This past week marked the anniversary of the bottom of bitcoin’s bear market. On November 21st 2022 bitcoin fell to 15790 USD. It is usually impossible to pinpoint the exact through in the real time other by the sheer luck. A year ago, however, there were some signs that the end of the decline may be near.

The price has recovered substantially since then and so I thought it would be interesting to compare the performance of the past year with the first years of the previous three bull markets. I’m omitting the first bull market (0.05 USD -> 30 USD), as it lasted less than a year in total. The second bull market started in Nov 2011, the third in Jan 2014, while the fourth in Dec 2018. Let’s look at their progress over the first year:

To my surprise, the performance of the current advance at one year mark has been nearly the same as in the previous two bull markets. Here are the summary statistics:

The three most recent bull markets had recorded an annual return of about 120% in their first year. The latest advance has been characterized by lowest volatility ever, which resulted in a phenomenal Sharpe ratio of 2.8.

Sometime in 2015 or 2016 I imagined that bitcoin advances would become less violent in the future and at some point resemble gold and silver during 2001-2011 bull market. This has materialized only partially in bull #4 (2018-2021), as the advance was indeed smaller than the bull of 2015-17, while the volatility stayed nearly the same at 73% (for the full cycle). In contrast, in the most recent advance the return in the first year has been nearly identical to the 2018-19 advance, while volatility dropped substantially, which resulted in an improved Sharpe ratio. It looks like we’ll have to wait several more years for the analogy to gold or silver to occur.

So, where do we stand today? Another advance of less than 100% would put us above the previous top of 69k BTC/USD, so we’re about 60-65% advanced in the “stealth” phase of the bull market – still in the shade of the previous peak. The annual increase and the Sharpe ratio suggest we had a good run recently compared to the previous two bull markets. Let’s look at the financing rates embedded in the prices of futures:

Here, too, we can start to see a little bit of froth. In contrast to the -25% annual financing rates embedded in futures prices a year ago, we currently are faced with 8-13% IFRs depending on the exchange. The theoretical value is equal to the risk free rate, or currently about 5.4%. On balance this suggest a pause, consolidation and perhaps a drift lower over the next several months. However, the trajectories of bull markets at this stage have been rather chaotic in the past, so one should take this into account when gazing into the crystal ball.

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Short Selling (Part 2)

This is the second post in a series describing the performance and effects of short selling. Part 1 dealt with three main effects: return to the underlying instrument, volatility slippage and the impact of the risk free rate. In this part we look at three lesser effects: borrowing fee, the deviation in financing from the risk free rate and management fee for the ETFs. In the end we’ll look at a real life examples from the recent past.

Fig. 2.1. A summary of effects impacting a long and a short position

4) Borrowing fee
Short selling is a strategy of selling financial instruments that we do not own. Therefore, before entering the transaction an investor needs to borrow the securities intended for future sale. For stocks and ETFs this comes at a fee; there’s no borrowing fee when short selling via futures. There are two main types of securities: easy-to-borrow and hard-to-borrow. The easy-to-borrow come with a very low borrowing fee: as low as 0.25% annually. On the other hand, the hard-to-borrow stocks and ETFs come with progressively higher, sometimes exorbitant fees, as high as several hundred percent annually. The following figure presents the distribution of borrowing fees for all securities available for shorting at Interactive Brokers on 19th of April 2023. About 6000 of them come with the very low borrowing fee of 0.25-0.30% annually. Another ~4000 securities have relatively low fees, up to current risk free rate of 5%. The remainder of securities gets progressively harder to borrow and, in effect, is characterized by very high borrowing fees. The fee can change daily and is subject to the usual forces of supply and demand. Please note the logarithmic scale on the y axis.

Fig. 2.2 Borrowing fees for short sale of US securities on Apr 19, 2023.

5) Deviation from Rf rate in financing
So far we have learned that shorting comes with a fee to the rightful owner of securities and the proceeds from sale can be invested at a risk-free rate. However in between you, the short seller, and the investor on the other side, there are intermediaries – brokers. They need to get their share of profits for facilitating the exchange between investors. Fig. 2.3 presents the yields from short sale of stocks/ETFs for Interactive Brokers investors. Benchmark rate is the risk free rate (at the time of writing: 4.83%). Short positions valued at less than $100k do not receive any proceeds from short sales. Larger positions, between $100k and $1M get 3.58%, as IBKR cuts its 1.25% fee. Only above the $1M the broker financing fees become rather small at 0.25%-0.5%.

Fig. 2.3 Interest paid for proceeds from a short sale at Interactive Brokers (Apr 19, 2023)

How about the futures? Here the situation looks more positive for the short sellers. As brokers do not need to locate & borrow shares and do not need to deal with position financing, no fee to brokers, other than the commission to open or close position, is necessary. In addition, there can be some discrepancy of financing “hidden” in the price of futures. Let’s look at an example of S&P 500 futures. Theoretically the price of futures vs the underlying index should reflect just the risk free rate and the impact of dividend payments. However, in practice, the price of futures is usually somewhat higher than theoretically expected. This is good news for short sellers, as the price needs to converge to index at expiry date, allowing for slightly higher realized returns. How much is the effect worth? In the 10 years following the GFC the so-called Futures Implied Rate was 0.30% annually on average, although it was nearly twice as high during the crisis itself:

Fig 2.4 Futures Implied Rate for S&P 500 futures


In summary, the deviation from theoretical financing fees is negative for stocks/ETFs due to the broker’s fee and amounts to between 0.25% and 1+% even for relatively large sizes for a retail or semi-professional investor – at a broker known for relatively low fees. The deviation can be positive when shorting via futures, but it will vary in time and for different instruments.

6) Management fee
This effect exists only for the ETFs, as there are no management fees for futures and individual stocks. High management fees are a negative for investors holding long position. But can an investor on the short side take advantage of the high management fee and pocket the profit? Let’s see. The following table lists 10 ETFs with the highest total expense ratio, taken from an article in In the rightmost column I added the borrowing fee for each of the ETFs for the date of 19th of April. In all cases except two, the borrowing fee is higher than the total expense ratio. It means that one usually cannot expect to capitalize on the recovery of expense ratio via shorting. However, it is important to factor in both effects when calculating the expected returns of shorting ETFs.

Fig. 2.5 Borrowing fee for the ETFs with higher Total Expense Ratio.

Ok, now it is time to put all the effects together. Let’s look at the theoretical and real performance of the ProShares Short S&P500 ETF (SH) between Dec 31, 2021 and March 31, 2023. This period of five quarters was characterized by a relatively weak performance of the index, making short selling a profitable strategy. The relevant data are as follows: S&P 500 had a Total Return of negative 11.97%, with annualized volatility of 22.95%. The cumulative return on 3M T-Bills was 3.27% and the management fee charged against the ETF assets was 0.89% p.a.:

Fig 2.5 Simulated vs. real return for SH ETF (Dec 31, 2021 – Mar 31, 2023)

The simulated return for the period was 11.18%, while the actual return for SH ETF in the same period was 0.18pp higher at 11.36%. The small discrepancy may be coming from several areas: the ETF uses total return swaps instead of futures and invests in T-Bills with a maturity both longer and shorter than the simulated 3 months. I also assumed that effect 5) was as equal to its average during 2009-2019, but did not independently check the actual value for the period.

Now, lets look at another real-life example for the same time period: shorting a 7-10 year Treasury bond index via the ProShares Short 7-10 Year Treasury ETF (TBX). As a basis for the analysis we’ll use the iShares 7-10 Year Treasury Bond ETF (IEF). It returned a negative 12.31% over the 5 quarters, but 0.16pp of that was the effect of the 0.15% management fee. Volatility was 10.4% annually. Let’s again use the 3 month T-bills as a proxy for the risk free rate not assuming any adjustments to position financing. We deduct the 0.96% management fee the ETF is charging on its assets.

Fig 2.6 Simulated vs. real return for TBX ETF (Dec 31, 2021 – Mar 31, 2023)

As we see, the simulated performance matched the real result exactly. We can notice that the performance of the short ETF (TBX) is substantially higher than just the reverse of long ETF (-IEF). IEF returned -12.31% in the analyzed period, while TBX returned 16.12%. The reason is that the volatility slippage was substantially lower than the effect of receiving the double of the risk free rate, just -1.36% compared to +6.53%.

Contrary to a naïve understanding, short selling is a strategy that can perform well not only in the falling markets, but also when markets are flat or (slightly!) advancing. There are at least 6 effects that may impact the total return of the short selling strategy. On top of the obvious one, the change in the underlying instrument, the two other large effects are the volatility slippage and the effect of adding the double of the risk free rate. In recent times, the high level of risk free rate, approaching and exceeding 5% p.a. allows for 10+% short selling returns p.a. even in relatively flat markets. However, this positive effect can be substantially diminished in rebalanced portfolios when shorting instruments with high volatility due to the so-called volatility slippage.

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Short Selling (Part 1)

This is a 2-part post about short selling. It deals with the theory and portfolio effects first, then looks at recent performance of portfolios short stocks and bonds in the US markets.

The layman’s understanding may be that holding a short position is just the opposite of holding a long position. If a shock goes up by 10%, the investor gets +10% return if they are long and -10% return, if they are short. This may be true for a very short holding period (less than a day), but when holding for a longer time, the performance of a short position is not the opposite of a long position. There are multiple factors affecting short selling as I will explain in detail below.

