Portfolio Theory
Sharpe Ratio & the Pareto Principle
Portfolio Theory
Incorporating the Sharpe Ratio & the Pareto Principle
All your models are broken. They were created in a world where there was no sovereign debt bubble, and the U.S. dollar was a stable currency. This is no longer the case. As the U.S. sovereign debt burden grows and the dollar becomes increasingly unstable, it is increasingly less suitable to be used as a unit of measurement. Credit cycles become shorter and more aggressive as the sovereign debt bubble inflates. When credit is created, new dollars come into existence. When existing credit becomes distressed, dollars are destroyed. In the aggregate, the supply of dollars is increasing exponentially. The volatility in the change of its supply is orders of magnitude greater than that of Bitcoin which has a steady and orderly supply schedule. Because of Bitcoins inherent stability, I have adopted what some refer to as the “Bitcoin Standard,” or using Bitcoin as my primary unit of measurement for accounting and finance. All our models are broken, and new models must be built. Many older, more rigid folks will consider this radical change, but it is not. The concepts in the old models still apply, but they can no longer be relied upon to create consistent results the way they are measured.
Any investment reward should be thought of as its ability to appreciate relative to the cost of the goods and services we could purchase with the proceeds. People often get stuck in the trap of looking at investment appreciation through the lens of nominal USD appreciation, rather than its appreciation against assets that are used as a store of value for monetary premium. If an investment is appreciating in the USD value but depreciating relative to the costs of goods and services in the economy, the investment is not profitable. Using Bitcoin as a unit of account can rectify this issue, especially when determining all upside. We will discover that there is more nuance on the downside, when incorporating the risk of Bitcoin market failure into a model.
When an investment appreciates relative to Bitcoin, the market is saying that the investment is profitable when using the new emergent form of money as a unit of account, the unit of account everyone will probably use in the future. By the same token, if an investment appreciates in USD terms but declines in Bitcoin terms, the investment is not profitable, and the risk reward dynamic of the investment is skewed to the downside. Bitcoin is competing with the US dollar to become the world’s reserve currency, to be money. Whenever anyone asks me what their Bitcoin allocation should be, I’ll ask them what they consider the odds of a Bitcoin network failure to be, reflected as a decline in hash rate over a period of years. Their allocation should be the inverse of that belief. If they believe there is a 50% chance of network failure, they are conceding that there is a 50% chance Bitcoin marches on and draws all monetary value onto itself. It is only fitting that Bitcoin itself is a binary bet. After all, it is just a string of ones and zeroes.
There is always less risk holding money because money does not have the same risk of failure as an investment in a security for example. Businesses often fail and go to zero, even the largest ones that are perceived as invulnerable. Just look at all the largest companies from a hundred years ago and recognize how many of those names are no longer with us. This is because the corporate structure encourages profitable businesses to ‘circle the wagons’ around the business practices that generate significant revenue. This causes them to be unaware of disruptions in their industry because the new emergent technologies often do not generate a lot of revenue at first. By the time someone has scaled them out to generate significant revenue, it is often too late for any competitors to catch up with the infrastructure already built around the new innovation. Therefore, the risk of any security going to 0 always exists and should be respected in any portfolio.
While most of the largest companies from 100 years ago no longer exist, the dollar still exists despite a decline in its purchasing power over those 100 years. The risk of currencies going to 0 is much lower than securities, and the rate at which they go to 0 is often much slower than the abrupt collapse of a company declaring bankruptcy. The risk of bonds going to 0 is tied to the risk of currency, but greater due to exposure to interest rate risks. If you bought a thirty-year bond for 1.7% and yields rise to 5%, who is going to buy your bond from you? Nobody in the free market will buy from you when they can buy one that yields x3 as much directly from the Treasury. The underlying value of your bond when marked to market is effectively 0. This is why most of the treasury issuance and demand will drift to the short end of the yield curve. It mitigates interest rate risk primarily through mitigating duration risk. Commodities have a low risk of going to 0 as they have consistent demand in agricultural and industrial applications, although technological advancement can shift demand to new commodities, increasing the risk of disruption in the existing commodity market.
Any portfolio manager worth his salt will start with an analysis of risk in a portfolio to avoid the risk of ruin, or as the plebs say “getting rekt.” Getting rekt is the financial equivalent of death. No one sets out to lose the value of their portfolio. It is the siren’s song of greed that warps our mind and our ability to perceive risk. Just as Boromir’s lust for power in the Lord of the Ring’s Trilogy led to his early death, a market participant consumed by greed with a high time preference is bound to get rekt. Everyone who has spent any significant amount of time in the market has seen an idea that seemed certain in their mind brutally and relentlessly smashed to pieces by the market. Given enough time, the market humbles all of us. Human beings share common needs among cultures across different corners of the globe. The need for certainty is by far the most dangerous. We can easily mistake what is most probable to occur with what will occur. A failure to distinguish the realities of these two statements is often what separates success from failure.
