* * * Original: Liu Jiaolian * * *
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Bitcoin continued to fluctuate above 29k overnight. Instead of continuing the slow recovery trend, it began to fluctuate up and down.
Figure: Thesis
A few days ago, the journal "The Journal of Alternative Investments" (Alternative Investment Journal) Issue 4, Volume 25 (Spring 2023) was released, and everyone found that three managing directors (investment managers) of BlackRock (BlackRock) contributed an article on it. A research paper titled "Asset Allocation with Crypto: Application of Preferences for Positive Skewness" (Crypto Asset Allocation: Application of Positive Skewness Preferences). The dissertation research will be carried out roughly in April 2022.
The pdf version of the full text of this paper has been uploaded to the planet, so that friends who have joined the planet can read it by themselves:
Figure: Full text of the paper
What is the issue of this paper? The talk is based on the classic 60:40 stock-to-debt ratio asset allocation plan, what kind of income enhancement effect will be brought about by increasing the allocation of bitcoin, and what is the best bitcoin allocation ratio should be estimated.
According to the industry media bitcoinist’s report [1], BlackRock’s research on the historical data of Bitcoin’s monthly performance from July 2010 to December 2021 concluded that for a 60-40 asset portfolio (60% stocks, 40% Bonds) and fixed risk preference gamma = 1.5, the optimal Bitcoin allocation ratio is 84.9% (nearly 85%), and the remaining 15.1% (about 15%) is in stocks and bonds at a ratio of 60:40 distributed between.
Figure: Three asset allocation ratios
However, the source of information for bitcoinist’s report is actually the Twitter big V @theemikehobart, because it also quotes the latter’s picture (above). Apparently, bitcoinist himself didn't bother to check out the original paper.
If you look at the original paper, you will know that this picture comes from the fourth picture (EXHIBIT 4 Allocatiions to BTC) of the original paper (page 17 of the journal). The original source of the picture was made by BlackRock in January 2022 based on data from Refinitiv Datastream and Bloomberg.
Immediately afterwards, bitcoinist quoted Joe Burnett of Blockwave's twitter remarks, arguing that the optimal bitcoin allocation ratio should be 80-100%. And Joe added, "Considering today's global wealth of about 800 trillion US dollars, Bitcoin will likely reach 190 million US dollars per coin."
Soon, the media in the Chinese currency circle reported and disseminated the topic of BlackRock's research recommending that the best investment portfolio should allocate 84.9% of Bitcoin, 9.06% of stocks and 6.04% of bonds. This proves once again that almost no media even took a look at the original paper.
So, is the data of 84.9% true? In BlackRock's original paper, there is indeed this figure. The picture above is also true. They appear in the original paper (page 16 of the journal) in the "Effect of Skewness in Practice" section, which is part of the "POWER UTILITY" chapter.
Figure: Effect of Skewness in Practice
The full text of this subsection reads:
“We conduct the following asset allocation exercise. Assume we start with a 60-40 stock-bond portfolio. Assuming that stock and bond returns are lognormally distributed, consistent with the moments reported in the data in Exhibit 1, we calculate the power utility) to arrive at a 60-40 allocation. In this case, g = 1.50 is equivalent to a risk aversion of 60-40. We then hold risk aversion fixed and assume that stocks and bonds are weighted according to 60-40 proportional allocation, estimate the optimal weight h{BTC} of BTC. That is, the stock and bond weights are set to (1 - h{BTC})h{eq} and (1 - h{BTC})h{bd respectively }. We use a mixture of normal distributions for BTC returns (see Equation 1 and Exhibit 3), capturing large positive skewness.
“Exhibit 4 shows the results. Starting with a 60-40 stock-bond portfolio generated with a risk aversion of g = 1.50, the optimal BTC allocation is 84.9%! In the rest of the portfolio 15.1% are divided into stocks and bonds, with a ratio of 60-40. Although BTC is very volatile, reaching 1.322 (see chart 1), the obvious positive skewness leads to a large allocation and dominates the utility function position (see Equation 9). The deterministic equivalent compensation required for not investing in BTC is close to 200%. In Exhibit 4, starting with a 20-80 stock-bond portfolio, the Bitcoin allocation is 12.5%, while owning 80-20 stocks Risk tolerance of bond portfolio Investors hope that the leveraged position of BTC will reach 106.6% [Jiaolian Note: A position allocation of more than 100% means that leverage is added to the spot] .”
Seeing that "the deterministic equivalent compensation required for not investing in BTC is close to 200%", it reminds us of what Satoshi Nakamoto said back then, "Not owning Bitcoin is a net loss."
But did BlackRock really conclude in the paper that a portfolio should be allocated up to 85% bitcoin? not at all.
The content of the above-mentioned widely reported subsection is really just a regression analysis of historical data. Everyone knows that for the capital market, whether it is the stock market or the currency market, the past does not represent the future. Carving a boat to ask for a sword is often nothing you can ask for.
So what exactly is the conclusion of BlackRock's paper?
The researchers hypothesized two scenarios for the future of Bitcoin: one is called normal mode, with an average annualized rate of return of 95% (already high!) and 114% annual volatility; the other is called It is called the happiness model, with an average annualized rate of return as high as 467% and an annualized volatility of only 51%!