There’s a reasonable introduction to short selling in Investopedia, here. However, it contains some inaccuracies and perhaps slightly misleading statements. Some may have been true when interest rates were at zero, but are not true anymore. At the outset the authors state that: “Short selling [is an] investment activity in which the investor borrows securities and sells them in the hopes of then purchasing the securities at a lower price in the future.” As we’ll see below an investor can be perfectly happy short selling when he expects the price of the underlying to be flat or even go up. This may be true even holding the short position outright, not as a part of a hedging strategy.


It may be worthwhile to start from the decomposition of returns to a long position and a short position. As we see in the table below, holding a short position is accompanied by several factors that do not exist if we just go long. The positive (negative) sign means that the return of the position is positively (negatively) correlated with the change of the line item. Zero sign means that the effect does not exist for this specific line item. I’m splitting the effect between investments for futures and stocks/ETFs, as there are some material differences between these types of instruments when shorting them. The difference between stocks and ETFs consists mainly of the management fee. In order to simplify matters, in all cases I’m assuming the portfolio is fully invested, i.e. an exposure of +100% for a long position and -100% for a short position.

Fig. 1.1 A summary of effects impacting a long and a short position

The effects while holding a long position is rather straightforward: you get the change in the underlying minus the management fee – in case of the ETFs. In case of dividend or interest paying instruments, such as stocks or bonds, the change in the underlying is the total return: price change + dividends or interest. Simple enough.

The effects impacting the short position are a bit more complicated.

1) The change of the underlying
We have the opposite effect of the long position here: when your investment goes up, your portfolio value goes down by the same percentage. Instead of receiving dividends or interest from the underlying instrument, you need to pay it to the owner of the instrument. Hence the negative signs in the table: your portfolio’s value is negatively correlated with the return of the underlying instrument.

However, the simplicity of the calculations breaks down after the first change in value of the underlying. Let’s explain it using an example. Let’s consider what happens to portfolio value and its exposure to the underlying instrument when the price change in the underlying is “proper” for both strategies, up for the long strategy and down for the short strategy. In the case of the long strategy, both the value of the underlying and the value of the portfolio change in tandem from $100 to $110. The exposure stays at 100% of portfolio. However, in the short portfolio, the changes go in the opposite directions: as the underlying drops from $100 to $90, portfolio value increases from $100 to $110. The exposure of the portfolio drops to 82%.

Fig. 1.2 The impact of price changes on a long and short position

This leaves the portfolio manager with a dilemma: to rebalance or not to rebalance. Choosing not to rebalance has three potential issues:
A) The exposure is never -100% as intended
B) It opens the possibility of catastrophic losses
C) It limits the upside to +100%

A) If we choose not to rebalance, the exposure of the portfolio to the underlying instrument is variable and at the mercy of the price changes. It will (almost) never be 100% as originally intended. This is why the short (inverse) ETFs (such as SH, PSQ or TBX) have to rebalance daily, in order to always offer the potential investors -100% exposure.

B) Not rebalancing opens the possibility of catastrophic losses of the total value of the portfolio, or even more. The reason is that the underlying can increase in price by 100% or more, resulting not only in wiping out the whole investment capital, but potentially putting the investor in debt. On the contrary, rebalancing requires a gradual reduction of the exposure – buying back part of the short position. This reduces the risk and likelihood of the loss of capital.

C) It is often said that the maximum profit while shorting is 100%, as the value of the underlying cannot go below zero. However, if one decides to rebalance, the upside from shorting is practically unlimited. The table below presents the potential profits from shorting in two versions: non-rebalanced and rebalanced at 1% intervals, assuming the price of the underlying goes down monotonically:

Fig. 1.3 The impact of rebalancing on realized short selling profits

As we see, rebalancing your shorts all the way down can (theoretically) offer 9.8x return when your underlying goes down by 90% and 94x return, when it goes down by 99%.

If it all looks too good to be true, with three distinct advantages of rebalancing, that’s because it is. No investment goes down in a straight line and short selling suffers from the so-called Volatility Slippage.

2) Volatility Slippage
Let’s return to the example where the underlying went down by 10%, the value of the portfolio went up by 10% resulting in an exposure of 82%. In order to bring the exposure back to 100% the investor needs to sell short additional 18% of the portfolio’s value. However, the sale is being done at lower prices than originally. So, the investor needs to sell low to rebalance. What happens when the price of the underlying goes back up to the original price? The rebalancing requires a repurchase (covering) of some of the short position. The volatility slippage is thus a drag on the portfolio’s performance. The investors needs to sell low and buy high – the opposite of the usual trader’s strategy.

How much is the drag worth? It depends on the underlying instrument’s volatility. To cut things short and not to bother the reader with the equations, it suffices to say that for the -1x short position the volatility drag is approximated by the variance of the underlying instrument. So, for the stocks with volatility of 20% annually, the volatility drag amounts to 4% p.a. Bonds with 8% volatility suffer from a 0.64% volatility drag annually. This is not good. Even if we manage to nail the decline in stocks and they go down by 10% in a year, volatility drag will eat as much as 40% of the profits we made. Can we count on some additional help? Yes, we can.

3) DOUBLE the risk free rate
Recent increase in Fed Funds and Treasury Bills yields towards 5% offers investors an opportunity to capitalize on them not only by holding cash that finally earns decent interest, but also juicing up profits from shorting. Short selling position has a positive financing of double the risk-free rate embedded. How so?

First of all, in order to short a financial instrument, you don’t need to deploy your own capital. Well, with caveats. You need to reserve some portion of your capital as margin, but it is quite small. For example, at the moment of writing you need to reserve a margin of just 5.3% for the S&P 500 futures (tickers ES and MES) and 2.6% for the Ultra 10-year bond futures (ticker TN). The rest can be invested in at the risk-free rate, yielding ~5% for your portfolio.

Secondly, the same risk free rate is embedded in the prices of futures. In order to have a parity pricing between holding the position outright and holding a position consisting of futures + T-bills, futures price needs to take T-bill rate into account. They will be priced high when launched and slowly converge to the price of the instrument underlying the futures at expiry.

There you have it: at current risk free rate, you get 10% financing help when holding a short position. However, there are some deviations from this rule. We will discuss them in more detail in points 4) and 5) in Part 2 of the series.s

This is getting slightly complicated at this moment. Total profit from a short position depends not only on the total return of the shorted instrument, but also on the whether we rebalance or not. When we do, the result depends on the volatility of the instrument. Additionally, we get help from the financing rate. In order to put this all together, let’s look at the following table. It presents the results of a short portfolio for different levels of volatility (5-25%) and total return (from -10% to +5%) of the underlying instrument.

Fig. 1.4 Return to a short portfolio for different levels of return and volatility of the underlying instrument

As we see, a short position will result in positive return not only when the price of the underlying goes down, but also when it is unchanged and even when it goes up. As an example, portfolio being short stocks with 20% volatility will yield 6% return when they are unchanged: 10% from 2 x risk free rate and -4% from the volatility slippage.

The following table tries to visualise a different dillema: for a given change in the underlying instrument and given volatility, is it more profitable to enter a short or a long position?

Fig. 1.5 Return difference between a short and a long portfolio for different levels of return and volatility of the underlying instrument

As we see, the line of indifference lies at slightly positive returns of the underlying: for an instrument with 20% volatility a positive 3% return of the underlying yields the same profits for the long and the short position. For an instrument with 10% volatility a 4.5% positive return in the underlying results in identical returns for the long and short positions.

We can establish in principle what the return of the underlying needs to be, in order for the investor to be indifferent between a long and a short position. For the non-rebalanced portfolios the expected return of the instrument under consideration needs to exceed the risk free rate. This makes intuitive sense: if an investment yields higher return than T-Bills, we go long. If the return is lower, we sell the investment short and invest the proceeds at the risk free rate. For a rebalanced portfolio the situation is a bit more complex, as we lose money to the volatility slippage. In order to go short the expected return of the underlying needs to be lower than risk free rate minus half of variance.

This concludes Part 1. In Part 2 we will look at the less pronounced effects 4-6 and some real-life examples from the recent past.

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Bull/bear market cycles for Bitcoin and Ethereum

Two and a half months passed since I have looked at the Bitcoin bull and bear market cycles. Since then we recorded a new marginal low in September and, last week, a continuation of the bear market, triggered by the collapse of FTX and Alameda . In this post I will extend analysis from August till mid-November and analyze the bull/bear cycles of Ethereum and market capitalization weighted portfolio of Bitcoin and Ethereum.

Let’s first look at the updated table summarizing past Bitcoin’s past 4 bull/bear market cycles. The changes vs. August have been italicized.

Source:,, own calculations

The most “encouraging” development is the fact that the bear market was extended from 7 moths to just over a year. That was one of my main concerns with cryptos – the bear market was not long enough to purge the necessary excesses of the bull phase. The depth of the drawdown has also increased – from 72% to 76%. Cycle 4 Sharpe ratio fell from 0.89 to 0.69, a combination of lower cycle profits and extended duration of the cycle.

