prior period’s return and the Relative Strength Index (RSI), which calculates the relative degree of average gains and losses over the prior 14 periods and normalizes these to a “0” to “100” score. Most technical analysts view strong momentum as bullish; however, the impact of return reversals and the RSI is debated. For example, while some technical analysts may view a high RSI beyond 70 out of 100 within a given market as bullish, others may view this as a signal that the underlying market is “overbought” and should be avoided or even shorted. In line with the inclination of most technical analysts, Carhart (1997) demonstrates the positive impact of return momentum in driving US equity mutual fund performance.

Thus, I expect that return momentum, or the degree of prior month returns, is positively associated with Bitcoin’s in-sample returns. However, I take no position on how the RSI may be associated within Bitcoin’s in-sample returns, as even technical analysts cannot agree on this matter. Furthermore, while I believe that the Bitcoin market has historically had a higher degree of inefficiency than the US equity market, I do not expect that the weak-form market hypothesis is blatantly violated within the Bitcoin market such that one can consistently outperform out-of-sample using only lagged price data and technical measures. Thus, I expect little, if any, out-of-sample return predictability of Bitcoin using return momentum or the RSI.

The final predictor of Bitcoin’s returns tested within this study is Bitcoin market sentiment. The relationship between market sentiment and forward returns has been widely studied within the behavioral finance literature, and market sentiment is very closely monitored by Bitcoin investors via a popularized Bitcoin “Fear & Greed Index”.

1.4. Market Sentiment

In addition to the stock-to-flow model, Metcalfe’s Law, and technical measures; many Bitcoin investors and traders focus on market sentiment as the Bitcoin and cryptocurrency markets are highly “hype” driven and susceptible to large market bubbles and bursts.

Within traditional markets, investor sentiment is negatively linked to long-term US stock returns, as at times investors become too exuberant and bid stock prices well above their fundamental values, thereby decreasing long-term future stock returns and visa versa (Baker and Wurgler 2007). Baker and Wurgler (2007) define sentiment as either ‘top-down’ or “bottom-up” and note that their now infamous sentiment measure is “top-down” as it aggregates market-wide data such as trading volume, IPO performance, and the closed-end fund discount to form a proxy of total market sentiment of individual investors. In contrast, a “bottom-up” sentiment measure would instead poll or otherwise ascertain the sentiment of individual investors (perhaps by examining retail account trading data) and aggregate this individual investor data to form a market-wide measure of investor sentiment. Unlike Baker and Wurgler’s (2007) sentiment index, the Bitcoin “Fear & Greed Index” is unique in that it is actually a combination of both “top-down” and “bottom-up” measures of market sentiment.

The Bitcoin “Fear & Greed Index” measures Bitcoin market sentiment on a “0–100” scale. On this scale, the higher the number the “greedier” Bitcoin investors are. Less than “30” indicates “Extreme Fear” and more than “70” indicates “Extreme Greed”. In both a “top-down” and a “bottom-up” manner, the Bitcoin “Fear & Greed Index” analyzes the following data: (1) Bitcoin’s recent volatility over the last 30 and 90 days, (2) Bitcoin market momentum measures over the last 30 and 90 days, (3) the interaction rate related to Bitcoin on social media, specifically Reddit and Twitter or “X”, (4) surveys of the public, in which investors are asked about how they currently view the Bitcoin market, and (5) Bitcoin dominance, which tends to trend down in bullish cryptocurrency markets and trend up in bearish cryptocurrency markets.

Since Baker and Wurgler (2007) demonstrate a negative in-sample and out-of-sample link between their US equity market sentiment index and forward US stock returns, one would posit a likely negative in-sample and out-of-sample link between the Bitcoin “Fear & Greed Index” and Bitcoin’s forward returns. The reason for this is that sentiment’s impact on the market is assumed to be driven by human behavioral investing biases and the “madness of crowds” and thus to the extent one believes such biases impact markets, the biases demonstrated within the world’s leading equity market should be duplicated, if not enhanced, within the relatively less efficient Bitcoin market.

Thus, based on the findings of Baker and Wurgler (2007), one should expect a negative link between the Bitcoin “Fear & Greed Index” and Bitcoin’s forward returns. Since this result is presumably driven by investor behavioral biases and thus creates an inefficiency in how investors allocate capital, one would expect this result to hold both in-sample and out-of-sample.

With the potential predictors of Bitcoin examined within this study now defined and the accompanying economic rationale of each explained, I next describe the data used and variables formed within this study within Section 2 below.

2. Materials and Methods

2.1. Data and Variable Definitions

The data for this study come from multiple sources. Historical Bitcoin price and return data, historical values of “Stock-to-Flow Deflection”, and historical time-series of total and active Bitcoin wallets are gathered from Glassnode. The historical time-series of “Fear & Greed Index” values is publicly available from the “Free Crypto API” Dashboard at https://alternative.me/crypto/api/ (accessed 15 May 2024).

The maximum sample period used for all in-sample tests within the study is the 117-month sample period from June 2014–February 2024. June 2014 is used as the start of the sample as predictive variables of interest are missing for some observations prior to June 2014 and the Bitcoin network was far too small to be useful to empirically examine prior to this period.

The Bitcoin “Fear & Greed Index” data are only available from February 2018, and thus the two sentiment measures related to Bitcoin’s “Fear & Greed Index” are not complete over the entire dataset and are necessarily excluded within all multivariate regression models. Of the 15 predictors tested within the study, all others are complete over the June 2014–February 2024 sample period.

The dependent variable of interest within this study is Bitcoin’s monthly return in month $t$ using Glassnode’s monthly price data. Within the dataset used, Glassnode uses the first day of every month as the monthly close. Thus, Bitcoin’s June 2017 monthly return is calculated by taking the 1st of July 2017 Bitcoin price as the ending or close price and the 1st June 2017 monthly price as the beginning or open price. In an effort to minimize lookahead bias, all independent variables are measured as of the 1st of each month in month $t$, and thus all could have been formed out-of-sample.

All independent variables tested within this study are clearly defined below:

(1) “Log(time)”: The natural logarithm of time, in days, since Bitcoin’s Genesis Block.

(2) “S2F Deflection”: “S2F Deflection” stands for “Stock-to-Flow Deflection” and is a variable provided by Glassnode that converts Plan B’s stock-to-flow model price prediction, described above in Equation (1), into a ratio relative to Bitcoin’s current market price. As such, the variable is defined as the current Bitcoin price divided by Plan B’s stock-to-flow model price estimate for Bitcoin (using the prior 463 days to evaluate flow). This relative measure indicates how undervalued or overvalued Bitcoin is, according to the stock-to-flow model. Thus, a “S2F Deflection” of 0.40 indicates that Bitcoin is currently 60% undervalued by the market (it would be a good time to buy Bitcoin) and an “S2F Deflection” of 2.20 indicates that Bitcoin is currently 120% overvalued by the market (it would be a good time to sell Bitcoin). Thus, if stock-to-flow is related to Bitcoin’s valuation, there should be a negative and significant coefficient on “S2F Deflection” within regressions of Bitcoin’s returns on “S2F Deflection”.

(3) “% Changein ${\mathit{N}}^2$ Active”: The percentage change in the number of active wallets squared within the Bitcoin network over the prior month. Active wallets (active addresses) come from Glassnode and represent the number of active senders or receivers of Bitcoin each day. “% Change in $N^2$ Active” is one the two Metcalfe’s Law-focused predictors of Bitcoin’s returns tested within this study.

(4) “% Change in ${\mathit{N}}^2$ Total”: The percentage change in the number of total addresses squared within the Bitcoin network, over the prior month. Total wallets (total addresses) come from Glassnode and represent “the total number of unique addresses that ever appeared in a transaction of (Bitcoin) in the network.” “% Change in $N^2$ Total” is one the two Metcalfe’s Law-focused predictors of Bitcoin’s returns tested within this study.

(5) “BTC Momentum”: BTC Momentum is simply Bitcoin’s lagged return momentum estimated using the methodology of Mark Carhart (1997). Numerically, momentum is simply the compound return of Bitcoin over the month $t-12$ to $t-2$ period. Thus, in month $t$ this metric is formally defined as:

$${ BTC Momentum}_t=\prod _{t=-12}^{t=-2}(1+{BTC Return}_t)-1$$

(4)

where ${BTC Return}_t$ is Bitcoin’s return in month $t$.

