比特币和MSTR

战略，以前称为MicroStrategy，是比特币的最大公司持有人。目前，战略以其比特币的净资产价值（MNAV）的元素进行交易。

The largest corporate bitcoin holder is Strategy (NASDAQ:MSTR), formerly known as MicroStrategy. Currently, Strategy trades at a multiple to its net asset value (mNAV) of bitcoin.

最大的公司比特币持有人是战略（NASDAQ：MSTR），以前称为MicroStrategy。目前，战略以其比特币的净资产价值（MNAV）的元素进行交易。

Best-known for its software analytics business, Strategy’s chairman, Michael Saylor, has since pivoted the company into a bitcoin treasury company. As a result, the company trades at a premium to the net asset value of its bitcoin holdings.

此后，战略主席迈克尔·塞勒（Michael Saylor）以其软件分析业务而闻名，此后将该公司枢转成比特币财政公司。结果，该公司以其比特币持有的净资产价值溢价交易。

There has always been debate in the markets as to whether MSTR should trade at a discount or premium to its bitcoin holdings. In the past, it traded at a premium, and even in recent years, it has continued to trade at a premium.

市场上一直在争论MSTR是否应以折扣或比特币持有量进行交易。过去，它以溢价交易，即使在近年来，它也继续以溢价进行交易。

There are good reasons for this, such as laws in foreign countries that prevent investors from buying bitcoin directly or even spot Bitcoin ETFs. Given that most buyers of MSTR are seeking Bitcoin exposure, a natural question is how closely correlated are the prices of MSTR and BTC.

有充分的理由，例如外国的法律阻止投资者直接购买比特币甚至发现比特币ETF。鉴于大多数MSTR的买家都在寻求比特币的曝光，因此自然的问题是MSTR和BTC的价格密切相关。

To examine this, I will pull price data on each asset daily over 2024. I will then calculate the statistical correlation over windows of different horizons.

为了检查这一点，我将在2024年每天在每个资产上获取价格数据。然后，我将计算不同视野窗口上的统计相关性。

Let’s first examine the one-year window. This means that for each day in 2024, I will calculate the statistical correlation over the last year. For example, a correlation of 0.64 on July 1, 2024, means that the statistical correlation between BTC-USD and MSTR from July 1, 2023, to July 1, 2024 is 0.64. Here is a plot of the BTC and MSTR correlation over a rolling one-year window:

让我们首先检查一年的窗口。这意味着，对于2024年的每一天，我将计算去年的统计相关性。例如，2024年7月1日的0.64相关性意味着从2023年7月1日至2024年7月1日，BTC-USD和MSTR之间的统计相关性为0.64。这是在滚动一年的窗口上的BTC和MSTR相关性的图：

BTC-USD and MSTR 1-Year Correlation

BTC-USD和MSTR 1年相关性

As you can see, the correlation is certainly above zero but not quite equal to one. So, there is positive but not perfect correlation. The correlation is actually quite narrow, ranging from 0.6 to 0.69, which is a tight band. There is no general trend over the year, though one might say that the correlation dipped a little bit right before the halving last May. But that dip is quite small in magnitude since it’s the difference between 0.61 and 0.64.

如您所见，相关性肯定超过零，但不等于一个。因此，存在积极但不是完美的相关性。相关实际上是相当狭窄的，范围从0.6到0.69，这是一个紧密的频带。一年中没有一般的趋势，尽管人们可能会说，在去年五月减半之前，相关性略有下降。但是，由于它是0.61和0.64之间的差异，因此倾角的幅度很小。

Now, let’s consider a shorter horizon of one quarter. We'll use the same technique, except now consider a rolling one-quarter window. So, a correlation of 0.65 on January 1, 2024, means that the statistical correlation over Q4 2023 between BTC and MSTR is 0.65. Here is a graph of that rolling one-quarter correlation for 2024:

现在，让我们考虑一个四分之一的较短地平线。我们将使用相同的技术，除了现在考虑一个滚动四分之一窗口。因此，2024年1月1日的0.65相关性意味着BTC和MSTR之间Q4 2023的统计相关性为0.65。这是2024年滚动四分之一相关的图：

BTC-USD and MSTR 1-Quarter Correlation

BTC-USD和MSTR 1季度相关

Now the variance in the correlation is larger, ranging from 0.5 to 0.75. Again, there is no real pattern here except a slight breakdown in the correlation towards the end of the year. This could be timed with MSTR’s $42 billion capital purchase plan announced in the last quarter of 2024, in which it was buying bitcoin aggressively. Much of that resulted in share dilution, which puts downward pressure on price, which will have the effect of breaking the link between BTC-USD and MSTR in the short term.

现在，相关的差异较大，范围为0.5至0.75。同样，这里没有真实的模式，除了在年底的相关性略有崩溃之外。这可以定时使用2024年最后一个季度宣布的420亿美元的资本购买计划，在该计划中，它正在积极购买比特币。其中大部分导致股票稀释，这给价格下降了压力，这将在短期内打破BTC-USD和MSTR之间的联系。

Let's now look at the rolling one-month correlation between BTC-USD and MSTR:

现在，让我们看一下BTC-USD和MSTR之间的滚动一个月相关性：

BTC-USD and MSTR 1-Month Correlation

BTC-USD和MSTR 1个月相关

Now we see an even further example of the trend. As the window shrinks, the variance in the correlation increases. Here we see the correlation ranges from 0.3 to 0.9. Again, no general trend throughout the year.

现在，我们看到了这一趋势的进一步示例。随着窗口的收缩，相关的差异增加。在这里，我们看到相关性范围为0.3至0.9。同样，全年没有一般趋势。

The most extreme example of this effect can be seen in the rolling one-week window over 2024 between BTC USD, which is here:

在BTC USD之间的2024年的滚动一周窗口中，可以看到这种效果的最极端示例，这是：

BTC-USD and MSTR 1-Week Correlation

BTC-USD和MSTR 1周相关

In this very short window, the correlation can be anything, ranging from a low of almost -0.8 to a high of almost 1.0. The weekly correlation is somewhat salient because this is what people tend to comment on Twitter/X. They complain that MSTR no longer moves in sync with BTC-USD.

在这个很短的窗口中，相关性可以是任何事物，范围从低点-0.8到高1.0。每周相关性有些突出，因为这是人们倾向于在Twitter/X上发表评论的内容。他们抱怨MSTR不再与BTC-USD同步移动。

From the graph above, you can see that that is not true. There’s been no change in the correlation on a weekly basis over the last year. It has simply always been extremely variable. Some weeks are highly correlated and some weeks are not at all. The weekly window probably proves the most fundamental point, which is that a leveraged Bitcoin equity like MSTR is not identical to the price of the underlying asset.

从上图，您可以看到这是不正确的。在过去的一年中，每周的相关性没有变化。它一直是极其可变的。有些星期高度相关，几周根本没有。每周的窗口可能证明了最基本的一点，即MSTR等杠杆比特币权益与基础资产的价格并不相同。

While there is certainly a connection reflected in the weeks, months, and many days when the weekly, monthly, quarterly, and even annual correlation is above 0.5 and sometimes even close to 1, there are other factors

尽管每周，每月，每季度甚至每年相关性都高于0.5，有时甚至接近1，但肯定有连接反映的连接，但还有其他因素