It is only now, that it seems like the necessary conditions for the bear market to end have been fulfilled: it has sufficient duration and sufficient depth. Which is not to say that it has necessarily ended. It may last several months longer and the drawdown may increase to 80+%. However, such developments would still not invalidate a long term positive outlook for Bitcoin in particular or crypto in general.

To extend the analysis, I have decided to include the same statistics for Ethereum and a market capitalization weighted portfolio of Bitcoin and Ethereum. This is a relatively agnostic and conservative position as to whether the #1 or #2 wins in the long term. I have followed this approach since mid-2017. Ethereum has a shorter market history, so I include only the last two cycles (2015-18 and 2018-22)

Source:, own calculations

One of the reasons for optimism in crypto space is that the FTX/Alameda fiasco has not impacted Ethereum to the extent that it made a new low in November. It currently trades at around 1200 ETH/USD, while the low was made in June at 994 ETH/USD. The drawdown then for ETH was still deeper than current drawdown for BTC (79% vs. 76%). The reason for that may be the successful Merge, which brought the ususal “buy the rumours” 100% increase in Jul/Aug, which was followed by “sell the fact” 40% decline in September. So, kind of mixed bag here – the ETH bear market phase was a bit short (just over 7 months), but sufficiently deep. Please note that the Sharpe ratio for ETH this cycle is still excellent at 1.08, despite the deep drawdown.

Source:, own calculations

The market capitalization weighted index of BTC and ETH made a new low in November. This extended the drawdown to -77% and duration to just over 1 year. Similarly to BTC, current cycle’s decline of the index seems sufficiently long and sufficiently deep for the bear market to end. Again, this is not a call of the bottom, we can obviously go down more.

For an easier comparison, I put the most important statistics of the last cycle for the three portfolios in a summary table:

As we see, Ethereum had substantially better growth rate compared to Bitcoin (102% vs 50% annually). It was not offset by higher volatility, hence the higher Sharpe ratio. The market cap weighted index volatility is only slightly higher than that of Bitcoin alone. BTC and ETH are very highly correlated, but not at 100%, hence the volatility is somewhat lower than the market weighted average of BTC and ETH.

Disclaimer: I keep ~10% of my usual crypto allocation through BTC, ETH and BITW CEF.

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Correlations between Money Supply, Inflation and GDP

With high inflation impacting almost everyone both in the developed and developing countries, there’s a discussion about its future course. There is the “Team Transitory” suggesting inflation is about to subside and those that think the price increases will continue for much longer, perhaps for many years. The discussion has been going on for about a year now and has luminaries on both sides of the isle. In the US perhaps the most well-known are Nobel laureate Paul Krugman for “Team Transitory” and former Harvard president Lawrence Summers for the ”Higher for Longer” team.

Bloomberg consensus is for inflation to fall more rapidly than in historical precedents.

Milton Friedman has famously said that that “Inflation is always and everywhere a monetary phenomenon”, but we know that short outbursts of inflation can be attributed to other factors, such as temporary imbalances in food and energy markets. Hence the distinguishment between core and headline inflation. It is not that black and white by any means.

In this post and analysis I wanted to establish some baseline position – to what extent inflation (as measured by the CPI index) is correlated with money supply expansion? I was also interested in the fact, whether increased money supply can help economic growth – as measured by Real GDP. Then, I have looked at another effect – can inflation positively impact money creation? In the end, to be thorough, I looked at all the possible combinations of these variables. The data for the analysis comes from St. Louis FED website (FRED). I took December 1959 as the earliest common starting point for M2 Money Supply, CPI index (headline and core) and Real GDP. I have run correlations between annualized changes of the variables – for different combinations of the length of time the change is measured for the correlated variables and delays of the starting points of the measurements. I think it will be best to explain the logic behind my approach looking at an example. The following table contains correlation coefficients for two variables: M2 Money Supply and Core CPI. In the columns (labeled 1 through 36) we have the length of time (in calendar quarters) for the measurements of changes of both the M2 and Core CPI. In the rows (labeled 1 through 20) we have the delay (in calendar quarters) of the start of measurement of the dependent variable (here: the Core CPI) vs. the independent variable (here: the M2).

To make the example even clearer: if we take the intersection of column ‘8’ and row ‘8’ it will include, among many others, the following data:
– M2 annualized increase between Dec 1970 and Dec 1972 (8 quarters of measurement) correlated with,
– Core CPI annualized increase between Dec 1972 and Dec 1974 (8 quarters delay).

An intersection of column ‘8’ and row ‘7’ included, among other data points, the following data:
– M2 annualized increase between Dec 1970 and Dec 1972 (8 quarters of measurement) correlated with,
– Core CPI annualized increase between Sep 1972 and Sep 1974 (7 quarters of delay).

Table 1. Correlations between M2 Money Supply and Core CPI (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

The table is the result of the longest possible dataset combination for the starting periods of Dec 1969- Jun 2022 (the first 40 quarters are needed for the formation of the longest measurement period). So, for the ‘1’/’0′ and ’36’/’0′ correlation results we correlate 210 datapoints in both data series, but for the ‘1’/’20’ or ’36’/’20’, just 190 datapoints, due to the 20 quarters of delay.

The thick black line separates data that is wholly independent timewise (lower-left part of the table) from data that is at least a bit time-overlapping (upper-right part of the table). We can see it in the examples above: ‘8’/’8′ intersection is non-overlapping, while ‘8’/’7′ intersection is overlapping (the Oct-Dec 72 quarter belongs to both time series in the second example, but not the first).

The table is a heatmap going from the lowest correlations (red) to the highest (green). The rightmost column is an average of the correlations in a given row (heatmapped separately from the table). The lowest row is an average of the correlations presented in a given column (also heatmapped separately from the table and the rightmost column).

We can notice that there’s virtually no correlation (-2%) in quarter-to-quarter changes of M2 Money Mupply and Core CPI. In other words, in a typical quarter, say between Dec 1996 and Mar 1997, the annualized change of M2 had no impact on the pace of change of the Core CPI. However the longer the measurement, the higher the correlations. If we take a 5 year (20 quarter) measurement period and a 5 year delay, the correlations increase to as much as 70%. An example would be a period of M2 increase during the period of Dec 1982-Dec 1987 correlated with the Core CPI increase 5 year later – between Dec 1987 and Dec 1992 (and all other combinations like that between 1959 and 2022).

The results highlighted in bold represent highest correlations for any given measurement period. We can notice that increase in money supply over any given 3 year period has the highest correlations with 3-year Core CPI increases 14 to 19 quarters later, at 68%. This is a rather long term impact: 3.5 to 4.75 years. Overall for all the measurement periods between 1 and 36 quarters the correlations seem to peak with a delay of about 3.5 years (13-14 quarters). We can clearly see that for longer measurement and delay periods there are high correlation between increase of M2 and Core CPI. How about Real GDP? Does the increase in money supply affect the Real GDP? It’s complicated:

Table 2. Correlations between M2 Money Supply and Real GDP (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

The short term correlation is negative (e.g. -29% for the 1 quarter measurement period). Then, with increased delay, correlations switch to positive, then back to negative again. My hypothesis is that it works as follows:
1) initial relatively strong negative correlation is due to a reactive nature of the FED and the financial system. When RGDP growth is slow or slowing down, monetary policy becomes looser, which results in higher growth of monetary aggregates (“money printing”)
2) money creation impact the economy positively over the next several (4-6) quarters – a positive impact on RGDP growth from increased money supply.
3) the effect partially reverses over the following 6-8 quarters, as the economy establishes a new equilibrium.

Please note, that this process can also work in an opposite way – FED slowing down the economy that is growing too fast – but my perception is that this was less common (I haven’t checked the data, though). It is also possible that this line of reasoning is totally flawed – the strength of correlations is quite weak anyway.

We can also notice, that any potential impact on Real GDP seems to be substantially weaker than impact on the CPI. Average correlation in Table 2 is 7% (bottom right corner), while average correlation in Table 1 is 58%. It seems that money supply has more than 8 times stronger impact on inflation than on the GDP – at least in the analyzed period and given the methods used.

Let’s look at another set of correlations. Does inflation impact the money supply?

Table 3. Correlations between CPI and M2 Money Supply (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

It seems that it does. The average correlation in this table is 35% – weaker than M2 -> Core CPI correlation, but much stronger than the impact of M2 on Real GDP. It is mostly coming from the overlapping periods – upper right corner, lower left correlations peak at relatively modest 36% for ’12’/’12’ and ’16’/’16’ combination of measurement period and delay period. So, how can we understand these results? It seems that money supply and, by extension, monetary policy is not independent from the level of inflation. If inflation is high, M2 will be somewhat high as well. The impact seems to linger for at least 2-3 years, perhaps longer.

The hypothesis here is that if inflation gets too high, the FED and the banking system cannot decelerate the money supply as fast as they would like to. If inflation is ~10% and RGDP grows by ~2% annually, perhaps it is difficult or detrimental to manage the financial system so that it delivers only a 4% M2 increase. The data suggests that the level of inflation, at least in the past, informed (correlated with) the level of future money supply increases. That may mean that instead of the preferred 4% M2 increase that would be consistent with 2% RGDP growth and 2% inflation, the FED has to, temporarily, opt for a 6% or 8% growth of the money supply for several quarters, even when they are in a tightening mode.