(6) “Lag(BTC Monthly Ret)”: This variable is similar to the “reversal” phenomena witnessed by Carhart (1997) and others in month $t-1$ within traditional equity markets. As such, this variable is simply Bitcoin’s monthly return in the prior month, month $t-1$.

(7) “50-day SMA relative”: Bitcoin’s current price less its lagged 50-day SMA of price (the simple average of price over the prior 50 trading days), divided by the lagged 50-day SMA of price. As such, this is the percentage degree that Bitcoin’s price is above or below its lagged 50-day SMA of price.

(8) “100-day SMA relative”: Bitcoin’s current price less its lagged 100-day SMA of price, divided by the lagged 100-day SMA of price. As such, this is the percentage degree that Bitcoin’s price is above or below its lagged 100-day SMA of price.

(9) “200-day SMA relative”: Bitcoin’s current price less its lagged 200-day SMA of price, divided by the lagged 200-day SMA of price. As such, this is the percentage degree that Bitcoin’s price is above or below its lagged 200-day SMA of price.

(10) “50-week SMA relative”: Bitcoin’s current price less its lagged 50-week (350 day) SMA of price, divided by the lagged 50-week SMA of price. As such, this is the percentage degree that Bitcoin’s price is above or below its lagged 50-week SMA of price.

(11) “100-week SMA relative”: Bitcoin’s current price less its lagged 100-week (700 day) SMA of price, divided by the lagged 100-week SMA of price. As such, this is the percentage that Bitcoin’s price is above or below its lagged 100-week SMA of price.

(12) “200-week SMA relative”: Bitcoin’s current price less its lagged 200-week (1400 day) SMA of price, divided by the lagged 200-week SMA of price. As such, this is the percentage that Bitcoin’s price is above or below its lagged 200-week SMA of price.

(13) “RSI”: The Relative Strength Index (RSI) of Bitcoin’s monthly returns over the prior 14 months. In general, the RSI takes into account the average gain or loss of an asset over a pre-specified lagged window, typically 14 time periods. The RSI achieves a higher “relative strength” when the average gains in prior up periods have been higher than the average losses in prior down periods within the lagged window.

The upper bound of the RSI has a mathematical limit at 100 and indicates the maximal price strength, and the lower bound has a mathematical limit at 0 and indicates maximal price weakness. In practice, for most technicians, an RSI above 70 would be considered “price strength” and below 30 would be considered “price weakness”.

Mathematically, the most commonly used formula for RSI, which I adopt directly, is as follows:

$${RSI}_t=100-{\displaystyle \frac{100}{1+\frac{\left(\frac{\sum _{i=-N}^{-1}{Ret Positive}_i}{K}\right)}{\left(\frac{\sum _{i=-N}^{-1}{Ret Negative}_i}{N-K}\right)}}},$$

(5)

where ${RSI}_t$ is the RSI of the asset within period $t$, $N$ is the number of periods in the RSI estimation window (typically 14, which I use herein), ${Ret Positive}_i$ is composed of all returns within the estimation window that are positive in period $i$, ${Ret Negative}_i$ is composed of all returns within the estimation that are negative in period $i$, and $K$ is the number of periods within the estimation window that exhibit positive returns.

Since monthly returns are used within this research, month $t-14$ to month $t-1$ monthly Bitcoin returns are used to calculate the “RSI” following Equation (5) above.

(14) “Fear & Greed Index”: “The Fear & Greed Index” of Bitcoin measures investor sentiment within the Bitcoin market, providing a 0–100 score classifying investor sentiment from “Extreme Fear” to “Extreme Greed”. Multiple data and variables are fed into the “Fear and Greed Index” model to provide the 0–100 score at any point in time.

These include the (1) average Bitcoin volatility over the last 30 and 90 days (higher volatility than recent periods indicates a more fearful market), (2) market momentum relative to measures over the last 30 and 90 days (more recent momentum trading indicates more greed), (3) interaction rate related to Bitcoin on social media, specifically Reddit and Twitter or “X” (higher interaction indicates more greed), (4) surveys of the public, in which investors are asked about how they currently view the Bitcoin market (more bullish sentiment is an indication of more greed), (5) Bitcoin dominance, which tends to trend down in very bullish cryptocurrency markets and thus lower Bitcoin dominance indicates greed and higher Bitcoin dominance indicates fear, and (6) search trends, which can be classified as indicators of fear or greed depending on what terms are searched alongside the word “Bitcoin”.

Due to quite noisy day-to-day variations within the “Fear & Greed Index”, the average (mean) value of the “Fear & Greed Index” over month $t-1$ is defined as the “Fear & Greed Index” variable.

(15) “Fear & Greed Index Annual Delta”: The annual change in the “Fear & Greed Index”. Thus, “Fear & Greed Index Annual Delta” is the average (mean) value of the “Fear & Greed Index” within month $t-1$ less the average (mean) value of the “Fear & Greed Index” within month $t-13$.

Summary statistics for all variables over the full June 2014–February 2024 sample period are reported in

Table 1. Summary Statistics: Table 1 below provides summary statistics for all variables of interest over the entire 117-month sample period from June 2014 to February 2024.

Summary Statistics
Variable	Mean	St. Dev.	Min	25th	50th	75th	Max
Year	2018.83	2.87	2014	2016	2019	2021	2024
Month	6.53	3.49	1	3	7	10	12
BTC Price	$14,964.91	$17,032.90	$223.57	$729.73	$8453.34	$25,800.73	$62,440.63
BTC Monthly Ret	6.37%	22.96%	37.50%	−9.17%	1.72%	19.83%	80.55%
Log(time)	8.19	0.29	7.59	7.96	8.23	8.45	8.62
S2F Deflection	0.90	0.78	0.15	0.45	0.78	1.07	4.90
% Change N-Squared Total	6.24%	3.95%	1.83%	2.76%	4.34%	9.94%	14.36%
% Change N-Squared Active	4.41%	17.10%	43.69%	−6.17%	3.46%	15.88%	55.72%
RSI	53.56	12.42	22.50	45.32	52.64	62.28	80.91
Lag (BTC Monthly Ret)	6.63%	23.03%	37.50%	−9.17%	2.46%	20.15%	80.55%
BTC Momentum	135.77%	238.28%	68.62%	24.98%	68.66%	185.28%	1260.30%
50-day SMA Relative	4.91%	16.62%	35.85%	−6.39%	4.57%	14.51%	55.18%
100-day SMA Relative	8.69%	25.38%	42.59%	−9.32%	5.75%	26.15%	93.26%
200-day SMA Relative	16.59%	42.35%	49.06%	15.80%	11.00%	34.56%	160.38%
50-week SMA Relative	29.85%	65.11%	55.42%	16.33%	24.35%	49.01%	279.71%
100-week SMA Relative	62.51%	110.83%	56.20%	15.72%	32.45%	101.46%	536.27%
200-week SMA Relative	139.27%	172.16%	31.86%	24.68%	82.75%	184.17%	940.44%
Fear & Greed Index	45.07	20.69	11	27	42	62	95
Fear & Greed Index Delta	0.68	20.44	−48	−11	0	12	47

below.

With all data and variables used within this study clearly defined, the methodology of the empirical tests employed is now described. The primary empirical tests within this work are very similar in spirit to those of Welch and Goyal (2008). Welch and Goyal (2008) provide predictive models of forward US aggregate stock market returns and test whether each proposed predictor is significant both in-sample and out-of-sample. I borrow from Welch and Goyal’s (2008) methodology but assess predictors of Bitcoin’s return rather than predictors of the equity market risk premium.

2.2. In-Sample Regression Methodology

Rapach et al. (2016) revisit Welch and Goyal’s (2008) research question, adding a new proposed predictor of the equity market risk-premium, aggregate short interest, as measured by the Short Interest Index (SII). Rapach et al.’s (2016) univariate regression tests are very clear and well-designed and thus I also directly borrow from Rapach et al.’s (2016) empirical methodology in estimating univariate models.