Risk and Return are two sides of the same coin. The ability to perceive risk is at its weakest coming off a massive winning streak, when the warm glow of euphoria has enveloped us, when we have convinced ourselves that we are a genius. Parabolic market moves have one thing in common: they all blow off. It is like a law of nature and the closest thing to a ‘certainty’ I have ever come across in the markets. While price itself is highly erratic in a parabolic advance, it has a more direct effect on market psychology than any other market behavior. For this reason, the way that the market will react to a parabolic advance is extremely predictable, because it is rooted in our psychology. It is difficult to disconnect and disengage from the market during these times, but it is absolutely critical to maintaining a long and successful trading career. Rather than add risk, these are the times to manifest trading success in the real world. Buy that house you always wanted, take your family on that trip you’ve always talked about, resist the siren’s song of greed with every fiber of your soul.
“The four most dangerous words in investing are: ‘This time it’s different.” – Sir John Templeton
We must live to fight another day, no matter how offsides we are caught in the market. Framing investment risk with the understanding that all assets can abruptly face extreme market disruption and go to 0 illustrates the reality that the only true way to lower risk is to limit position size. One should always use a stop loss as well, but in extreme market conditions, the market will often gap over stop losses. Stop losses may not trigger, or trigger at a price that is miles away from the intended price of execution. This is not an argument against stop losses, but rather an argument for consideration of position size alongside utilization of a stop loss. Imagine a scenario where you are short of an alternative crypto asset(altcoin) and that altcoin network experiences a significant failure that disrupts the ability for that network to send value. If your position is margined with the native crypto token you are shorting, your balance will approach infinity, but there will be no way to realize your gains, because the spot market has collapsed. If you are truly bearish on an asset, it often makes sense to short it on the cash settled futures market, where this problem does not exist.
I start with the understanding that any vehicle for capital can go to 0 because this is the fundamental reality of the world. Things have value because humans assign them value, and because we as individuals do not control the value assumptions of all of humanity, we are subject to the value assumptions of everyone else, not our own. An older, more conservative person may choose to hold a mixture of cash, treasury bills, gold, and bitcoin to hedge themselves against the risk of ruin in any one of these monetary vehicles. I also add real estate here because it is a preferred form of collateral. Anything that serves as valued collateral can be included in the category of ‘monetary’ goods because it can be used to acquire additional credit.
Bitcoin deserves the largest allocation in any portfolio because it is the emergent form of money with the highest Sharpe ratio ever recorded, but all other assets falling into the ‘monetary’ category deserve a decent position, if only as a hedge against the possibility that Bitcoin fails to achieve its ambitions. This may sound like an argument for diversification, but it’s not. Diversification entails selling winners to losers to rebalance. Take for example a portfolio with an allocation to 20% cash, 20% treasury bills, 20% gold, 20% bitcoin, and 20% real estate that is inactive over a 4-to-8-year period. The weighting of Bitcoin in the portfolio would have swelled to over 90% relative to the other positions over the 4-to-8-year period. Real Estate and gold would have demonstrated minor gains relative to treasury bills and cash. Selling Bitcoin to get back to the initial allocations of the portfolio would be a mistake, as Bitcoin is likely to continue its outperformance of the other assets. Still, there would need to be some rebalancing to buffer the portfolio against the risk that the Bitcoin market collapses. This process demonstrates how assets with higher returns almost always have higher risk-adjusted returns, and as a portfolio manager, we care primarily about risk-adjusted returns.
Understanding the Sharpe Ratio:
Sharpe Ratio= (Rp−Rf)/σp
Rp=return of portfolio = the actual return of Bitcoin against USD over a specified period of time.
· Can be used to extrapolate historical returns into the future, aka ‘expected return’.
Rf=risk-free rate = the overnight rate or the annual rate of return one can receive from interest bearing cash accounts without interest rate risk or duration risk. (It is currently 5.33%).
· Any return of an asset above the risk-free rate is referred to as the market risk premium or ‘excess return’.
σp=standard deviation of the portfolio’s excess return.
· It is a measure of risk-based volatility. The lower the standard deviation, the lower the risk.
Dividing ‘excess return’ by its standard deviation, gives us our Sharpe ratio, illustrating how much excess return is received for the additional risk. The higher the ratio, the greater the risk-adjusted return of the asset. You’ll notice that the longer the time frame used for calculating the Sharpe ratio of Bitcoin, the higher the Sharpe Ratio. Bitcoin is extremely and unpredictably volatile on the lower time frames, but it’s expression of volatility on the higher time frames is extremely orderly and predictable. This is why it is beneficial to store long term capital in Bitcoin and use cash and treasury bills for short term capital. There’s an argument to be made for keeping enough cash to pay 3 months of expenses, a portfolio of treasury bills of blended maturities to pay an additional 6 to 9 months of expenses, and a Bitcoin position to store all excess value into the future. This is just a general idea, and the numbers would vary based on where Bitcoin is in its 4-year cycle, with larger cash and treasury bill positions at the peak of a parabolic rally and less at the depths of the bear market capitulation.