Overall this analysis of the past supports, to some extent, the team “Higher for Longer”. There seems to be a moderate correlation between past money supply increases and future inflation – for many subsequent quarters. The annualized M2 increases have been 13.7%, 9.3%, 5.9%, 1.7% and -1.3% for the past 12, 8, 4, 2 and 1 quarters to June 2022. It is only in the past 2 quarters that the Money Supply started to stabilize, decelerate and decrease. However, the overhang of the money creation of the past 3 years seems to be substantial.

Higher than average inflation is far from certain outcome. If money supply decreases for several more quarters, as it did recently, it would be a braking force. We would have a tug-of-war between the effects of money created in 2020-2021 and money supply extinguished or stable in 2022 and beyond.


The following table presents the average correlations (lower right corner) of all 12 combinations between variables (M2, Core CPI, headline CPI and RGDP).

Table 4. Summary of correlations between 4 macro aggregates (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

With the exception of the two CPI index cross-correlations, the highest correlation is between M2 as an independent variable and Core CPI (dependent): 58%. The lowest correlation is between Real GDP as independent variable and M2 as a dependent variable: just 3%. This is ironic and perhaps a little bit sad. The full quote from Friedman was: “Inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output.” On the one hand GDP growth does not seem to inform/impact future Money Supply increases (and it should), while Money Supply seems to inform/impact future inflation growth (while it better shouldn’t, or should to a lesser extent).

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Bonds & Money Supply

Over the past week I have noticed several voices from respectable investors or investment managers that the expected returns on bonds are finally attractive. See the thoughts of Jeffrey Gundlach’s and Ben Carlson’s.

The biggest risk to (nominal) bonds is, obviously, inflation. The latest figure for the US is for the month of August and is as high as 8.3%. It has come down from the four decade high of 9.1% in June. That’s quite a bit higher than recent yields for Treasury bonds, which are generally in the 3.70%-4.20% range for maturities between 1 year and 30 years. Quite simply, the inflation is generally expected to come down substantially, towards the 2% mark, as the FED is very serious about fighting the dragon.

Not everyone agrees. Larry Summers, who was the Secretary of Treasury under Clinton and President of Harvard afterwards warned recently: “If we’re going to bring down inflation, you likely need a policy more restrictive than the policy that’s contemplated by the markets or the Fed. The Fed continues to be excessively optimistic.” There you have it. FED is tightening at a fastest pace in several decades, some think it has gone too far, others think it will not be enough. The thing is, Larry Summers was generally right being concerned about too much money being created/given away, so one should definitely listen to him as a valid side in this discussion.

I had a look at the data for the money supply (M2), Real GDP growth (RGDP) and inflation (CPI) in order to look for some hints concerning the future trajectory of inflation. I took long time series of data (since 1960) and have analysed the growth of these aggregates over 10 years. I was mildly surprised to notice that the average 10y growth rate of M2 was 6.9%, RGDP averaged 2.9%, while CPI averaged 4.0% over this period. In a sense, this should be expected: the M2 should increase with the growth of the economy, and the “excessive” M2 growth should be reflected in the average price growth – the CPI index’s. But my surprise was that this relationship was so close: 6.9% = 2.9% + 4.0%. This is likely a coincidence, as the compounded average growth rates over the past 62 years (as opposed to average 10 years growth rates) are slightly off: 7.1% for the M2, 3.0% for the RGDP and 3.8% for the CPI. In any case, the relationship seems to hold. This is how the growth rates look over the past 5+ decades:

What one can notice is that there are two distinct periods. The first one is of monetary tightness (1978-2004), when the 10y growth of the monetary supply was below the combined growth rates of RGDP and CPI. In the second period (2004-present) the opposite is true: the M2 growth rates were in excess of the growth of GDP and price index. Note that these are 10y growth rates, the dates mentioned are the end-dates of a 10y period. What we can notice is that ever since 2004, and more so from 2008, the growth in the monetary aggregate was stronger than the growth of RGDP and CPI. While GDP and prices grew at about 2% pace, M2 grew at 6% or slightly higher for ~15 years. The pandemic exacerbated the disconnect – over the past 2 years the difference between the money supply growth and the GDP+price growth increased to more than 4pp. I have quantified the cumulative monetary ‘overhang’ of the past 14-18 years (since 2004-08) and it amounts to 60-65%. This is the red area between the blue and orange lines. What might it all mean?

It might mean that there has been a lot of money printed over the past decade+ which is more than enough to ‘service’ future GDP and price growth. If the whole overhang is to be ‘used’ over the next decade, we’d get about 5% annual RGDP+CPI growth. With a GDP growth of 2% we’d get a 3% CPI growth, which is not bad. But that assumes no increase in money supply for a decade! Which has never happened and is unlikely to happen. If the money supply expanded at a slow pace of 4% p.a. and the whole overhang were to be reflected in prices, we’d get a 7% inflation for a decade. Not a good environment for bonds – especially nominal bonds.

However, the uncertainty concerning future inflation does not concern the TIPS – inflation protected Treasury bonds. They have offered 2.2% real return at the end of September ’22 (for short term TIPS of 1-5 years – STIP ETF) or 1.86% for the TIP ETF, which holds all of the TIPS bonds (with average maturity of 7.3 years). The STIP ETF had a volatility of 2.6% over the past 3 years, while the TIP ETF – 5.7%. This seems like a safer bet to me given all the uncertainty surrounding future inflation rates.

– the model might be wrong, inaccurate or too simplified. Even though the relationship between M2, RGDP and CPI held closely over the past 5+decades, doesn’t mean it will hold in the future.
– the starting point for the period of excessive money printing (2004-08) might be too early and one should only look at the past several years. If one took the monetary overhang only since the start of the pandemic, it is just ~17% and the potential for future inflation is much smaller.

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Bitcoin Bull and Bear Markets

With Bitcoin hovering just several percent above the low set in June 2022, let’s have a look at the bull and bear markets that it underwent since 2010. There were 4 bull markets and 4 bear markets, as presented in the chart below.

Cycle 1 lasted between 2010 and 2012, cycle 2 between 2012 and 2015, while cycle 3 from 2015 until 2018. Cycle 4 started in Dec 2018 and one important question is whether it has ended already or not yet. In other words, will the June ‘22 low of 19,018 BTC/USD (on a closing basis) hold or will we experience new lows. We know the peak of cycle 4 is behind us, but we do not know, if we’ve seen the bottom. In order to have a better understanding of each cycle, let’s look at the data:

Maturation of bitcoin as an asset class seems to have brought, with each cycle, the following:
– lower annual returns
– lower volatility
– lower Sharpe ratio

Cycle 2 had a longer duration than cycle 1 and, in turn, cycle 3 has been longer than cycle 2. While the bull phase of cycle 4 was about as long as bull market of cycle 3 (1059 days vs. 1066 days), the bear market has been much shorter – just 222 days vs. 364 days. Also, the drawdown of cycle 4 so far has been 72%, while in the past 2 cycles the maximum drawdowns have been 82% and 83%. Now, if the volatility of an asset class decreases, one could plausibly expect lower drawdowns. Unfortunately, bitcoin’s volatility in cycle 4 has been more or less the same as in cycle 3: 74% vs. 73% on the annual basis. Coupled with lower annual returns (66% vs. 104%) this resulted in lower Sharpe ratio. The unfortunate consequence here is that there is a potential for even higher drawdown in cycle 4 when compared to cycle 3. If we assume that a bear market results in a 2 standard deviation move to the downside, the expected drawdown for cycle 4 (annual return of 66% and volatility of 73%) is, unfortunately, 86%. That translates to a bottom of about 9460, or -53% from current prices of ~20k USD/BTC. Ouch! Of course, this does not need to happen, as there’s no rule that a bear market “needs” to reach 2 standard deviations below the trend. If drawdown of cycle 4 matches those of cycle 2 and 3, we could see the trough of 10800-11200, still a ~45% drop form ~20k BTC/USD. Another way to get to this number is to look at the ratio of peaks and ratio of bottoms. The peak of cycle 4 (67 570 BTC/USD) was 3.47 times higher than peak of cycle 3 (19 500 BTC/USD). The expected bottom could then be 3.47*3237 or about 11200 BTC/USD.

Comparing current situation to previous market cycles is obviously an just one exercise to establish a baseline scenario. Perhaps the drawdown will be lower than expected due to more mature market and higher institutional ownership of cryptos. Perhaps it will be deeper, because we have substantial tightening from the FED and rising real long term interest rates. I’m just thinking that the short duration of current bear market, just 7 months, compared to 12-13 months in the previous two cycles, and still a relatively low drawdown of 72% vs. expected 80-85% (I know how this sounds!), makes it plausible that more pain is to be expected in the crypto world in the coming months.

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The Moneyness of Fiat, Gold, and Crypto

I’m aware that I’m using the term “moneyness” outside the typical meaning of the word. It usually describes the likelihood that a financial option can be exercised and earn money, rather than expire worthless. The measure can vary between 0% and 100%. I like the word “moneyness”, so I decided to repurpose it for a slightly different use. The intended meaning of the statement: “The Moneyness of Crypto” is: to what extent cryptos are or could be considered money? 0%? 100%? Or somewhere in between?