The first in-sample model estimated is similar in spirit to Welch and Goyal’s (2008) proposed “kitchen sink” model. Within this model, Bitcoin’s returns are estimated using all proposed potential predictors of return within a multivariate linear regression model. The multivariate in-sample regression model can then be described as follows:

$${ Y}_t=\alpha +{{\rm B}X}_{it}+{ϵ}_{it},$$

(6)

where $Y_t$ is the target variable at time $t$ (Bitcoin’s monthly return over month $t$)2 and $X_{it}$ is a vector of the relevant subset of the $i$ predictors at time $t$.

After the in-sample multivariate “kitchen sink” approach is estimated, much of Welch and Goyal’s (2008) and Rapach et al.’s (2016) in-sample analysis focuses on univariate linear regressions of aggregate US stock market returns on each individual predictor.

To test the statistical significance of each predictor separately in-sample, Rapach et al. (2016) estimate linear regressions of the 1-month, 3-month, 6-month, and 12-month forward average equity market risk premium on each potential predictor of the equity market risk premium at the start of month $t$. To mirror this procedure, but with Bitcoin’s returns, I estimate univariate regressions of Bitcoin’s month $t$ return on each potential predictor in month $t$. These univariate models can be formally described as follows:

$$Y_t=\alpha +{{\rm B}X}_t+{ϵ}_t,$$

(7)

where $Y_t$ is Bitcoin’s return over month $t$ and $X_t$ is one of the 15 independent variables tested herein at time $t$.

The univariate model, in-sample regression results are reported using Newey and West (1987) heteroskedasticity and autocorrelation robust standard errors. Heteroskedasticity robust standard errors are desired as the distribution of errors is not normal for an asset with as much positive return skew and excess kurtosis as Bitcoin.3 Autocorrelation robust standard errors are desired as many of the 15 predictive variables of interest are positively serially correlated.

With in-sample regression methodology described, I next describe the methodology of all out-of-sample tests. I follow Rapach et al.’s (2016) regression methodology to examine the relation between Welch and Goyal’s (2008) proposed predictors and the SII (Short Interest Index) on US aggregate stock returns out-of-sample. However, I apply this methodology to the question at hand, examining the effect of the proposed predictors herein on Bitcoin’s monthly returns.

2.3. Out-of-Sample Regression Methodology

For any out-of-sample regression models, a “burn-in” period, or initial training period, for the model is needed. I choose a 24-month “burn-in” period so that the initial model estimated coefficients are not too unstable within the early months, as they would be with a 12-month “burn-in” period. This results in the first month of reported out-of-sample tests starting in June 2016 (as the first month in the data sample for this study is June 2014). Put simply, the 24-month period from June 2014–May 2016 is the initial training period for the OOS regression models.

Out-of-sample univariate regression models are estimated for each independent variable of interest using the data from months $t=25,\dots ,t-1$, where $t$ is the current month within the dataset. Each month, $K$ regression models are estimated in which $K$ is an index representing the 15 independent variables defined above. The dependent variable $Y_{k,t}$ is the monthly return to Bitcoin in month $t$, used within a univariate regression in which variable $k$ is the predictor.

Formally, the process to estimate all out-of-sample univariate regression models can be described as:

$$\begin{gathered} For t=25,\dots , T \\ For k=1,\dots , K: \\ {Y}_{k,t}={\alpha }_{k,t}+{{\beta }_{k,t}X}_{k, t}+{ϵ}_{k, t}, \end{gathered}$$

(8)

and thus the OOS model predicted return to Bitcoin in month $t$ using solely variable $k$ as a predictor, ${\widehat{Y}}_{k,,t}$ can be written as:

$${\widehat{Y}}_{k,t}={\widehat{\alpha }}_{k,t}+{\widehat{{\beta }_{k,t}}X}_{k, t}$$

(9)

This results in a vector of out-of-sample predictions each month $t$ for all $k$ predictive variables of interest.

After the OOS univariate regressions are estimated for all possible months within the data, a simplistic and effective procedure is utilized to estimate the predictive accuracy and statistical significance of each predictor out-of-sample. Following Campbell and Thompson (2008) and Rapach et al. (2016), the proportional reduction in mean squared forecast error (MSFE) is estimated. Campbell and Thompson (2008) denote this statistic as $R_{os}^2$, and I denote it as $R_{OOS}^2$. When calculating the MSFE, a benchmark is needed to assess improvement relative to. The benchmark model that Campbell and Thompson (2008) and Rapach et al. (2016) choose, and I follow, is simply a naïve return estimation model of ${\widehat{Y}}_t$ in which predictions are solely based on the average prior realization of $Y_t$ from time $1,\dots ,t-1$. Within such a naïve benchmark estimation model, the average (mean) past realization of $Y_t$ is used as the prediction for ${\widehat{Y}}_t$ at time $t$, and this naïve model estimate is denoted ${\overline{Y}}_t$, as it is simply the mean value of the prior realization of $Y_t$ over the time $1,\dots ,t-1$ interval. Formally, for each independent variable of interest $k$, the proportional reduction in mean squared forecast error (MSFE) relative to a naïve model prediction is then defined as:

$$R_{OOS}^2=1-{\displaystyle \frac{\sum _{t=t^{\ast }}^T{\left(Y_t-{\widehat{Y}}_{k,t}\right)}^2}{\sum _{t=t^{\ast }}^T{\left(Y_t-{\overline{Y}}_t\right)}^2}},$$

(10)

where $t^{\ast }$ is the greater of the first month after the burn-in period (month 25) or the first month in the dataset in which the predictor of interest $k$ has data available and month $T$ is the final month within the dataset. Intuitively, as the OOS regression model predictions become more accurate relative to naïve predictions as $\sum _{t=t^{\ast }}^T{\left(Y_t-{\widehat{Y}}_{k,t}\right)}^2$ decreases relative to $\sum _{t=t^{\ast }}^T{\left(Y_t-{\overline{Y}}_t\right)}^2$ and $R_{OOS}^2$ increases.

Following Rapach et al. (2016), I assess the statistical significance of $R_{OOS}^2$ using the Clark and West (2007) statistic to test the null hypothesis that the prevailing naïve model MSFE is less than or equal to the MSFE using the predictive OOS regression. Thus, the null hypothesis is that $R_{OOS}^2\le 0$ and the alternative is that $R_{OOS}^2>0$.

With an understanding of all in-sample and out-of-sample univariate regression tests in place, I next describe the OOS model trading strategy I propose, which can be used to dynamically allocate between Bitcoin and USD cash (or any other liquid asset) and “market time” in the Bitcoin market.

2.4. Blended, Univariate OOS Model Trading Strategy

The purpose of the OOS model trading strategy is to form a predictive model of Bitcoin’s forward returns that can be reliably used out-of-sample to determine a percentage allocation to Bitcoin within a portfolio while holding the rest of the portfolio in cash. Within backtests of such a strategy, a successful strategy must offer, at a minimum, superior out-of-sample risk-adjusted portfolio performance statistics relative to the passive strategy of simply buying-and-holding or “HODLing” Bitcoin. The risk-adjusted return statistics I report and analyze include portfolio Sharpe Ratio, Sortino Ratio, CAGR, maximum drawdown, CAPM alpha, and CAPM beta.

The OOS model trading strategy formed allocates between Bitcoin and cash after predicting Bitcoin’s next month return via blending normalized return predictions from all OOS univariate regression models.

Within the approach, in any month $t$, $K$ univariate linear regressions of Bitcoin’s 1-month forward returns are estimated using OOS data from month 1 to month $t-1$. $K$ represents the number of predictors of Bitcoin’s monthly returns, and the $K$ predictors exactly match the 15 predictors listed within Section 2.1 above.

Naturally, this process results in $K$ estimated univariate regression models per month, each of which can be used to predict Bitcoin’s return in month $t$. The historical Campbell and Thompson (2008) OOS $R^2$ of the $K$ univariate models is then assessed and a blended prediction of Bitcoin’s month $t$ return is formed via weighting each univariate model prediction by its OOS $R^2$.

Then, this blended prediction of Bitcoin’s monthly return in month $t$ is ranked against all prior monthly blended return predictions for Bitcoin, and this ranked, blended prediction is used to allocate towards Bitcoin with the remainder of the portfolio allocated to cash. Finally, any leverage desired is applied.

This blended, univariate Bitcoin model trading strategy is formally explained step-by-step below.