It's important to recognize that the risk adjusted return of Bitcoin is extremely high even when considering its volatility. Our inability to handle the volatility of Bitcoin is psychological in nature, rather than anything based in mathematics. If the volatility becomes too great to psychologically bear and someone is losing sleep because of their Bitcoin position, they can always lower their position size slightly which will actually increase the overall Sharpe ratio of their portfolio and afford them the opportunity to add to their position if Bitcoin becomes available at cheaper prices.
Another principle of portfolio management involves the Pareto Principle often known as the 80/20 rule. The Pareto Principle is a law of nature governing the relationship between inputs and outputs in biological systems. It stipulates that roughly 20% of the inputs account for 80% of the outputs in any given system. A small fraction of efforts or inputs generates the lion’s share of results. Disproportionate impacts can be achieved by concentrating on the ‘vital few’ amidst the trivial many. Maximizing returns within a portfolio embraces the reality that we cannot know which components of our portfolio will provide the greatest returns beforehand, but we can respond to market information in a way that cultivates the best performing aspects of our portfolio. The Pareto Principle applies across a vast array of systems beyond biology, applying to business and finance as well. The Pareto Principle was an initial observation that 80% of Italy’s wealth belonged to 20% of its population.
· 20% of the richest people in the world receive roughly 80% of the world’s income.
· 20% of pea pods produce 80% of the peas.
· 20% of workers produce 80% of the result.
· 20% of an individual’s daily tasks produce 80% of their results.
· 20% of the customers create 80% of the revenue.
· 20% of the technical errors cause 80% of the crashes.
· 20% of the features cause 80% of the usage.
· 20% of men are desired by 80% of women.
· 20% of organisms contribute to 80% of an ecosystem’s stability.
The Pareto Principle can also be observed in the distribution of energy within a system. In a thermodynamic system, a large portion of the system's energy tends to be concentrated in a small fraction of its components. This can be illustrated in the behavior of gas molecules within a container. In a container of gas at a certain temperature, a small fraction of the gas molecules (around 20%) possess significantly higher energy compared to the majority. These high-energy molecules, despite being a minority, contribute substantially to the total kinetic energy of the gas. They are the ones that collide more frequently and with higher force, impacting the overall pressure and dynamics of the gas system.
This principle aligns with the Maxwell-Boltzmann distribution, which describes the distribution of speeds (and therefore kinetic energies) of particles in a gas at a given temperature. According to this distribution, while most particles have average energies, a smaller proportion have significantly higher energies, influencing the overall behavior of the system. Understanding this distribution is crucial in various fields of physics, from explaining gas behaviors to understanding energy distributions in different systems, providing insights into the most significant contributors to the overall dynamics of a physical system.
The 80/20 rule is an observation that inequality is an inherent quality of life and nature. Nature is not fair. The modern day urge to fight inequality may be rooted in noble intentions, but it is a war against nature. Society should spend resources to ensure that people do not face homelessness, hunger, and lack of healthcare, but it is doomed to failure if it embarks on the task of ensuring that all citizens achieve a similar outcome in life. Society should mitigate societal risks to the downside but should not be in the business of mitigating success to the upside. We should have learned from the failures of the Socialist movements in the 20th century that trying to guarantee equality of outcome is an exercise in futility. Ensuring equality of outcome involves drawing resources away from the most productive members of society. Any nation that embraces this ideology will be outcompeted by the nations that do not, just as the American economy outcompeted the Soviet economy during the Cold War. The 20th Century demonstrated this to be a disaster. Even today, there are some investors who are captivated by the recent achievements of modern China and have decided to invest significant sums of capital into the Chinese capital markets, a nation that willfully exploits capital for their gain.
Back to the Pareto Principle. A company cannot increase the number of workers falling into the 20% category by simply hiring more workers as each new worker would fall into a new Pareto Distribution. If they retain only the employees that produce 80% of the results, they maximize their risk-adjusted return, but this new distribution will start to settle into another 80-20 Pareto Distribution over time. This concept applies to our portfolios as well. The Pareto Principle is expressed by a power law distribution where the change in one quantity results in a proportional change to another quantity, relative to the power of the change.
We can incorporate this concept into a portfolio by keeping initial position sizes small to minimize ‘risk of ruin’ at the outset, but to simultaneously maximize returns by ‘letting the winners run.’ Through this process, the investments falling into the 20% category of the Pareto Distribution when the portfolio was constructed will acquire a larger allocation on merit. This process incorporates market information into a portfolio allocation. The market is always right. If it provides information that contradicts our opinion, we need to adjust our opinion and align with the market.