Amber, beads, beaver pelts, bottle caps, bronze ingots, candy, cigarettes, cocoa beans, copper, cowry shells, cows, fish, gold, knives, lead ingots, meteorite iron, obsidian, parmesan cheese, potato mashers, rum, salt, silver, squirrel pelts, stone wheels, tea bricks, whale teeth.

The list looks like a zoo of things that have nothing to do with one another. An yet – all these things have been used as money in the past. So, what is money? Money can best be described by either its characteristics or economic functions it serves. The characteristics of money are: durability, homogeneity/uniformity, divisibility, limited supply, recognizability/acceptability and portability. The economic functions of money are: a unit of account, a medium of exchange, and a store of value. The analysis is divided into two parts. This essay deals with the characteristics of money, while part 2 with its economic functions.

I’ll attempt to score three types of money: the money issued by governments (often called the “fiat” money), precious metals and cryptos on a scale of 0-10 in these areas. This is not a systematic review, as it is nearly impossible to consider the details of all state-issued monies, all cryptos, all potential uses or all transaction methods. The scoring system is also pretty subjective, so I’m sure the reader would score some of them differently, even given the data and perspective provided in these essays.

The government-issued or fiat money is a system consisting of at least three forms of money: coinage, paper money and electronic money. Therefore, even within one type of money there will be considerable difference of characteristics and functionalities. Consider, for example, the portability of coins vs. wire transfer for intercontinental transaction. Gold and silver are more uniform, but there are still some differences depending on whether we’re talking raw metal, coins, retail bars and ‘Good Delivery’ bars. Concerning cryptos, at the time of writing lists 20,597 cryptocurrencies. They vary considerably, and it would be impractical to analyse even a small subset of them. I have concentrated on the main ones – Bitcoin (BTC), Ethereum (ETH) as well as several smaller ones that enable much higher transaction speed and throughput.

Let’s start with a summary table of how well a given type of money (fiat, precious metals, cryptos) fulfils the required characteristics. A detailed discussion follows.


 State issued (fiat) moneyGold and silverCryptos
Limited supply0-88-98-10

The durability of fiat money depends on its form. Coins are rather durable, US Mint provides a 30-year life time while UK’s Royal Mint states that coins can stay in circulation for 40+ years. I assign a score of 9 to durability of coins.

We tend to call the banknotes “paper money”, but nowadays they are rarely made of wood pulp. US dollars are 75% cotton and 25% linen, while euro banknotes are 100% cotton fibre, with protective coating. Notes issued by Bank of Canada and Bank of England are made of polymer. Widely circulating banknotes can last only as little as 1-2 years, but longer on average. US denominations between $1 and $20 last 5-8 years before succumbing to wear and tear, while the more rarely used $100 note lasts 23 years on average. UK’s new polymer banknotes are supposed to last 2.5 times longer than the previously issued notes, but the expected durability is in line with the US, 5 to 20 years. Notes are susceptible to damage, the paper based ones could rather easily be creased or torn. High temperatures and fire destroy both fibre-based and polymer notes. Paper banknotes can also be damaged by a washing machine, when forgetfully left in garment’s pockets, but fortunately usually not to the extent that they cannot be replaced by a bank. On the low side, I assign a score of 6 to the durability of paper and fibre banknotes, when used for daily transactions. On the one hand, their lifetime is really low, on the other they can get replaced by central bank rather “invisibly” to daily users. On the high side, I assign a score of 8 to the high denomination polymer bank notes as they can theoretically be used as a store of value for decades, assuming no or low increase in money supply.

The electronic money we own as deposits are maintained as part of bank’s IT infrastructure. Ultimately, the data pertaining to your balance are likely stored on a hard drive and/or magnetic tape. While the failure rate of hard drives is relatively high at nearly 1% annually, this does not mean that the durability of the electronic money should be counted in years or decades. Banks have extremely sophisticated systems that need to take into account not only equipment failure but also, much more importantly, the malice of cybercriminals. Banking institutions employ near-instant data backups, recovery and restoration, sometimes with backup intervals as frequent as mere minutes. Copies of data are geo-redundant, meaning that on top of on-site backup, several remote or cloud storage sites will likely be used. IT infrastructure (operating systems, applications and configurations) is also similarly backed up for a fast restoration in case of outage. Clients are more likely to lose money in bank’s run and/or bank’s failure. Fortunately, the deposits are currently insured in over 100 countries; the sums are for up to $250k in the US, €100k in European Union and £85k in the UK for one depositor and one bank. Safeguarding €500k or $1 million from bank’s failure is possible, all one needs is several accounts in different institutions.  Choosing banks with stronger balance sheets also helps. Large, systematically important banks will likely be saved by governments via bailouts. As the modern world is on the current banking/money system for just several decades, it not certain what the durability of electronic money really is. It is plausible we should assume timeframes of centuries or longer. I score the durability of electronic money as 10 for smaller depositors and 9 for those above insurance limits.

Gold and silver are notable for their durability, as stashes of coins from 2000 years ago are still being discovered. They are considered noble metals for a host of reasons: they are resistant to elements, fire, and nearly all chemical substances with the exception of cyanide, strong acids or their mixture (aqua regia). Contrary to James Bond “Goldfinger’s” movie plot, it is even impossible to irradiate pure gold, as it has only one stable isotope, and the unstable one has a half-life of about six months. Unfortunately, as unique as they physical and chemical properties are, they are not 100% resistant to wear and illegal debasement. There are two types of the so-called “sweating” techniques, a mechanical one and a chemical one, that allow to illegally obtain metal from circulating coins. The first method, known for centuries, required putting a large number of gold coins in a bag and shaking it for an hour or so. This would produce small metal clippings and gold dust that would be gathered by criminals. The newer the coins, the better the results. The second method required immersing gold coins for a short period of time in a solution of aqua regia, then washing and polishing them. Gold dissolved in the mixture of acids was easily obtained by evaporating the solution and melting the residue.  This methods gained popularity in American West towards the end of 19th century. I’m scoring both metals as 10 for long-term store of value. For the durability as medium of exchange I’m scoring gold as 9 due to its softness and susceptibility to aqua regia. Silver is slightly lower at 8, as it wears faster due to daily use, tarnishes in air and is soluble in rather easily available acids.

The distributed nature of blockchain nodes that contain the history of all crypto transactions ensures that the durability of data in the storage is very long lived. Given the sheer processing power required to confirm the Proof of Work (PoW) transactions on BTC and ETH blockchains, the system is likely better protected than banking systems. Even though Bitcoin has been around for only a dozen or so years, it seems very safe so far, as the blockchain itself is resistant to hacking or double-spend. We can assume that large enough number of programmers pored through its code, so that an incident like creating 184 billion BTC in one block is impossible now or will be corrected without any long-term consequences. Given current state of affairs, the durability of PoW blockchains could be described as indefinite – likely lasting many decades or perhaps even centuries, allowing for a score of 10. However, blockchain has several potential vulnerabilities. One of the better known is the so-called 51% attack. While Bitcoin has not yet suffered it, other cryptocurrencies (e.g. BSV, BTG, ETC) did. The costs to conduct a 51% attack are high, but not insurmountable and are within reach of a state agent or wealthy individual(s). Perhaps a solution to this problem is changing the consensus mechanism to Proof of Stake, as Ethereum is planning to do in the near future. Another threat comes from improvement in quantum computing. Some experts claim that progress in this area might make cryptocurrencies vulnerable as soon as 2035. Others point to potential vulnerability of the first 4 million or so Bitcoins mined prior to 2010, when the hashing function used a different, less safe format than now.

It is possible that solutions to potential problems will be found before they materialize and worrying more than a decade ahead is being overly cautious. However, even if there are no significant issues with Bitcoin or Ethereum in the future, it is possible that better solution to serve investors and clients within the crypto sphere will be developed. In that case, the durability of cryptos will be maintained, but the leaders will change. “On a long enough timeline, the survival rate for everyone drops to zero”, Fight Club taught us. “Diamonds Are Forever”, but we can’t be so sure about the most popular coins. I’m assigning a score of 9 on the low side of the estimate of durability, trying to account for current and future potential problems described above, but it is worth remembering that there’s non-zero probability of complete failure of any given coin.

The electronic money used in any given country is uniform, as any transaction is represented just by a number (score 10). The coins and banknotes are not uniform. There come in different designs, colours and they are made from different materials. This is done primarily to increase recognizability, but coupled with lack of divisibility, this may create occasional problems, such as inability to give back change due to lack of appropriate notes or coins in the cash register. You can’t tear a 20$ or 20€ note in half, to represent 10$ or 10€ of value. On top of that, uniformity is weakened when a new banknote series is issued, for example to increase security, and the old one maintains legal tender status. I’m assigning a score of 8 to account for these issues with coins and banknotes.

In theory gold and silver are extremely uniform as they are chemical elements (score 10). In practice, different countries employ(ed) different coins using different alloys and precious metal purity. Even when a coin lasted several centuries, the design changed with every ruler. I’d assign scores of 8 to 9 for most places and most times that have been on precious metals standards, but there were certainly times and places of monetary chaos, where a much lower score of coinage uniformity would be warranted.

Individual cryptocurrencies are fully uniform (score 10), as transactions values and balances are represented by a single number. The split into Bitcoins and satoshis or Ethers and weis is not actually reflected in the structure of blockchain transactions.