Step 1: At the beginning of each month $t$, estimate $K$ univariate regression models of Bitcoin’s 1-month forward return based on historical data from month $1$ to month $t-1$. Allow for a 24-month burn-in to estimate the model, so that the first month of OOS estimation is in month 25. Denote the first month of out-of-sample model estimation as $t_{\ast }$. Thus, the $K$ models estimated in month $t$, using OOS data from month $1$ to month $t-1$, can be written as:

$$Y_{k,t}={\alpha }_{k,t}+{{\beta }_{k,t}X}_{k, t}+{ϵ}_{k, t}$$

(11)

Step 2: The process in Step 1 results in $K$ regression models, each of which are used to form a point estimate of Bitcoin’s return in month $t$, ${\widehat{Y}}_{k,t}$. For each of the $K$ predictors, assign the predictions of Bitcoin’s month $t$ return to an expanding vector of values along with all prior monthly univariate model predictions. This vector of historical univariate regression model predictions using predictor $k$ is then denoted ${\widehat{Y}}_k$. Thus,

$${\widehat{Y}}_k=\{{\widehat{Y}}_{k,t\ast },{\widehat{Y}}_{k,t\ast +1}, {\widehat{Y}}_{k,t\ast +2},\dots ,{\widehat{Y}}_{k,t}\}$$

(12)

Step 3: Now, assess the accuracy of each univariate model’s historical ability to predict returns by forming an OOS $R^2$ statistic following the methodology of Campbell and Thompson (2008) based on the proportional reduction in MSFE relative to a naïve model. For the univariate model using predictor variable $k$ at time $t$, the synthetic Campbell and Thompson (2008) OOS model $R^2$, based on proportional reduction in MSFE relative to a naïve model, is denoted as:

$${ R}_{OOS, k, t}^2=1-{\displaystyle \frac{\sum _{t=t_{\ast }}^t{\left(Y_t-{\widehat{Y}}_{k,t}\right)}^2}{\sum _{t=t_{\ast }}^t{\left(Y_t-{\overline{Y}}_t\right)}^2}}$$

(13)

where $R_{OOS, k, t}^2$ is an unbiased measure of the model OOS forecast error in return prediction from the inception of model training $t_{\ast }$ to time $t$. Within the MSFE formula in Equation (13), ${\widehat{Y}}_{k,t}$ is the univariate regression model predicted value of Bitcoin’s return in month $t$ only using variable $k$ as a predictor, ${\overline{Y}}_t$ is the naïve model estimation of Bitcoin’s return in month $t$, and $Y_t$ is Bitcoin’s actual return in month $t$.

Step 4: Next, weight each univariate regression return prediction of Bitcoin’s month $t$ return, ${\widehat{Y}}_{k,t}$, by its historically estimated Campbell and Thompson (2008) OOS $R^2$ to form a blended prediction of Bitcoin’s month $t$ return. Denote this blended return prediction of Bitcoin’s month $t$ return as ${\tilde{Y}}_t$. This can be represented formally as follows:

$${\tilde{Y}}_t= {\displaystyle \frac{{\sum }_{k=1}^K{ R}_{OOS, k, t}^2\ast {\widehat{Y}}_{k,t}}{{\sum }_{k=1}^K{ R}_{OOS, k,t}^2 }}$$

(14)

Step 5: Once formed, ${\tilde{Y}}_t$ is a blended prediction of Bitcoin’s month $t$ return, weighting each univariate regression model by its historical out-of-sample accuracy. Next, form a vector of all such blended model predictions from month $t_{\ast }$ to month $t$ as $\tilde{Y}$. Thus,

$$\tilde{Y}=\left\{{\tilde{Y}}_{t\ast },{\tilde{Y}}_{t\ast +1},\dots , {\tilde{Y}}_{t-1}, {\tilde{Y}}_t\right\}$$

(15)

Finally, form a vector of the percentile rank of each element of $\tilde{Y}$ as $\dot{Y}$. Thus, ${\dot{Y}}_t$ is the percentile rank of the univariate, blended predictions of Bitcoin’s return over month $t_{\ast }$ to month $t$.

$$\dot{Y}=\left\{{\dot{Y}}_{t\ast },{\dot{Y}}_{t\ast +1},\dots , {\dot{Y}}_{t-1},{\dot{Y}}_t \right\}$$

(16)

Step 6: In the starting month of model training, $t\ast$, define a target portfolio steady-state allocation of the portfolio’s assets held in Bitcoin, ${\alpha }_{\ast }$. This value must lie on the continuous line $[0, 1]$, as one can only have a minimum of 0% of one’s portfolio in Bitcoin and maximum of 100%, assuming no short-selling of Bitcoin and before applying any leverage. Assume that the rest of the portfolio’s asset allocation will be to cash (USD) so the steady-state value invested in cash is $1-{\alpha }_{\ast }$. Also, if in month $t\ast$, define the amount of leverage the portfolio will take on as $l$. $l$ is static within the model and a no-leverage but fully invested portfolio would have a leverage $l=1$, a 2x (100%) leveraged model would have a leverage $l=2$, and so on.

Then, the model’s unlevered allocation to Bitcoin in the current month, $t$, is:

$${ w}_b={\alpha }_{\ast }+2 \left({\dot{Y}}_t-0.5\right)\left(1-{\alpha }_{\ast }\right)$$

(17)

and the remainder of the portfolio that is its unlevered allocation to cash is naturally:

$${ w}_c=1-\left({\alpha }_{\ast }+2 \left({\dot{Y}}_t-0.5\right)\left(1-{\alpha }_{\ast }\right)\right)={1-w}_b.$$

(18)

By definition, the unlevered weight towards Bitcoin plus the unlevered weight towards cash must equal 1, such that $w_b+w_c=1$. Now, the levered portfolio weight of the portfolio to Bitcoin after the chosen leverage is applied is:

$${ w}_{bl}={ lw}_b$$

(19)

and the levered portfolio weighting towards cash is:

$${ w}_{cl}={ lw}_c$$

(20)

Step 7: Finally, if a full model backtest is desired (instead of just the current month’s model allocation towards Bitcoin and cash) repeat Step 1 thru Step 6 for month $t+1$ until $t=T$.

With all the data used and methodology applied within this study fully described, I next discuss the results of all empirical tests within Section 3 below.

3. Results

3.1. In-Sample Regression Model Results

The results of the multivariate and univariate in-sample regression tests described in Section 2.2 are reported in

Table 2. In-sample (IS) multivariate regression model results: The results of the in-sample (IS) multivariate regression models described in Section 2 above are detailed below. In order to prevent losing too many observations, the “Fear & Greed Index” and “Fear and Greed Index Annual Delta” are not estimated since both only have history dating back to February 2018. This multivariate “Kitchen Sink” model is estimated with and without time fixed-effects. In both models, standard errors are estimated using the Newey and West (1987) procedure to adjust for the impacts of heteroskedasticity and autocorrelation. “*” denotes statistical significance at a p-value of 0.10, “**” denotes statistical significance at a p-value of 0.05, and “***” denotes statistical significance at a p-value of 0.01.

Multivariate Regression Model: In-Sample (IS) Results
Dependent Variable: BTC Monthly Ret
Variable	(1)	(2)
Log (time)	−0.3485	0.2523
	(0.18)	(0.94)
S2F Deflection	−0.0811 *	−0.0858
	(0.07)	(0.39)
% Change N-Squared Total	−1.9860	−3.2963
	(0.30)	(0.32)
% Change N-Squared Active	0.4313 ***	0.5221 ***
	(0.00)	(0.00)
RSI	0.0022	0.0016
	(0.23)	(0.42)
Lag (BTC Monthly Ret)	−0.1413	0.1714
	(0.67)	(0.65)
BTC Momentum	0.0384 **	0.0257
	(0.05)	(0.23)
50-day SMA Relative	0.1364	−0.3137
	(0.82)	(0.64)
100-day SMA Relative	0.0575	0.1142
	(0.88)	(0.76)
200-day SMA Relative	0.0655	−0.0619
	(0.82)	(0.84)
50-week SMA Relative	0.0110	0.0769
	(0.96)	(0.74)
100-week SMA Relative	0.1289	−0.0184
	(0.28)	(0.92)
200-week SMA Relative	−0.1240 **	−0.0253
	(0.03)	(0.78)
Time FEs	NO	YES
Number of Obs.	117	117
Adj. R-Squared	0.268	0.439

and

Table 3. In-sample (IS) univariate regression model results: Below, the results of the in-sample univariate regression tests described in Section 2 are reported. The dependent variable of interest in all models is “BTC Monthly Ret” (the 1-month forward or month $t$ Bitcoin return). Univariate model coefficients are reported in the 2nd column with p-values reported below the model coefficient. In the 3rd column, coefficients are reported again with p-values adjusted using the Bonferroni correction. The number of model observations is reported in the 4th column. Regression R-squared values are reported in the 5th column. Finally, a “Variable Rank” or importance measure is reported in the 6th and final column, which is simply the rank of the relevant regression model’s R-squared relative to all other univariate models tested. “*” denotes statistical significance of the variable at a p-value of 0.10, “**” denotes statistical significance of the variable at a p-value of 0.05, and “***” denotes statistical significance of the variable at a p-value of 0.01.

