🔍Deep Dive: Volatility-Adjusted Power Law Index

In this article, we introduce the Volatility-Adjusted Power Law Index (“VPLI”), a metric designed to assess Bitcoin's over- or under-valuation relative to its fair value derived from the Power Law model.

The primary benefit of the model is that it incorporates volatility adjustments where other ratios don’t. The MVRV ratio for example, peaked at 7 in the first cycle but only reached 3.95 in the most recent cycle, creating a shifting top range which complicates data forecasting for future cycles.

By correcting for this and building upon the previous limitations of existing Power Law models, the VPLI helps provide investors and analysts with clear Bitcoin value regions indicating market “heat” across the Bitcoin lifecycle.

Table of Contents

1. Traditional Bitcoin Valuation Metrics

2. Using the Power Law Model for Building a Valuation …

3. Basic Power Law Index (PLI)

4. Market Depth and Price Volatility

5. Measuring Price Volatility

6. The Final Index: VPLI

7. Key Takeaways

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Traditional Bitcoin Valuation Metrics

Over the years, several financial valuation metrics and modeling methods have been proposed to assess Bitcoin’s valuation. Some of those include:

• MVRV ratio (ratio of ‘paper’ profit vs loss)

• Stock-to-Flow model (existing supply stock vs new production)

• Puell Multiple (miners earnings valuation vs their historical average)

• Mayer Multiple (BTC price vs its 200-day moving average)

• SOPR (profit of all moved bitcoin over a period)

And the list goes on.

In many of these metrics, analysts can identify ranges of value that indicate under/overvaluation, but these ranges and the meaning of the specific metric change with Bitcoin’s lifecycle.

For example, the MVRV went as high as 7 in Bitcoin’s first cycle but then peaked at only 3.95 in the previous cycle. The changing “top” of the range over time limits our ability to make accurate judgments in the next cycle. Where will extreme overvaluation begin in the current cycle? Perhaps it will be below 3.95, but we lack a precise way to determine this.

This article aims to solve this problem by finding a theoretically sound basis for adjusting a power law index so that it offers reliable and stable valuation ranges for every Bitcoin cycle.

Using the Power Law Model for Building a Valuation Metric?

In the last two editions of BN Research, we did a deep dive into the Power Law model.

The model predicts the average price Bitcoin in each cycle and has both a strong fit and strong predictive power. For this reason, we have adopted this model as our base model going forward.

Below is the chart of this Power Law model, which gives an accurate measure of Bitcoins fair value.

But can we use this fair value to extract an indicator or oscillator that gauges the over- or under-valuation of Bitcoin?

Even though the price breaches above or below the power law model, there appear to be limits on how far Bitcoin’s spot price deviates from this “fair value” assessment.

By analyzing the price fluctuations versus the power law prediction line, we notice that prices breaks above from the prediction significantly to the upside and downside in bull runs and bear markets respectively. However, these fluctuations have shrunk every cycle (see below).

• Cycle 1: Bitcoin returned 337x ($29/.086)

• Cycle 2: Bitcoin returned 83x ($1K/12)

• Cycle 3: Bitcoin returned 31x ($20K/652)

• Cycle 4: Bitcoin returned 7.5x ($68K/9K)

Basic Power Law Index (PLI)

If we simply chart the deviations from the fair value (aka, the residuals) over time, we get a very interesting index that oscillates around zero. It went as high as 1.21 and as low as -0.66 in cycle 1. The peaks have again been diminishing every cycle, while the bottoms hover around -0.4 for cycles 2 through 4.

One of the primary problems with this index is that while -0.4 appears to be a robust lower bound (purple line above), we don’t have a robust upper bound (purple dashed line above).

Because the peaks are diminishing, we cannot readily judge what the peak may be next cycle and what range indicates overvaluation. So, this is an incomplete model, and we need to also model the peaks.

Market Depth and Price Volatility

To address this issue, we note that the reason Bitcoin’s price could increase much higher than its fair value in cycle 1, was due to a lack of liquidity and market depth.