Electronic money are divisible, allowing for any transaction sum (score 10). Coins and banknotes are not fully dividable. They come in several denominations (for example, 1€, 2€, 5€, 10€), which makes a cash payment of sums like 33.77€ a bit cumbersome (score 8).

In theory, gold and silver are divisible to a single atom, hence a potential maximum score of 10. However, in practical applications (payment with gold and silver coins) they did suffer from the same denomination issues as modern coinage (score of 8).

Cryptocurrencies are sufficiently dividable (score 10). The smallest unit of Bitcoin (one satoshi or 10-8 BTC) is currently worth ~0.0002 USD, while the smallest unit on the Ethereum blockchain (one wei or 10-18 ETH) is worth an infinitesimally small amount, even expressed in US cents. In other words, the price of Bitcoin would have to increase to over 1 million USD in order to have first divisibility issues, as 1 satoshi would then be worth 1 US cent.


Fiat money has the biggest range of possible outcomes. Countries that hyperinflate their currencies receive the score of 0. Countries that enjoy the GDP growth of ~2% and target CPI inflation of ~2% will likely inflate the money supply by about 4% annually over the long term, receiving a score of 8. In mid-2022 there’s a whole range of CPI increases in different countries, with the worst offenders experiencing CPI inflation rate of between 30% and 500%, deserving very low scores, perhaps in the range of 1-5.

World Gold Council estimates above ground gold stocks of 205 thousand tonnes, while mine production of the yellow metal has been around 3000-3300 tonnes in recent years. This translates to about 1.5-1.6% of annual increase of gold supply and a score of 9. Silver’s above ground inventories are substantially more difficult to estimate, but let’s go with the CPM Group’s estimate of stock-to-flow ratio of 30-60. That’s an inflation of 1.7-3.3% and a score of 8-9.

Bitcoin’s supply increased by 1.8% in the year to June 30, 2022 while Ethereum’s supply increased by 4.2%, with respective scores of 9 and 8. However, the Bitcoin algorithm ensures that the new annual supply will asymptotically reach zero, so the future score of Bitcoin will be 10. Ethereum Foundation experiments with burning a small amount of ETH coins with every transaction are opening a possibility of a declining total money supply and a score of 10+.

The state issued money that we use every day has no issues with recognizability. In most countries we can readily identify both the banknotes and coins for what they are, as there are no objects closely resembling them due to strict laws against counterfeiting. Forged bills are very rare – about 0.02% of bills are fake in the UK, 0.01% to 0.025% in the US and only 0.001% in the EU. In most countries individual banknotes differ substantially in colour and size, while coins are often manufactured using different metal alloys or two alloys (see €1 and €2 coins). The electronic money is also easily recognizable as part of payment systems, whether wire transfers or card payments. I assign a score of 10 to all forms of fiat money.

Precious metals have an established place in nearly all cultures. Gold jewellery has a long history and even in modern times is rather popular. As most people get married it is more likely than not for an average adult to wear a gold ring at some point of their lives. Gold is relatively easy to recognize as metal, due to its unique yellow colour. In the antiquity silver was the only ‘silvery’ metal, however nowadays it has many lookalikes. Palladium, platinum, rhodium, nickel, chromium, aluminium, even cobalt are largely similar in colour. While nobody would use more expensive metals, such as rhodium, palladium and platinum to imitate silver, alloys of base metals, such as alpaca or ‘German silver’ had been. Various methods of counterfeiting precious metals have been used, from silver electroplating of copper coins to using tungsten inside gold bars. Receiving gold or silver from an unknown source carries risk. Acceptability of gold and silver coins varies substantially depending on the country and demographics. In this context it is perhaps worthwhile to mention a long tradition of using gold coins and gold objects as emergency money for US military and UK RAF’s pilots in WW II, Vietnam War and even in 1991 Gulf War. Apparently, it was established that recognizability and acceptability of these objects of value will be high, even behind enemy lines. However, given actual responses in videos like this and this, and many more like them in this particular youtube channel, it is tempting to assign a value of 0 or 1 to gold as money or an object with a recognizable value to an average citizen in the United State nowadays. One would, perhaps, be forgiven for suspecting that these responses have been staged or at least chosen from a larger subset given dramatically different responses elsewhere. On the streets of Singapore the knowledge of gold in is substantially better, perhaps warranting an acceptability score between 5 and 7. This could be attributed to Singapore being a financial centre as well as the impact of Chinese and Indian culture. One knowledgeable lady in the video apparently speaks a dialect of Chinese and skilfully translates gold values into renmibi. One gentlemen specifically states that he is Indian and his wife buys gold jewellery, so he knows the value of gold. The recognizability and acceptability of precious metals as money or investment seems to be rather low in most Western countries, perhaps with the exception of Switzerland, Germany and Austria, but higher in India, China and other Asian countries, especially in the Middle East. The analysis is further clouded by the fact that in some countries consumers buy gold mainly as coins and bars, in others mainly as jewellery. In the latter case it is sometimes not easy to disentangle to what extent the purchase has been done as an adornment or as an investment.

It is difficult to come up with one assessment for worldwide recognizability and acceptability of precious metals, as it seems to range between 1 and 10 depending on the specific population. I’ll go with a 5, but with low conviction of the estimate.

15 years ago the concept of cryptocurrencies did not exist, in the past 10 years there has been a gradual adoption and recognition of the idea. In a Pew Research’s September 2021 poll 86% of Americans said that they have heard at least a little about cryptocurrencies, while 24% heard a lot. 16% hey personally have invested in, traded or otherwise used one. It is a substantial increase vs. 2015, when only 48% of Americans recognized Bitcoin and just 1% said they had ever collected, traded or used it. On the high side there are countries where cryptocurrencies are even more popular. In a 2020 survey, 32% of Nigerians said they use or own crypto, as well as 21% of respondents in Vietnam, 20% in the Philippines and 16% in Turkey. However, the worldwide average is lower. The number of crypto users was estimated at about 300 million as of 2021, which translates to about 4% of global population.

So, acceptability is rather low currently, I score it as 1. Recognizability is much higher. As mentioned before, 86% of Americans have heard about cryptocurrencies. The numbers are similar in Japan (88%) and UK (93%). In 2018, an ING bank report put the UK awareness at 61% and American at 51%. It was somewhat higher in continental Europe (66%) with Poland and Austria even higher – 78% and 79% respectively. So, the basic recognizability in the Western countries likely is between 85% and 95% as of mid-2022. Another ING report, from 2019, asked several questions to measure the level of crypto-related knowledge. It categorized the responders as possessing either low (13%), medium (57%) or high knowledge (31%). Based on the Pew’s Research and ING Report it seems that about 25%-30% of Western population has the level of knowledge that could be described as sufficiently high. I assign a score of 3 to crypto recognizability. Given the high number of people who have heard about cryptos in general, this number is likely to grow with time.

The dictionary definition of portability is “the ability to be easily carried or moved”. With regards to money we have two concepts here: transportability and transferability. The former considers the ease of move over large distances, while the latter the ease of exchange between persons or institutions.

Coins and notes are easily transferred between people and on short distances, but due to their physical nature, not so easily over large, especially intercontinental distances. It takes just several seconds to reach to a wallet and hand over some notes and/or coins to another person. Arguably the process is too easy, given how effortlessly cash can sometimes be stolen. I assign a score of 10 for cash (coins and notes) transferability and a score of 5 for long distance cash transportability.

Gold and silver coins can be exchanged between persons on short distances with similar ease as the ‘normal’ coins and banknotes, which made them the staple of monetary systems for over 2500 years. However, given the global reach of our modern economy, a transfer between countries or even an intercontinental transfer is sometimes warranted. In 2013 Germany decided to repatriate a portion of its gold reserves held in New York and Paris to be stored in Frankfurt. Between 2013 and 2017 Bundesbank transferred 743 tonnes or about 1/5th of its reserves. The bars held in New York had to melted and recast in order to conform to ‘Good delivery’ standard of the LBMA. The whole transfer took 5 years and the price tag was €7.6 million. While undoubtedly high in nominal terms, it amounted to only 0.03% of the €31 billion worth of gold moved. I assign a score of 10 for person-to-person transferability of gold and silver coins and a score of 5 for large-distance, large-value gold transportability.

The core functionality of cryptocurrencies is that they can be transferred between any electronic devices in the world, be it personal computers, laptops or mobile phones. It is usually very efficient over long distances, but arguably not as convenient for short distances as hand-to-hand method of coins and notes. Transporting crypto around the world is very fast. While the transactions of the first crypto “incarnation” – bitcoin – require 10-60 minutes to get confirmed, there are plenty of solutions that allow for finality that is near-instant or takes seconds. However, transferability is a bit cumbersome compared to notes or coins as it takes more time and effort to transfer crypto than hand over cash, even with a convenient app and scanning of a QR code. As with any form of electronic money there can sometimes be problems with access due to poor internet connection – in the wilderness, outside of main cities, in tunnels, underground or inside buildings – which precludes us from making a transaction at a given place and time. I score the transportability very high, at 10, but the transferability currently at 8-9.