Univariate Regression Model: In-Sample (IS) Results
Dependent Variable: BTC Monthly Ret
Variable	Coefficient	Coefficient Bonferroni	Number of Obs.	R-Squared	Variable Rank
Log (time)	0.0341	0.0341	117	0.002	11
	(0.64)	(1.00)
S2F Deflection	−0.0648 ***	−0.0648	117	0.049	2
	(0.01)	(0.12)
% Change N-Squared Total	0.0784	0.0784	117	0.000	14
	(0.44)	(1.00)
% Change N-Squared Active	0.3798 ***	0.3798 **	117	0.080	1
	(0.00)	(0.01)
RSI	0.0038 **	0.0038	117	0.041	3
	(0.03)	(0.43)
Lag (BTC Monthly Ret)	0.1113	0.1113	117	0.012	9
	(0.23)	(1.00)
BTC Momentum	0.0026	0.0026	117	0.001	12
	(0.77)	(1.00)
50-day SMA Relative	0.2068	0.2068	117	0.022	8
	(0.11)	(1.00)
100-day SMA Relative	0.1642 *	0.1642	117	0.033	6
	(0.05)	(0.76)
200-day SMA Relative	0.1059 **	0.1059	117	0.038	4
	(0.04)	(0.53)
50-week SMA Relative	0.0618 *	0.0618	117	0.031	7
	(0.06)	(0.87)
100-week SMA Relative	0.0219	0.0219	117	0.011	10
	(0.26)	(1.00)
200-week SMA Relative	0.0003	0.0003	117	0.000	15
	(0.98)	(1.00)
Fear & Greed Index	0.0020	0.0020	73	0.035	5
	(0.11)	(1.00)
Fear & Greed Index Delta	0.0003	0.0003	72	0.001	13
	(0.84)	(1.00)

.

Examining the multivariate in-sample regression results within Table 2, only “S2F Deflection”, “% Change N-Squared Active”, “BTC Momentum”, and “200-week SMA relative” are statistically significant within Model 1, in which there are no time fixed-effects.

Within Model 1 of Table 2, “S2F Deflection” is statistically significant with a p-value of 0.07 and a coefficient of −0.0811, indicating that for each 10% of apparent overvaluation of Bitcoin via the stock-to-flow model, its monthly returns are approximately −0.811% lower. However, it is important to note that within Model 2 of Table 2, in which time fixed-effects are estimated, the coefficient on “S2F Deflection” is no longer statistically significant, having a p-value of 0.39. This is likely because the stock-to-flow model is spurious in the sense that the model estimate is directly dependent on time since Bitcoin’s Genesis Block. In fact, empirically, there is an 80.58% historical correlation between Plan B’s stock-to-flow model and the logarithm of time since the Bitcoin Genesis Block.

Examining the Metcalfe’s Law-related variable results within the multivariate in-sample setting, while there is no statistical relationship between “% Change N-Squared Total” and Bitcoin’s monthly returns, there is a strong statistical relationship between “% Change N-Squared Active” and Bitcoin’s monthly returns within both Model 1 and Model 2 of Table 2. This indicates empirical support in favor of Metcalfe’s Law when considering only active wallets, which are those that have incurred a transaction within the prior year. Since there are many old Bitcoin wallets that have not had transactions for years and many lost private keys, it is quite sensible that active Bitcoin wallets are much more directly related to network value than stagnant and potentially lost wallets. The coefficient on “% Change N-Squared Active” within Model 1 of Table 2 is 0.4313, with a highly significant p-value of less than 0.01, indicating that if Bitcoin active wallets increase by 10% within the prior month (“% Change N-Squared Active” would then be ${\displaystyle \frac{{1.1}^2-1^2}{1^2}}=0.21$), then Bitcoin’s monthly return increases by roughly 9.06%. Thus, the impact of Metcalfe’s Law on Bitcoin’s in-sample monthly returns is clear and of significant magnitude.

With the exception of the “200-week SMA relative” variable and “BTC momentum”, all other predictor variables are insignificant within Model 1 of Table 2. However, both the “200-week SMA relative” and “BTC momentum” become statistically insignificant after incorporating time fixed-effects within Model 2 of Table 2, perhaps due to a degree of monthly and longer-term seasonality within Bitcoin’s historical returns.

Overall, the multivariate in-sample results within Table 2 indicate support in favor of Metcalfe’s Law and limited support in favor of the stock-to-flow model, with the strong caveat that the stock-to-flow model estimate may be spurious with time. The reported multivariate in-sample results within Table 2 offer little to no support for the argument that technical moving averages or the RSI are related to Bitcoin’s monthly returns.4

Within the univariate in-sample regressions reported in Table 3, the results in favor of the stock-to-flow model and Metcalfe’s Law are quite similar to the multivariate regressions reported within Table 2.

Within Table 3, the coefficient of the univariate regression model using “% Change N-Squared Total” is again statistically insignificant; however, the coefficient of the univariate regression using “% Change N-Squared Active” is 0.3798 and statistically significant at a p-value of 0.01, indicating that if Bitcoin active wallets increase by 10% within the prior month, then Bitcoin’s monthly return increases by roughly 7.98%. Even after applying the Bonferroni correction, which conservatively corrects for multiple testing bias via penalizing the p-value of a coefficient proportionate to the number of independent tests conducted, the p-value of “% Change N-Squared Active’ is still only 0.01, indicating very clear evidence that there is a strong, positive link between the percentage change in active Bitcoin wallets and Bitcoin’s in-sample returns and that the statistical significance of this link is not simply due to multiple testing bias.

The “S2F Deflection” univariate in-sample model coefficient estimate reported in Table 3 is −0.0648 and statistically significant at a p-value of 0.05, indicating that a 10% overvaluation of Bitcoin’s price relative to the stock-to-flow model estimate is associated with a −0.648% decrease in Bitcoin’s monthly return. However, unlike the “% Change N-Squared Active” variable, after applying the Bonferonni correction the p-value of the coefficient becomes .12 instead of 0.01, indicating that there is roughly an 11% probability that the negative in-sample, univariate regression link between “S2F Deflection” and Bitcoin’s returns is simply driven by multiple testing bias. After applying the Bonferroni correction, there still appears to be a likely link between “S2F Deflection” and Bitcoin’s in-sample returns; however, the result is not nearly as statistically significant as the link between “% Change N-Squared Active” and Bitcoin’s in-sample returns after applying the same correction.

While both coefficients are positive, neither the coefficient on “Fear & Greed Index” nor the coefficient on “Fear & Greed Index Delta” within Table 3 is statistically significant. This indicates that there appears to be no clear association between Bitcoin market sentiment as measured by the “Fear & Greed Index”, or changes in the index, and Bitcoin’s monthly returns. This is surprising as the Bitcoin and cryptocurrency markets appear to be very sentiment or “hype” driven and anecdotally it appears that many Bitcoin and cryptocurrency traders use the “Fear & Greed Index” as a gauge of when to consider getting into or out of the market. Considering the results of Baker and Wurgler (2007) and the seemingly greater inefficiency of the Bitcoin market relative to the US stock market, it is surprising that there is no in-sample link between Bitcoin market sentiment and Bitcoin’s forward monthly returns.

