比特幣和MSTR

戰略，以前稱為MicroStrategy，是比特幣的最大公司持有人。目前，戰略以其比特幣的淨資產價值（MNAV）的元素進行交易。

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.

最大的公司比特幣持有人是戰略（NASDAQ：MSTR），以前稱為MicroStrategy。目前，戰略以其比特幣的淨資產價值（MNAV）的元素進行交易。

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.

此後，戰略主席邁克爾·塞勒（Michael Saylor）以其軟件分析業務而聞名，此後將該公司樞轉成比特幣財政公司。結果，該公司以其比特幣持有的淨資產價值溢價交易。

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.

市場上一直在爭論MSTR是否應以折扣或比特幣持有量進行交易。過去，它以溢價交易，即使在近年來，它也繼續以溢價進行交易。

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，例如外國的法律阻止投資者直接購買比特幣甚至發現比特幣ETF。鑑於大多數MSTR的買家都在尋求比特幣的曝光，因此自然的問題是MSTR和BTC的價格密切相關。

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.

為了檢查這一點，我將在2024年每天在每個資產上獲取價格數據。然後，我將計算不同視野窗口上的統計相關性。

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:

讓我們首先檢查一年的窗口。這意味著，對於2024年的每一天，我將計算去年的統計相關性。例如，2024年7月1日的0.64相關性意味著從2023年7月1日至2024年7月1日，BTC-USD和MSTR之間的統計相關性為0.64。這是在滾動一年的窗口上的BTC和MSTR相關性的圖：

BTC-USD and MSTR 1-Year Correlation

BTC-USD和MSTR 1年相關性

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.

如您所見，相關性肯定超過零，但不等於一個。因此，存在積極但不是完美的相關性。相關實際上是相當狹窄的，範圍從0.6到0.69，這是一個緊密的頻帶。一年中沒有普遍的趨勢，儘管人們可能會說，在去年五月減半之前，相關性略有下降。但是，由於它是0.61和0.64之間的差異，因此傾角的幅度很小。

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:

現在，讓我們考慮一個四分之一的較短地平線。我們將使用相同的技術，除了現在考慮一個滾動四分之一窗口。因此，2024年1月1日的0.65相關性意味著BTC和MSTR之間Q4 2023的統計相關性為0.65。這是2024年滾動四分之一相關的圖：

BTC-USD and MSTR 1-Quarter Correlation

BTC-USD和MSTR 1季度相關

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.

現在，相關的差異較大，範圍為0.5至0.75。同樣，這裡沒有真實的模式，除了在年底的相關性略有崩潰之外。這可以定時使用2024年最後一個季度宣布的420億美元的資本購買計劃，在該計劃中，它正在積極購買比特幣。其中大部分導致股票稀釋，這給價格下降了壓力，這將在短期內打破BTC-USD和MSTR之間的聯繫。

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

現在，讓我們看一下BTC-USD和MSTR之間的滾動一個月相關性：

BTC-USD and MSTR 1-Month Correlation

BTC-USD和MSTR 1個月相關

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.

現在，我們看到了這一趨勢的進一步示例。隨著窗口的收縮，相關的差異增加。在這裡，我們看到相關性範圍為0.3至0.9。同樣，全年沒有一般趨勢。

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之間的2024年的滾動一周窗口中，可以看到這種效果的最極端示例，這是：

BTC-USD and MSTR 1-Week Correlation

BTC-USD和MSTR 1週相關

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.

在這個很短的窗口中，相關性可以是任何事物，範圍從低點-0.8到高1.0。每週相關性有些突出，因為這是人們傾向於在Twitter/X上發表評論的內容。他們抱怨MSTR不再與BTC-USD同步移動。

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.

從上圖，您可以看到這是不正確的。在過去的一年中，每週的相關性沒有變化。它一直是極其可變的。有些星期高度相關，幾周根本沒有。每週的窗口可能證明了最基本的一點，即MSTR等槓桿比特幣權益與基礎資產的價格並不相同。

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

儘管每週，每月，每季度甚至每年相關性都高於0.5，有時甚至接近1，但肯定有連接反映的連接，但還有其他因素