As we can see, determining whether a given type of money holds required characteristics is a complex task. Some qualities are stable and easy to score, but others quite cumbersome to analyse, different in various places and times and subjective. State issued money suffers mainly from instability of supply, which in the past year or two affected even the most venerable currencies of developed nations. Low durability of (paper) cash and inability to transfer it over large distances is mitigated by modern electronic money. Gold and silver score rather high on most characteristics, which is not surprising, as they have been at the core of monetary systems for 98-99% of human economic history. They currently have moderate-to-low recognizability, as they have been dethroned by fiat money. Crypto scores high on most traits, but suffers from low recognizability and even lower acceptability. It is also not certain whether cryptocurrencies are really durable, given their short history and potential threats.

Part 2 will deal with the functions of money: a unit of account, a medium of exchange, and a store of value. They are connected with characteristics of money, but we will look at these three types of money from different angles.

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Bridgewater & bitcoin

This note is written as a discussion/response to the recent bitcoin research piece by Bridgewater.

I have read the article by Ray Dalio and the Bridgewater team with great interest. It is an important voice about bitcoin and cryptocurrencies from one of the world’s premier asset managers and it is likely that it will help to legitimize this asset class in the eyes of institutional investors and their clients. My previous experience and analyses are in agreement with many parts of their analysis. There is the regulatory section, where I cannot provide perspective, as the situation substantially differs, depending on jurisdiction and investor or organization type. I decided to concentrate on several areas, where I thought my experience and analyses coming from nearly 10 years of investing in bitcoin may be of interest to the reader. Mr Dalio shared his thoughts on the topic in the introduction, and then deferred to his research/analytical team. I will, therefore, provide a perspective to and discussion of the main body of their research.

Before I start the main part of my commentary, I think it may be worthwhile to share some of my background, which may have influenced my thinking. I have been an investor in bitcoin since June 2011 and have co-founded a start-up in cryptocurrency area. This may have resulted in me having a pro-bitcoin bias. I have invested in precious metals since 2004 and have been a portfolio manager for several precious metal mutual funds in 2012-17. It is possible that I have a pro-precious metals bias. Discussions concerning bitcoin to some extent circle around it being a competitor to gold, so it is my hope that these two biases of mine largely cancel one another out.

Bridgewater team analyses the nature and future of bitcoin as a potential new asset class. I have decided to discuss these three areas:
1) Volatility
2) Liquidity
3) Bubble dynamics and speculation

1) Volatility
One of the main concerns of the Bridgewater team was that bitcoin remains an “extremely volatile asset”. I propose that, in fact:
A) bitcoin’s volatility, while high compared to other asset classes, “should” have been substantially higher in the past,
B) asset class volatility can be a neutral factor in many portfolio implementations,
C) in some portfolio implementations high volatility can be a positive factor and add to portfolio return and Sharpe ratio.

A) Bitcoin’s volatility has undoubtedly been nominally high when compared to other asset classes. Annualized volatility between September 2011 and January 2021 has been unusually high at 99%. This is more than six times higher than S&P 500’s volatility that was 16% over the same period. US Treasuries with 7–10 years to maturity were less volatile still – just 5.8%. However, any risky investment should be considered in conjunction with the return it provides(d). Bitcoin delivered annualized return of 157% over these 9+ years, which resulted in an exceptional Sharpe ratio of 1.58. Stocks have delivered a respectable SR of 0.76, while bonds a more modest SR of 0.16. Averages for most asset classes have been around 0.30-0.35 over the very long term. It is quite clear that holding bitcoin over the past 9 years has been an excellent proposition from a risk–adjusted standpoint, as much as 4.5 times better than long term averages recorded for other asset classes.

In this context, I do not consider bitcoin’s past volatility to be high. It could have been as much as 4x higher and it would still be a reasonable investment. 80% corrections in bitcoin are obviously painful, but admittedly they could have been much deeper. The question still remains concerning future expected returns and whether they will be high enough to compensate for the heightened volatility. It is certainly reasonable to expect bitcoin’s returns and Sharpe ratio to drop in the future towards levels typical for established asset classes. However, as it will be shown in point C), even in a scenario of zero price appreciation bitcoin can potentially be a valuable addition to diversified portfolios.

B) I feel a bit eerie writing this part in a response to Ray Dalio and the Bridgewater team. Ray was THE person that invented what was subsequently named Risk Parity and Bridgewater is running the biggest Risk Parity fund in the world. They helped to popularize the idea that assets should be evaluated based on the risk-adjusted basis and that investments characterized by both very high and very low realized and expected volatilities could be considered equals in a rational and well constructed portfolio. As Risk Parity’s universe is very wide and most implementations span government bonds and commodities, it is reasonable to assume that as of this moment the All Weather portfolio holds both the 2 year Treasuries and natural gas futures. The first asset class had an annualized volatility of 1.2% over the past year (as measured by the volatility of SHY ETF), while the second had the volatility of 58.4% (as measured by the volatility of UNG ETF). So, asset class with the highest volatility held by a Risk Parity fund can experience as much as 46 times (!) higher volatility than the asset class characterized by the lowest volatility. A wide asset class universe is similarly used by other asset managers, beyond Risk Parity implementations. In that light, adding bitcoin to a portfolio, with historical volatility of just 1.7 times higher than that of natural gas futures does not seem too extraordinary to me. Once an analysis is performed that takes into account portfolio assets’ historical and expected returns and volatilities as well as their correlations, it is quite reasonable to assume that assets with annualized volatilities of 1%, 10% or even 100% can be valuable additions. The exposure to each asset class could, obviously, be scaled by the inverse of expected volatility, which would make bitcoin’s share proportionately lower. An asset class does not have to be excluded just because its volatility is unusually high. To the contrary – there is one good reason to include it, as described in the following section.

C) It seems that it is still a relatively little-known fact, that there are portfolios in which the higher the volatility (ceteris paribus) – the better. For those who have not looked closely at the nature of the rebalancing return (RR) this may sound like a heresy. One reason RR is relatively unknown may stem from the fact that it is an insignificant part of returns in traditional portfolios consisting mostly of stocks and bonds. A portfolio consisting of 50% bonds (IEF ETF) and 50% cash would record a RR of just 0.01% over the past year, while in a portfolio with 50% of stocks (SPY) and 50% of cash RR would add 0.29% to its overall return. In contrast, rebalancing return would add as much as 7.8% annual return to a portfolio consisting of 50% bitcoin and 50% cash. The second reason is that for securities which receive return from income and/or growth, additional volatility is obviously an anathema – it “dilutes” the main sources of return and results in a lower Sharpe ratio. For instruments and portfolios that receive no income and have no growth component (such as commodities), rebalancing return is the only viable source of return.

So, how does RR work? One of the first systematic reviews of the topic was performed by Willam J. Bernstein in 1996 (Rebalancing Bonus: Theory and Practice). He provides the following equation for a portfolio of two assets:

 Where RR is rebalancing return, w1 and w2 are weights of the rebalanced securities, σ2 are their variances. σ1,2 is the covariance between the two. To simplify a bit, let’s assume we analyse a portfolio consisting solely of a single instrument and cash. We get:

As we see, rebalancing return is proportional to security’s variance. This means, that as volatility increases, Sharpe ratio INCREASES in direct proportion to volatility. Rebalancing return is also dependent on weights. The first two terms reach a maximum at 50%/50% weights, which is one reason why equally-weighted portfolios may be optimal in many implementations.

Let’s see how this works in practice. We will look at the impact of rebalancing return on two portfolios – one consisting of 50% bitcoin and 50% cash, the second with 10% bitcoin and 90% cash. The portfolio is rebalanced weekly and cash yields zero. We look at the period of nearly 3 years – from the peak of 19,200 BTC/USD on Dec 16, 2017 to Nov 24, 2020 when it again reached that level. This is to show, that an investor can still enjoy gains, even in a period when bitcoin’s total return was exactly zero. Portfolio holding 50% of funds in bitcoin would have delivered 28.1% return (annualized to 8.7%), while portfolio holding 10% of funds in bitcoin would have recorded 9.1% return (3.0% annualized). Results are summarized in the table and illustrated in the figure below.

As we see, a low 10% allocation to bitcoin would allow to realize a Sharpe ratio of 0.38, which is comparable to long-term averages for most asset classes. This has been achieved in a period of zero overall price change. Further reduction in bitcoin allocation results in only small Sharpe ratio increase – a portfolio holding 1% in bitcoin and 99% in cash would enjoy a SR of 0.396.

To summarize: while nominal volatility of bitcoin has been high in comparison to traditional asset classes, it has been quite low, when compared to returns that the instrument delivered, resulting in an exceptionally high Sharpe ratio of over 1.5. It could still be held in traditional portfolios in low allocations of 1-10%. Even in times of overall zero price appreciation for bitcoin, such implementation would result in achieving a Sharpe ratio of 0.38-0.40, assuming the remaining components were uncorrelated to BTC. A low allocation to bitcoin would help with another problem flagged by the Bridgewater team – liquidity.

2) Liquidity
The Bridgewater team writes:
“current levels of liquidity still constitute real structural challenges to holding Bitcoin for large traditional institutions such as Bridgewater and its clients”

While one does not need liquidity to “hold” an asset, just to enter or leave a position, we can understand what was meant here by the Bridgewater team. Bitcoin is, as of now, an emerging asset class, and any institution and its clients need to have an OPTIONALITY to close a part or the whole position at any given time. There is a possibility of a better crypto implementation, regulatory risk, etc., that may prompt a client to liquidate a position at a moment’s notice. Even the simple strategy that I analysed in the previous section (hold 10% of portfolio in bitcoin) needs some liquidity for weekly or monthly rebalancing, although in one implementation variant the investor pursuing such a strategy would be a liquidity provider rather than a taker.