Finally, within their respective univariate regression models, the coefficients on the “100-day SMA relative”, “200-day SMA relative”, “50-week SMA Relative”, and “RSI” are all positive and statistically significant within Table 3. This appears to indicate that there may be an in-sample association between Bitcoin’s lagged returns and the current monthly returns in a “trend following” sense, as when Bitcoin’s price is above its lagged 100-day, 200-day, or 50-week moving averages, Bitcoin’s upcoming monthly return is typically higher. However, after applying the Bonferroni correction, the coefficients within Table 3 on the “100-day SMA relative”, “200-day SMA relative”, “50-week SMA Relative”, and the “RSI” all become statistically insignificant, with adjusted p-values of 0.43 or above. This indicates a very high likelihood that multiple testing bias may be driving the apparent statistical significance of these variables within univariate regressions. Thus, any inference based on this finding should be very tempered, especially considering the in-sample multivariate regression results reported in Table 2, which broadly demonstrate little to no link between the same technical measures and Bitcoin’s in-sample returns. Altogether, considering the results of both the multivariate and univariate in-sample tests reported in Table 2 and Table 3, there appears to be little, if any, meaningful link between technical measures, including lagged SMAs, the RSI, and momentum, and Bitcoin’s in-sample returns.

Overall, the multivariate and univariate in-sample regression results reported within Table 2 and Table 3 indicate clear support in favor of Metcalfe’s Law when using active wallets to measure Bitcoin network participants and limited support in favor of the stock-to-flow model. While there is a clear statistical relationship between stock-to-flow model predictions and monthly returns, the relationship appears to be somewhat spurious. Surprisingly, technical analysis measures including lagged, SMAs, the RSI, and momentum appear to have little, if any, relationship to Bitcoin’s in-sample returns. This indicates that the technical measures widely studied and followed by Bitcoin market participants are, to a great extent, unimportant. Perhaps most surprisingly, there is no in-sample association between Bitcoin market sentiment and Bitcoin’s monthly returns. Since Baker and Wurgler (2007) demonstrate convincing evidence of an inverse link between market sentiment and forward returns within the US equity market, one may expect a similar relationship (but perhaps to a greater degree) within the Bitcoin market. However, the in-sample results do not support this hypothesis. A possible explanation for this finding is that while Baker and Wurgler (2007) examine the impact of sentiment on long-term forward returns within the US equity market, this study considers the impact of Bitcoin sentiment on near-term (1-month forward) Bitcoin returns. Thus, it is possible that there may be an inverse link between Bitcoin market sentiment and forward Bitcoin returns over a much longer-term time horizon. Examining this question could be the valuable focus of another study.

With all multivariate and univariate in-sample findings now fully described, in Section 3.2 I next report and discuss the results of all univariate out-of-sample regression models.

3.2. Out-of-Sample Regression Model Results

Table 4. Out-of-sample (OOS) univariate regression model results: Below, results of the out-of-sample univariate regression tests described in Section 2 are detailed. Model-estimated OOS R-squared values are calculated following the methodology of Campbell and Thompson (2008), in which OOS R-squared is defined as the proportional (percentage) reduction in mean squared forecast error (MSFE) relative to a naïve return estimation model (please see Equation (10) and the description within Section 2 for further detail). The statistical significance of the OOS R-squared value is calculated using the Clark and West (2007) t-statistic following Campbell and Thompson (2008) and Rapach et al. (2016). The univariate model rank in terms of its Campbell and Thompson (2008) OOS R-squared relative to all other models tested is reported in the 4th and final column. “*” denotes statistical significance of the OOS R-squared value at a p-value of 0.10, “**” denotes statistical significance of the OOS R-squared value at a p-value of 0.05, and “***” denotes statistical significance of the OOS R-squared value at a p-value of 0.01.

Univariate Regression Model: Out-of-Sample (OOS) Results
Dependent Variable: BTC Monthly Ret
Variable	OOS R-Squared	Number of Obs.	Variable Rank
Log (time)	−0.070 **	93	12
	(2.05)
S2F Deflection	0.031	93	2
	(0.11)
% Change N-Squared Total	−0.072 **	93	13
	(−1.74)
% Change N-Squared Active	0.057	93	1
	(0.54)
RSI	0.026	93	3
	(0.68)
BTC Lag Monthly Return	−0.011 *	93	7
	(1.29)
BTC Momentum	−0.054 *	93	10
	(−1.39)
50-day SMA relative	0.004	93	5
	(0.74)
100-day SMA relative	0.014	93	4
	(0.58)
200-day SMA relative	−0.001	93	6
	(−1.09)
50-week SMA relative	−0.016	93	8
	(1.15)
100-week SMA relative	−0.052 *	93	9
	(1.45)
200-week SMA relative	−0.066 **	93	11
	(1.73)
Fear and Greed Index	−0.468 **	49	14
	(1.73)
Fear and Greed Index Annual Delta	−0.524 **	48	15
	(1.55)

reports results of the OOS univariate regressions of Bitcoin’s monthly returns on each of the 15 predictors of interest, with the primary statistic of interest being the Campbell and Thompson (2008) out-of-sample R-squared or $R_{OOS}^2$.

Examining the results in Table 4, the predictors have very weak out-of-sample predicative ability, and the majority even underperform a naïve return estimation model, as most have a negative OOS R-squared. The sentiment variables “Fear & Greed Index” and “Fear & Greed Index Delta” perform vastly worse than a naive return estimation model out-of-sample with highly negative and significant Campbell and Thompson (2008) OOS R-squared values.

Examining technical analysis predictors, the OOS predictive ability of SMA relative variables is weak as the 100-week and 200-week SMA relative variables have negative and significant Campbell and Thompson (2008) OOS R-squared values of −0.052 and −0.066, respectively, while the 50-day, 100-day, 200-day, and 50-week SMA relative variables have statistically insignificant Campbell and Thompson (2008) R-squared values right around 0 (ranging from −0.016 to 0.014). Thus, when forecasting returns out-of-sample, SMA relative variables perform no better than, and sometimes significantly worse than, a basic naïve return estimation model. The RSI does perform better out-of-sample, with a positive Campbell and Thompson (2008) R-squared value of 0.026, but again the Clark and West (2007) t-statistic of the estimate is statistically insignificant.

Examining the out-of-sample predictive ability of the stock-to-flow model and Metcalfe’s Law, there is no clear evidence that either model can accurately predict Bitcoin’s out-of-sample returns. The Campbell and Thompson (2008) OOS R-Squared value of “S2F Deflection” is 0.031; however, the estimate is nowhere close to being statistically significant, as the Clark and West (2007) t-statistic is only 0.11. Similarly, the Campbell and Thompson (2008) OOS R-Squared value of “% Change in N-Squared Active” is 0.057 but the Clark and West (2007) t-statistic of the estimate is again statistically insignificant at 0.54.

Overall, the OOS return regressions reported in Table 4 below indicate that none of the 15 stock-to-flow, Metcalfe’s Law-related, technical, or sentiment variables significantly outperform a naïve return estimation model in predicting Bitcoin’s returns out-of-sample.

3.3. Out-of-Sample Model Trading Strategy Results

While various parameterizations of the OOS blended, univariate model trading strategy are estimated, the focus within

Table 5. Blended, univariate model trading strategy OOS backtest results: Below, out-of-sample backtest results are provided for the OOS blended, univariate model trading strategy described in Section 2. The model strategy tactically allocates to Bitcoin and cash (USD) each month. The model is backtested over the June 2018–February 2024 time period and estimated for varying steady-state allocations to BTC ${\alpha }_{\ast }$ and varying levels of leverage $l$. The statistical significance of the CAPM alpha and beta estimates is denoted via “*” (significant at a p-value of 0.10), “**” (significant at a p-value of 0.05), and “***” (significant at a p-value of 0.01). The benchmark or “market” asset used to calculate CAPM alpha and beta is Bitcoin itself and the risk-free rate is the 1-month US Treasury bill yield. Model backtests assume trading costs and fees of 40 bp (0.4%) of the trade size. All returns reported are net of estimated trading costs and fees. The top row with the ‘BTC Allocation” of “HODL Bitcoin” reports Bitcoin’s buy-and-hold (HODL) return statistics over the period.