The paper believes that the probability of happiness mode happening is only about 3% (Liu. Jiao. Chain. thinks it is already very high!), and Bitcoin million dollars can also be modeled by happiness mode.
Then, the thesis studies two investor utility models, and conducts a quantitative analysis of the asset allocation of investor positions under different utility models. The first model is called "Power Utility", and the second model is called "Behavorial CPT Utility, CPT = Cumulative Prospect Theory".
Under the power utility model, when the realization probability of the happiness mode is p = 0.0003, the Bitcoin configuration ratio hBTC = 1%; p = 0.0052, hBTC = 2%; p = 0.0193, hBTC = 3%.
The lowest and lowest case, p = 0.0001 (one in 10,000, it is really "the dream is still there, what if it comes true"), at this time the BTC allocation ratio hBTC = 0.92%. Of course, the paper also admits that if the realization probability p = 0, then the holding hBTC will also be equal to 0.
Investors in the CPT utility model are much more optimistic and aggressive. When the happiness mode realization probability is p = 0.0005, the Bitcoin allocation ratio hBTC = 1.3%; p = 0.0006, hBTC = 3.1%; p = 0.0016, hBTC = 17.8%.
When p > 0.002, that is to say, the investor holds the belief that there is more than two-thousandth possibility of Bitcoin realizing the happiness mode, then for him, the allocation ratio of Bitcoin hBTC is equal to infinity!
Going back to the beginning of the paper, the authors write that there is about a 3% chance of the happy mode. Under the power utility model, the position ratio exceeds 3%. Under the CPT utility model, the more the better.
The conclusion section at the end of the paper reads:
“Bitcoin (BTC) log returns exhibit an extremely large third central moment of 144% on an annualized scale, orders of magnitude greater than those for stocks and bonds at -0.43% and 0.01%, respectively. We show that a mixture of normal distributions of BTC returns can capture a large right skew. There is a "normal" mode with relatively high volatility and a low conditional mean. The other is a "happy" mode with mean Extremely high, corresponding to price appreciation measured in the hundreds of percent, with relatively low volatility. Happiness patterns are very unlikely to occur. Large positive skewness from rare happiness patterns can even induce (i.e., local mean-variance) investors hold large Bitcoin allocations.
"Behavioral investors with cumulative prospect theory (CPT) utility are more sensitive to large positive skewness because they overweight happiness patterns compared to objective probabilities. With CPT, investors need only believe that happiness patterns will be around 0.0005 Occurs with a probability of , which is the best BTC allocation to hold about 3%.
“Our findings on BTC allocation sensitivity due to large positive skewness are also valid for other positively skewed asset classes. Venture capital (VC) returns (see Cochrane 2005) and individual stock returns (see Bessembinder 2018) show A mixture of positive skewness and normal distributions, and a preference to capture higher moment effects, may also help identify optimal holdings in these asset classes.
“An important caveat is that we only considered BTC returns and did not examine very large cross-sections of cryptocurrencies. This deserves separate attention because skewness is not a coherent measure of risk as defined by Artzner et al. (1999). Therefore The third moment property of a diversified cryptocurrency portfolio is likely to be greater than the third moment of each cryptocurrency individually. The style factor strategies documented by Liu, Tsyvinski, and Wu (2019) and Liu, Liang, and Cui (2020) can be found in cryptocurrency The resulting alpha in the cross-section, such as market cryptocurrency factors, size, and momentum, makes the distribution of cryptocurrencies more attractive. On the other hand, given the relatively short history of cryptocurrency returns, survivor bias may not be accurately measured (see Brown et al., 1992). The true probability of the happiness mode may be lower than the empirical estimates we found, or lower than the probability in the static exercise where we study hypothesis comparisons. In fact, the large sensitivity of investor positions with positive skewness preferences Sexuality means that small downward revisions in the likelihood of earning BTC returns could lead to a large decline in the optimal holding of the BTC asset.”
Finally, the teaching chain should point out that the presupposition of the thesis may be inappropriate. Because, high volatility and high yield are usually two sides of the same coin. The two models assumed in the paper, low income and high volatility, and high income and low volatility, may both be inappropriate assumptions.
In any case, the enlightenment given by the paper is that asset allocation largely depends on our subjective cognition. Cultivating yourself and improving your cognition are the internal strength and cornerstone of investment. As for the proportion of bitcoin assets that should be allocated, it depends on multiple internal and external factors. Internally, we must be constrained by our own financial situation, and externally, our investment goals and ambitions. In this regard, Jiaolian previously published on 2023.6.28 The article on Liu Jiaolian's official account "How much BTC should you hoard?" " Maybe you can read it.
References:
- [1] https://bitcoinist.com/blackrock-study-optimal-bitcoin-allocation/
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(Public account: Liu Jiaolian. Knowledge Planet: Reply to "Planet" from the public account)
(Disclaimer: The content of this article does not constitute any investment advice. Cryptocurrency is a very high-risk product, and there is a risk of zeroing at any time. Please participate carefully and be responsible for yourself.)