Bridgewater is one of the most successful asset managers of all times. They know what they need to implement their proven strategies and liquidity is one of prerequisites. However, there is the possibility that profit opportunities in crypto area may be to a substantial degree inversely proportional to liquidity. This may or may not be equivalent to traditional illiquidity premium – due to market fragmentation and lack of sophisticated institutional investors. As an extreme exercise, almost ad absurdum, let’s consider what would happen, if an institution such as Bridgewater, disregarding miniscule liquidity available at that time, invested a paltry one million US dollars in Q4 of 2011. Total supply was just 4-5 million BTC at that time, while the average price was ~3.25 USD. Accumulating 6-8% of total BTC supply would be a very difficult task indeed, although devoting several offices at Bridgewater’s HQ to BTC mining rigs would certainly be of substantial help. By late January 2021 this very modest investment would turn into a cool 10 billion dollars – a substantial sum, even for a giant like Bridgewater. It is obvious that this opportunity is gone and instead of a 10000x increase we are looking at 10x increase, at the most. However, it is possible that liquidity-constrained opportunities are still there, proportionally reduced in potential percentage increase, but not necessarily in the absolute dollar size.

As a separate observation, I would like to draw the reader’s attention to the large disparity that spans this section and the next. When discussing liquidity constraints, Bridgewater assumes that daily liquidity available to their strategies amounts to ~7.4 USD bln in cash and derivatives or 1.3% of total BTC supply. When discussing speculative excesses in contrast to long-term-store-of-value trades, they provide a chart that documents daily liquidity some 15 times higher – amounting to ~19% of total BTC supply. In their defence, they do admit that the 1.3% daily-liquidity-available-to-our-strategies figure is likely conservative and the 19% speculation-not-long-term-investment figure is likely impacted by “questionable volume data reported by unregulated exchanges”. There is always a spread between the bid and the ask, but I leave it up to the reader to decide, whether quoting two estimates of the same metric in one document that differ ~15-fold when supporting the “take the risk” and “do not take the risk” arguments is justified to such an extent.

3) Speculation & bubbles
First, some of my general thoughts about speculation and bubbles, and how they relate to bitcoin. documents 396 instances of different websites declaring bitcoin’s apparent death. The first entry is from late 2010, when BTC price was 0.23 USD. In the past there were hundreds of failed predictions of bitcoin being in a bubble and there may be dozens more. There will likely only ever be one prediction that will come true. The Bayesian in me takes these odds/probabilities as priors.

I suppose most observers who declared bitcoin being in a bubble in the past might not have noticed one important aspect that made this particular asset class different from many other asset classes that underwent substantial price appreciation. Satoshi Nakamoto went public with the concept before the first bitcoins were mined. Everybody on the planet could have gotten first bitcoins by the thousands – for free. It is likely that their value was negative, as valuable computers and electricity had to be used to create assets of zero value. Anybody with the basic understanding of maths can calculate what the expected return is, when an asset that was initially worth zero increases in value to be worth SOMEWHAT – whether that somewhat is a million USD or a trillion USD. Yes, it is +∞ (plus infinity). In theory, there is an infinite number of sequential “bubbles”, of any size, that can “fit” in an advance from a value of zero, to any finite value – whether that value is a million or a trillion. In practice, when the first transaction is made, this collapses to some finite number of sequential “bubbles”. Laszlo Hanyecz agreed in May of 2010 to pay 10 thousand bitcoins for two pizzas, worth approximately 25 dollars, thus setting the price of BTC to 0.25 US cents. Oftentimes an asset class is called a “bubble” when it advances 5-10 fold. Since that first transaction, bitcoin’s price increased some 12 million times, which allowed for about seven back-to-back bubbles, each advancing 10-fold. We could add several more bubbles, if we included the intermittent corrections in the process. With bitcoin market capitalization of 600 billion USD as of this writing and value of all the gold used as an investment worth about 5 trillion USD, it seems, at least to this author, that bitcoin can scarcely be expected to deliver one more 10-fold bubble.

I think the reader would agree that it is generally accepted that bubbles are considered unwise and irrational; there is a negative aura attached to them. However, I propose that FASTER advance from zero value to the final value of an asset may be a sign of rationality, rather than irrational behaviour. This can be demonstrated by near-instantaneous vertical advances that follow many economic and earnings releases. Slower price advance might mean that information is being absorbed at a slower pace. In this light, unusually fast advances in the price of bitcoin (especially in comparison to other asset classes) may simply be a sign of it being substantially below its target price and absorption of this information by new market participants.

Now, back to commentary on the Bridgewater article. I think they provide a rather balanced and guarded assessment of bitcoin being in a bubble or a speculative asset. On the one hand, they draw the reader’s attention to some concrete metrics: volume traded, rising financing rates and option pricing. On the other hand, they admit that such bubble dynamics “can persist for extended periods”.

Concerning volume traded, I’m not sure if it supports the thesis of bitcoin being in a bubble, but it likely supports the thesis that there is substantial amount of speculative trading going on in cryptocurrencies. I have no strong conviction here, as Bridgewater rightfully draws attention to “questionable volume data” provided by some exchanges. I will not delve deeper into this topic but would like to point out the fact, that volumes traded as percentage of supply reached the maximum when BTC fell in March 2020 from about 9000 BTC/USD to the low of 3600 BTC/USD – the very opposite of it being in a bubble.

I am in full agreement, that rising borrowing rates (and higher financing rates embedded in futures pricing) correlate with increased speculative fervour. In my experience they coincided with later parts of consecutive price advances since at least 2016. Financing costs are currently lower than in late 2017, but this may reflect higher availability of capital earmarked for lending and futures financing than 3+ years ago.

I’m not sure, if the details concerning options pricing support the speculation/bubble argument. Bridgewater team writes: “Bitcoin options are currently pricing a very wide and highly optimistic cone of outcomes for future returns”. In support they provide a chart, that indeed is that of a cone. However, in the period analysed (Sep-Dec 2020) bitcoin’s price increased about threefold. As the Y scale on their chart is an arithmetic one, not logarithmic, the shape of 10%-50%-90% outcomes over time SHOULD look like a cone when bitcoin price advances, even with no change to other parameters. 10% and 90% outcomes could still be in similar distance “away” from the 50% outcome when measured in terms of percentages, but “further away” when measured in thousands of dollars. It is not readily obvious to me, which is the case here. Additionally, between September and late December there was an increase in 3M implied volatility of bitcoin options, from about 3-4% daily to 5-6% daily. A similar, but perhaps smaller, increase for 6M options IV could be expected as well. So, the widening of the “cone” could come not only from bitcoin’s price increase, but also from increased implied volatility. This is a sign that market participants price in additional risk (both to the upside and to the downside), not optimism.

It is possible that the 50% outcome for June 2021 has been higher than the spot price throughout the analysed period. This may be due to higher financing costs which, as I agreed to earlier, likely is a sign of optimism. As the cryptocurrency markets are not yet fully integrated into the overall financial system, there is no capital available at 0.25% per annum to finance crypto derivatives, such as futures and options. A crypto-specific interest rate (“Risk free” rate) needs to be used, in order to bring options and futures prices to some equilibrium.

Therefore, in order to estimate what can be read from bitcoin option prices concerning market sentiment it would, perhaps, be helpful to disaggregate “the cone” into four effects:

  • Bitcoin price increase
  • Change in implied volatility
  • Change in (crypto-specific) financing costs (that could move outcomes vs. spot price)
  • “Smirks” that may indicate optimism or pessimism embedded in option pricing.

To summarize my commentary: I recognize that bitcoin’s volatility is high in comparison to other asset classes. However, given returns and the Sharpe ratio it delivered in the past, it (ex-post) made sense to take such high risks in the past. It may continue to do so for some time into the future, though not indefinitely. One could treat bitcoin’s volatility a bit like ethanol or acetic acid. These substances are highly toxic at 100% concentration, but safer and potentially beneficial, when thinned to 3-6% and used as light beer or vinegar. Similarly, an allocation of several percent of assets to bitcoin may be beneficial for portfolio’s performance, especially due to the benefits realized from the Rebalancing Return.

I understand that the sheer size of Bridgewater Assets Under Management precludes the institution from taking a substantial position in cryptocurrency markets. I propose that the scale of profit opportunities is likely inversely proportional to liquidity and institutional presence. Perhaps it is also a signal to smaller and non-institutional participants that the opportunities are there, but large and successful institutions cannot engage in them as much as they would like to.

Concerning bitcoin’s bubble-like behaviour, I propose that in the past it largely stemmed from the fact, that this asset class started its ascent from a value that was as close to zero as possible. In such a situation multiple bubbles of 10-fold increases can form in sequence, before an asset class reaches its “fair” value, whatever that value is. Fast price increases may be coming from the fact that new market participants are being familiarized with bitcoin’s target value and consider it substantially higher than current spot price.

In any case, I am grateful to the Bridgewater team for sharing their thoughts in such an extensive and thorough research piece. It has stimulated my thinking and allowed to look at bitcoin from several new angles.

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