Blended, Univariate Model Trading Strategy OOS Backtest Results (June 2018–February 2024)
BTC			Annualized	Sharpe	Sortino	Monthly	Max.
Allocation	Leverage	CAGR	Vol.	Ratio	Ratio	Return	Drawdown	Alpha	Beta
HODL Bitcoin	NA	44.44%	73.66%	0.82	1.79	5.20%	72.78%	0.00%	1
0.3	1	48.34%	33.86%	1.27	4.73	3.75%	15.36%	18.03% **	0.40 ***
0.5	1	50.75%	43.72%	1.10	3.37	4.18%	35.06%	12.57% **	0.57 ***
0.7	1	50.23%	55.17%	0.96	2.45	4.59%	52.81%	6.72% **	0.74 ***
0.3	2	101.47%	67.73%	1.30	4.84	7.51%	29.64%	38.03% ***	0.80 ***
0.5	2	96.05%	87.44%	1.12	3.44	8.36%	59.92%	27.12% **	1.14 ***
0.7	2	76.27%	110.34%	0.98	2.50	9.17%	82.34%	15.41% **	1.48 ***

below is on a “base” model parameterization in which the steady-state portfolio allocation to Bitcoin, $w_b$, is 50% (or 0.5) and the portfolio utilizes no leverage so that $l=1$. Thus, under this “base” parameterization, an investor will, on average, hold a “50/50” allocation towards BTC and USD given a long enough investment time horizon.

Under this “base” model parameterization, the OOS blended, univariate model trading strategy achieves an impressive 50.75 % CAGR over the backtest sample period of June 2018–February 2024. Further, under the “base” parameterization, the strategy has a 43.72% annualized volatility, with a 1.10 Sharpe Ratio, 3.37 Sortino Ratio, 35.06% maximum drawdown, 12.57% annualized CAPM alpha (significant at a p-value of 0.05), and a 0.57 beta relative to Bitcoin (significant at a p-value of 0.01). For comparison, Bitcoin achieves an 44.44% CAGR over the backtest period, with a 73.66% annualized volatility, a 0.82 Sharpe Ratio, a 1.79 Sortino Ratio, and a 72.78% maximum drawdown.5 It is important to note that the OOS blended, univariate model trading strategy backtest returns include estimated trading costs and fees assuming that trading costs and fees are 40 bp or 0.4% of the trade size.6

Thus, the “base” parameterization of the OOS blended, univariate model trading strategy has historically had superior raw and risk-adjusted returns than simply buying and holding or “HODL”ing Bitcoin.

In fact, the “base” parameterization of the strategy is stochastically dominant relative to buying and holding Bitcoin, with all risk and return metrics being superior. Other model parameterizations with different steady-state allocations to Bitcoin or leverage levels also historically significantly outperform buying and holding Bitcoin. Thus, while the 15 Stock-to-flow model, Metcalfe’s Law-related, technical, and sentiment variables tested perform poorly in predicting Bitcoin’s out-of-sample returns within a univariate setting, they surprisingly appear to perform quite well when used in synchrony with one another as within the OOS blended, univariate model trading strategy. In particular, the OOS blended, univariate model trading strategy does very well in avoiding the severe downside risk and volatility inherent in Bitcoin investment, which aids the model in vastly overperforming across all risk and return metrics.

One potentially valid concern regarding the OOS blended, univariate model trading strategy backtests is whether the model trading strategy offers similarly strong performance across varying market states. Therefore, as a robustness check, I backtest the performance of the strategy separately within historical Bitcoin bull and bear markets.

I define Bitcoin “Bull Markets” as starting in the month after Bitcoin’s four-year cycle low price and continuing until the month that contains Bitcoin’s four-year cycle high price. All other markets are “Bear Markets”, which start in the month following Bitcoin’s four-year cycle high and continue until the month in which Bitcoin hits its four-year cycle low. Following this definition, Bitcoin was in a “Bear Market” during the OOS backtest sample start period, June 2018, when the price was over USD 17,000. It continued in a “Bear Market” until February 2019, when Bitcoin hit a four-year cycle low of just USD 3391. Bitcoin began a new “Bull Market” starting in March 2019 and continuing until November 2021. This is because Bitcoin hit a four-year cycle market bottom of USD 3391 in February 2019 and hit a four-year cycle top of USD 68,789 in November 2021. Starting in December 2021, Bitcoin hit a new “Bear Market” as the price precipitously declined from USD 68,789, and it continued in a “Bear Market” until the price hit a cycle low of USD 15,599 in November 2022. In December 2022, the Bitcoin price began rebounding above the USD 16,000 region and Bitcoin continued on into another “Bull Market”, making new higher highs and higher lows throughout the rest of the OOS backtest sample period through February 2024.

Within

Table 6. Blended, univariate model trading strategy OOS backtest results: bull markets only: Below, out-of-sample backtest results are provided for the OOS blended, univariate model trading strategy described in Section 2 for only “Bull Markets”. Bitcoin “Bull Markets” are defined as the March 2019–November 2021 period and the December 2022–February 2024 (end-of-sample) period, as these form the periods immediately after Bitcoin’s bear market low through Bitcoin’s bull market high (or the end-of-sample) for each market cycle. The model strategy tactically allocates to Bitcoin and cash (USD) each month and is estimated for varying steady-state allocations to BTC ${\alpha }_{\ast }$ and varying levels of leverage $l$. The statistical significance of the CAPM alpha and beta estimates is denoted via “*” (significant at a p-value of 0.10), “**” (significant at a p-value of 0.05), and “***” (significant at a p-value of 0.01). The benchmark or “market” asset used to calculate CAPM alpha and beta is Bitcoin itself and the risk-free rate is the 1-month US Treasury bill yield. Model backtests assume trading costs and fees are 40 bp (0.4%) of the trade size. All returns reported are net of estimated trading costs and fees. The top row with the “BTC Allocation” of “HODL Bitcoin” reports Bitcoin’s buy-and-hold (HODL) return statistics over the “Bull Market periods”.

Blended, Univariate Model Trading Strategy OOS Backtest Results: Bitcoin Bull Markets Only (March 2019–November 2021 and December 2022–February 2024 (End-of-Sample))
BTC			Annualized	Sharpe	Sortino	Monthly	Max.
Allocation	Leverage	CAGR	Vol.	Ratio	Ratio	Return	Drawdown	Alpha	Beta
HODL Bitcoin	NA	171.71%	73.49%	1.71	4.04	10.68%	43.22%	0.00%	1
0.3	1	86.50%	38.13%	1.79	6.35	5.85%	15.36%	7.06%	0.48 ***
0.5	1	111.05%	47.25%	1.79	5.22	7.23%	22.04%	4.43%	0.63 ***
0.7	1	135.75%	57.37%	1.76	4.59	8.61%	30.77%	1.80%	0.78 ***
0.3	2	207.49%	76.26%	1.81	6.45	11.71%	29.64%	16.25%	0.95 ***
0.5	2	268.34%	94.51%	1.81	5.29	14.46%	42.27%	11.00%	1.25 ***
0.7	2	319.37%	114.73%	1.78	4.63	17.22%	57.83%	5.74%	1.55 ***

, the OOS blended, univariate model trading strategy’s performance during historical Bitcoin “Bull Markets” is detailed. The Bitcoin “Bull Markets” over the backtest sample period include the March 2019–November 2021 and December 2022–February 2024 (end-of-sample) windows. Examining Table 6, one sees that the strategy maintains a higher Sharpe Ratio and a higher Sortino Ratio than buying-and-holding Bitcoin across all model specifications. More so, the CAPM alpha of all specifications relative to Bitcoin itself, while not statistically significant due to the small sample size, is positive in the range of 1.80% to 16.25% annualized. Finally, the beta of the strategy relative to Bitcoin is higher than the strategy’s average, long-run allocation to Bitcoin across all model specifications. For example, the “base” parameterization of the strategy has a leverage of “1” (no leverage) and an average, long-run Bitcoin allocation of 0.5 but achieves a statistically significant 0.63 beta over historical “Bull Market” periods. Since this “base” parameterization of the strategy is mechanically designed to have a long-run 0.5 allocation and 0.5 beta to Bitcoin, the fact that it achieved a much more aggressive Bitcoin allocation during historical Bitcoin “Bull Markets” seems to be an indication of successful market timing. This same pattern of higher strategy betas than expected holds across all model specifications tested during the “Bull Market” periods, highlighting that all models successfully overweighted Bitcoin during “Bull Markets” within the sample backtest.

