Formation Fi: Velocity of Volatility and Variance (VVV)
Crash Protection For Crypto-DeFi Portfolios
Executive Summary
We propose a novel portfolio weighting technique that considers certain stylized facts about the financial markets. During market crashes, assets tend to have higher correlations. An additional observation is that volatilities tend to be higher during market crashes. We adjust the volatilities and the variances (including covariances) of assets depending on how fast they are likely to change during market crashes. Hence, we term this methodology the VVV crash protection mechanism.
Our approach is ideally suited for crypto assets which, even during normal times, are very volatile and are also heavily correlated. Hence, we can expect much higher volatilities and correlations in the crypto investment landscape during a downturn. Our protection scheme is tailor made for beating benchmarks when markets head downward. Our methodology also performs better than other weighting schemes over an entire bull and bear market cycle with no significant underperformance during upward market trends.
Crash Course in Financial Markets
All of finance, through time, has involved three simple outcomes: “Buy, Sell or Hold”. The complications are mainly to get to these results. These three outcomes can also be viewed as only two actions since “Hold” is doing nothing. These two actions are driven by a simple singular objective: to obtain higher returns or to get more money from the money we already have by putting it into financial securities. Hence, we could state that finance has always been about one simple goal with two simple actions. This simple perspective on finance can be seen to have persisted throughout history and all forms of markets and instruments.
The differences in the markets have been mainly about the number of participants that could get involved and the frequency of their interactions. The different financial instruments, both in terms of their nomenclature and their properties, are merely manifestations of which and how many parties are involved in a transaction and the contractual circumstances or the legal clauses that govern the transaction. The prices of assets are dictated to a great extent by the discounted expected values of future benefits, which are cash flows, that one hopes to obtain by holding a security.
Despite the several advances in the social sciences, and in particular economic and financial theory, we have yet to discover an objective measuring stick of value, a so called, True Value Theory. Some would compare the search for such a theory to the medieval alchemists’ obsession with turning everything into gold. For our present purposes, the lack of such an objective measure means that the difference in value, as assessed by different participants under nearly identical conditions, can effect a transfer of wealth or a buy or sell decision. This lack of an objective measure of value, (value can be synonymously referred to as the price of an instrument), makes prices react at varying degrees and at varying speeds to the pull of different factors.
As markets have evolved, gotten bigger and interconnected to one another, the effect on participants becomes evident in the form of movements in the prices of assets. Movements in prices are labelled as volatility and there are precise statistical techniques used to measure it, which we discuss in a later section. Along with the movement in the price of an asset, we also need to consider the co-movements of two or more asset prices, which is statistically measured as correlations. There have been many attempt to understand and explain the source of price movements with the aim of trying to predict future returns. Markets where a large number of interactions happen among the players, with large amounts of wealth moving in and out of assets, exhibit greater movements in the prices.
Researchers have observed and documented a few stylized facts about traditional financial markets. The propensity for markets to suddenly crash is much higher than the probability of an upward movement of similar magnitude. When markets crash the prices of most assets move in tandem or they fall together. This correlated movement of prices is due to the extensive linkages that have developed between financial markets over the years. Another point to note is that when markets crash, asset prices tend to become more volatile. In such an environment, due to fund liquidations and liquidity needs even “good” assets get sold, which leads to further downward pressure on the prices.
We now turn our attention to the Crypto-Defi space. Blockchain technology has now created a fascinating marketplace where any-one can participate from any-where and at any-time to trade any-instrument. An unintended consequence of this excessive trading capability, and the ease with which massive amounts of wealth can move in and out of financial securities, is greater volatility in the prices. In addition, this market place is highly interlinked which is apparent as larger correlations than traditional securities. The next generation of wealth management tools and techniques need to account for the greater volatility and correlation of assets in the blockchain domain with additional adjustments that are necessary when volatilities and correlations are exacerbated during large downward movements.
Limitations of Mean Variance Optimization
The cornerstone of modern financial risk management has been the mean variance optimization (MVO) of financial securities, originally conceived by Harry Markowitz, to form portfolios that can provide risk adjusted returns. This foundational breakthrough leads to the formation of the so called efficient frontier of assets, based on their individual risk and return and the mutual correlations among the assets. Numerous subsequent innovations, built on top of MVO, have created many successful practical devices for managing wealth. Risk is expressed in terms of volatility, which is commonly calculated as the standard deviation of the continuously compounded returns.
Despite the powerful advances in MVO related portfolio management techniques over the past several decades, there are some crippling limitations that can erode returns. The primary concern is that MVO based techniques overweight certain assets and completely ignore, or zero weight, most other assets. The main insight of MVO is that diversification is better for longer term wealth gains. But practical implementations of MVO suffer from corner solutions (many zero weights) that are anything but truly diversified. If some assets are overweighted, the overall performance will depend a lot on how well these assets do. In addition, we are exposed to the idiosyncratic (asset specific) risks of these securities in a disproportionate manner.