Market depth reflects how easily an asset can be bought or sold without affecting its price. A deep market has many buy and sell orders at various prices, indicating high liquidity. This means large orders can be fulfilled without drastically moving the price because there are enough interested buyers and sellers on the other side.

When a market is young and immature, it is easier for buyer and sellers to move the price by large percentages. As the market matures, it takes more and more capital to move the price by the same percentage.

Bitcoin has become significantly more mature and liquid every cycle, explaining why price bubbles are less extreme every cycle. It follows that if we can include a measure of market depth and correct for it, we can arrive at a more useful indicator.

Market depth is typically measured by analyzing the order book. The more buy (bid) and sell (ask) orders exist at various price points, and the larger the size of those orders, the deeper the market is considered to be. 

However, we don’t have the order book data going back to Bitcoin’s early days. Many exchanges have died and with them so too has the data!

The solution is to use a proxy to market depth by using price volatility. An asset with lower price fluctuations hints at a deeper market where large orders are less likely to cause significant price swings.

Measuring Price Volatility

To measure price volatility, we take the standard deviation of price percentage change on a rolling 1-year time window. This measure allows us to gauge the overall level of market volatility in any year.

The chart below shows the evolution of market volatility over time.

The chart exhibits decreasing volatility over time for Bitcoin, evidenced by the standard deviation of price change (%) beginning as high as 0.13 in cycle 1 and dropping to a low of 0.02 as of the last bear market.

We notice that ss the bull markets begin, market liquidity thins and creates an increasingly unstable price. Once price peaks and the speculative bubble bursts, volatility then returns to lower levels until the next bull market begins.

The Final Index: VPLI

Having found a proxy for market depth, we can now correct for the decay in the basic power law oscillator. If we divide the Power Law Index by Volatility, we get the Volatility-Adjusted Power Law Index (“VPLI”).

This index oscillates in the (-20, +20) range, with a minimum of -13.37 and a maximum of 17.27. Values above 10 indicate extreme overvaluation and values below 10 indicate extreme undervaluation.

If we color the dots according to the level of over/undervaluation to indicate market “heat,” we get the following chart. Red dots indicate extreme overheating and deep blue ones indicate deep value.

If we overlay VPLI with the price, we can verify that the tops and bottoms are properly identified.

We can also examine the empirical distribution of the metric to measure how long it spends in each value range.

Below, we have broken down the range of the index into smaller intervals and measured the approximate frequency of days Bitcoin spends in each value range:

• Deep Value (Min, -10): 10%

• Value (-10, -5): 25%

• Cool (-5, 0): 25%

• Warm (0, 5): 20%

• Hot (5, 10): 15%

• Extreme Bubble (10, Max): 5%

It is interesting that Bitcoin spends most of its time in the cooler range. VPLI is negative about 60% of the time. The extreme bubble phase accounts for only 5% of the time, and the deep value for only 10%. Importantly, these ranges have been valid in every cycle.

Key Takeaways

Various models have been used for Bitcoin valuation, but it is often difficult to find a metric that offers a consistent range for what is defined as “over” or “under” valued over time.

The Power Law model, predicts the average price in each cycle with a high degree of accuracy, however the basic oscillators deriving the power law have the same problem of shifting their meaning of “value” every Bitcoin cycle.

Charting deviations from the Power Law’s fair value creates an index that oscillates around zero. While lower bounds of the index are consistent, upper bounds diminish over cycles, requiring a more nuanced model to predict peaks.

Bitcoin's price volatility serves as an excellent proxy for market depth, with lower volatility indicating a more mature market. The market's increasing depth over time has resulted in less extreme price bubbles with each subsequent cycle.

By dividing the Power Law Index by volatility, the VPLI adjusts for market depth. The VPLI oscillates within a defined range, with specific values indicating levels of over- or under-valuation, and historical data confirming VPLI's ability to mark Bitcoin's cycle tops and bottoms.