Within

Table 7. Blended, univariate model trading strategy OOS backtest results: bear markets only: Below, out-of-sample backtest results are provided for the OOS blended, univariate model trading strategy described in Section 2 for only “Bear Market periods”. Bitcoin “Bear Markets” are defined as the June 2018 (start-of-sample)–February 2019 period and the December 2021–November 2022 period. The model strategy tactically allocates to Bitcoin and cash (USD) each month and is estimated for varying steady-state allocations to BTC ${\alpha }_{\ast }$ and varying levels of leverage $l$. The statistical significance of the CAPM alpha and beta estimates is denoted via “*” (significant at a p-value of 0.10), “**” (significant at a p-value of 0.05), and “***” (significant at a p-value of 0.01). The benchmark or “market” asset used to calculate CAPM alpha and beta is Bitcoin itself and the risk-free rate is the 1-month US Treasury bill yield. Model backtests assume trading costs and fees are 40 bp (0.4%) of the trade size. All returns reported are net of estimated trading costs and fees. The top row with the “BTC Allocation” of “HODL Bitcoin” reports Bitcoin’s buy-and-hold (HODL) return statistics over the “Bear Market periods”.

Blended, Univariate Model Trading Strategy OOS Backtest Results: Bitcoin Bear Markets Only (June 2018 (Start-of-Sample)–February 2019 and December 2021–November 2022)
BTC			Annualized	Sharpe	Sortino	Monthly	Max.
Allocation	Leverage	CAGR	Vol.	Ratio	Ratio	Return	Drawdown	Alpha	Beta
HODL Bitcoin	NA	−65.93%	53.98%	−1.66	−2.68	−7.32%	84.98%	0.00%	1
0.3	1	−12.10%	8.06%	−1.76	−2.23	−1.04%	18.12%	−6.01%	0.09 ***
0.5	1	−30.14%	19.25%	−1.83	−3.20	−2.79%	45.94%	−5.03%	0.34 ***
0.7	1	−46.37%	32.90%	−1.73	−2.93	−4.61%	66.31%	−3.78%	0.61 ***
0.3	2	−23.35%	16.11%	−1.66	−2.10	−2.08%	33.70%	−10.29%	0.19 ***
0.5	2	−53.62%	38.50%	−1.79	−3.13	−5.59%	72.95%	−8.31%	0.69 ***
0.7	2	−75.69%	65.80%	−1.71	−2.88	−9.23%	91.31%	−5.82%	1.21 ***

, the OOS blended, univariate model trading strategy’s performance during Bitcoin “Bear Markets” is reported. This includes the June 2018 (start of sample)–February 2019 and December 2021–November 2022 time periods. While all of the model specifications backtested have negative CAGRs within Bitcoin “Bear Markets”, model CAGRs are less negative than buy and hold Bitcoin investing during such periods, with the exception of the specification that holds a very high Bitcoin average allocation of 0.7 and applies 2x leverage. Similarly, five of the six model specifications, again with the exception of the specification that holds a very high Bitcoin average allocation of 0.7 and applies 2x leverage, achieve significantly lower volatility and significantly lower maximum drawdowns than Bitcoin over these “Bear Market” periods. The Sharpe Ratio and Sortino Ratio statistics lose their traditional interpretation when all asset returns are negative and are thus best ignored within the “Bear Markets” only backtest. The CAPM alpha of all specifications tested relative to Bitcoin is negative and statistically insignificant during Bitcoin “Bear Markets”. This indicates that the model specifications generally achieved higher returns than Bitcoin during “Bear Markets” due to the fact that almost all model specifications hold less than 100% of their portfolio allocation in Bitcoin at any time, thus when Bitcoin declines sharply in price the strategy mechanically outperforms. However, based on the reported CAPM alpha estimates in Table 7, the model specifications did not actually market time Bitcoin successfully during historical “Bear Market” periods. This interpretation becomes further nuanced when examining the model betas relative to Bitcoin across model specifications, as each is lower than the long-run, average Bitcoin allocation within each model specification. For example, the “base” model parameterization holds a 0.5 average allocation to Bitcoin and applies no leverage (1x leverage). This “base” specification has a statistically significant 0.34 beta relative to Bitcoin over historical Bitcoin “Bear Markets”, indicating that the strategy successfully underweighted Bitcoin during sharply declining markets. However, the exact months in which the “base” model specification of the strategy shifted portfolio weights dramatically downward were not ideal, causing the alpha of the strategy to be a statistically insignificant −5.03% annualized. Put simply, while the OOS blended, univariate model trading strategy historically underweights Bitcoin during “Bear Markets” and overweights Bitcoin during “Bull Markets”, the predictive power of the strategy, and thus the strategy’s alpha relative to Bitcoin, appears to be superior during Bitcoin “Bull Markets”.

Altogether, the out-of-sample model backtests of the OOS blended, univariate model trading strategy reported in Table 5, Table 6 and Table 7 demonstrate that the strategy has historically allocated very favorably to Bitcoin, with impressive raw and risk-adjusted return performance relative to simply buying-and-holding or “HODL”ing Bitcoin. More so, the strategy has historically always shifted its average allocation and beta to Bitcoin up above the long-run, average strategy allocation during “Bull Markets” and shifted its average allocation and beta to Bitcoin down below the long-run, average strategy allocation during “Bear Markets”, indicating that the strategy is successfully risk-weighting towards Bitcoin in line with market conditions.7

Thus, the out-of-sample model trading strategy results reported in Table 5, Table 6 and Table 7 add credence to the argument that Bitcoin’s returns have been at least been somewhat predictable out-of-sample, as by only using the stock-to-flow model, Metcalfe’s Law, basic technical measures, and sentiment, a simplistic statistical algorithm is formed that historically vastly outperforms buying-and-holding Bitcoin in both raw and risk-adjusted terms. In Figure 1, the growth of a USD 10,000 investment in the “base” parametrization of the strategy is plotted relative to simply buying and holding Bitcoin over the June 2018–February 2024 backtest sample period.

With all results of this study now fully discussed, I next provide my conclusions regarding Bitcoin’s in-sample explanatory power and out-of-sample predictability within Section 4.

4. Conclusions

The two most popular Bitcoin valuation models, the stock-to-flow model and Metcalfe’s Law, are both statistically related to Bitcoin’s in-sample returns in the manner that each model would surmise. However, as the stock-to-flow model estimate is simply a derivative of time since the Bitcoin Genesis Block, the association between the stock-to-flow model’s predictions and Bitcoin’s monthly returns is lost after time fixed-effects are included within an in-sample regression.

Generally speaking, it appears that technical analysis measures are not associated with Bitcoin’s in-sample monthly returns. Surprisingly, the popular Bitcoin market sentiment measure, the “Fear & Greed Index”, is also statistically unrelated to Bitcoin’s in-sample monthly returns.

Within univariate out-of-sample regression tests following the methodology of Campbell and Thompson (2008), none of the 15 stock-to-flow model, Metcalfe’s Law-related, technical, or sentiment-related predictors tested significantly outperforms a naïve return estimation model. This finding indicates that none of these predictors, used in isolation, provides a significant edge to investors interested in predicting Bitcoin’s out-of-sample monthly returns.

Despite the very poor out-of-sample return predictability of the stock-to-flow model, Metcalfe’ Law-related variables, technical measures, and Bitcoin market sentiment, a relatively simplistic out-of-sample model trading strategy is formed which intelligently blends predictions from the out-of-sample univariate return regressions. Over the model trading strategy sample backtest period of June 2018–February 2024, all parameterizations of the algorithm, known as the OOS blended, univariate model trading strategy, vastly outperform buying-and-holding Bitcoin in terms of CAGR and CAPM alpha. Furthermore, the strategy generally provides better risk-adjusted returns than Bitcoin, in terms of Sharpe Ratio and Sortino Ratio, and generally has lower volatility and drawdown than Bitcoin during both Bitcoin “Bull” and “Bear” markets while shifting risk to Bitcoin favorably in line with market conditions. Thus, it appears that while no single predictor is able to accurately forecast Bitcoin’s returns out-of-sample, a basket of out-of-sample Bitcoin return predictions can be efficiently combined to successfully “market time” Bitcoin and outperform the classic “buy-and-hold” or “HODL” strategy.