The workaround to these drawbacks has been the use of setting constraints in terms of the maximum and minimum weights on the assets. The principles of optimization, which are used in almost all fields that require a decent amount of numerical accuracy, dictate constraint based approaches. The crucial issue with these prescriptions boils down to the fact that optimization is usually done over historical data and the solution obtained will yield the best result over those previous observations. Any MVO solution will overweight assets which are closest to in terms of the constraints. But when the past conditions change, even slightly, many of the constraints will be either broken or on the cusp of getting violated. This is simply because the more constraints we have, the more the chances are that some constraints will end up outside their boundaries as the dynamics of the system evolve. Too many constraints end up becoming obstacles that will make the system fragile. Solutions that are a result of constraint based optimization could deviate significantly from the optimal solutions. The portfolio will require constant tweaking of the weights or it will underperform under a large set of scenarios.
Traditional Risk Parity and Beyond for Crypto-Defi
Another insight from the study of financial markets is that returns are obtained as a result of bearing risk. Hence, an approach which allocates equal risk across all assets will yield a more robust weighting scheme. This approach is known as the risk parity approach. Here, the weights allocated to an asset are proportional to the amount of risk investing in the asset will contribute to the overall portfolio, as measured using volatility and accounting for correlations. Many studies have demonstrated that a risk parity approach does not suffer from corner solutions, idiosyncratic risks and the need for constant re-weighting since the weights are more evenly allocated. Risk parity weights of traditional financial portfolios also hold up under a much wider set of market conditions since this approach does not try to find the best solution for one set of observations, but instead it puts the portfolio in a region of good performance that will do well under a much broader set of situations.
Implementing risk parity techniques for crypto-defi assets will require paying special attention to the nuances of how these markets operate. Crypto markets are more volatile and highly correlated (Tables [fig:Correlation-Matrix]; [fig:VVV-Weights-Comparison]) compared to traditional finance. A weighting approach that is geared to outperform most benchmarks when markets are crashing, which is more common in crypto-defi than traditional markets, and yet provide solid returns under other market conditions is a recommended approach.
Our innovation is based on the following insights regarding volatility. Volatility cannot be directly observed. By looking at prices, we get an intuitive feel for the level of volatility by looking at the variations in asset prices. Precise measures of volatility are estimates based on historical data or forecasts from volatility models or calculated based on future expectations of market participants usually from option implied volatilities. The other important aspect of volatility is that it is constantly changing. The extent of changes in volatility varies across assets just as the volatilities are also different across different securities. Similar statements can be made about correlations between assets: they are not directly observed but estimated and constantly changing.
The main question we need to address when using the risk parity approach is: what will the volatilities (or risk) and correlations be when markets are crashing? The answer of course is that it is very hard to know the exact value since volatilities can only be estimated. Our novel methodology will adjust volatilities upwards based on how volatilities have been changing in the past. The rationale for this is: if the volatility of an asset has been fluctuating more rapidly in the past, during a downward movement the amount by which volatility could get higher will depend on the magnitude of the volatility changes in the past. We term this movement in volatility the velocity of volatility.
Adjusting the volatilities based on the velocity gives the following equations,
Here, is a factor that we calibrate based on the average length of observed downward movements, across a broad category of assets, in the past. Clearly the velocity of volatility depends on the volatility of volatility. The more volatile the volatility of an asset is, the more likely it is that the price of that asset will fall more during a downturn. A similar upward adjustment can be done for correlations as well while noting that correlations can never exceed one, though there is no upper bound on volatilities. The co-variance, based on the correlations among the assets, is labelled under variance to arrive at a nice sounding name, VVV (Velocity of Volatility and Variance), for this technique.
The weights that we derive based on the VVV volatility will underweight assets that have a greater possibility of falling more. The other question is, of course, whether the VVV weighting will cause any issues during normal times. The answer is that the VVV weights are geared to do better than other portfolios during downturns with no major underperformance during other market scenarios as shown by the expected returns, portfolio risk and sharpe ratios measured over an entire year, with many up and down cycles, as shown in Table ([fig:VVV-Weights-Comparison]).
Conclusion
The VVV weighting methodology factors in several empirical observations about financial markets and tailors them to the more volatile and correlated crypto-defi environment. This approach does well under a wide variety of market conditions and is custom built to outperform benchmarks during market downturns. Building portfolios in this manner epitomizes our belief that upward movements will take care of themselves, but it is the downward movements that require the most preparation. As we have discussed, volatility is caused by the actions of investors. It is inevitable when huge number of investors, with different perceptions of value, transfer large sums of money. Volatility is a small price to pay for the convenience of trading anything from anywhere and anytime, as long as we are sufficiently equipped to deal with downward movements. VVV is the protection mechanism sorely needed for the crypto-defi space.
Tables and Explanations
Each of the tables in this section are referenced in the main body of the article. Below, we provide supplementary descriptions for each table. The full data sample consists of daily observations over the last 365 days. The names of the assets have been anonymized for various portfolio management considerations, though all the information presented is based on actual historical numbers.
Table ([fig:VVV-Weights-Comparison]) — Each cell represents the correlation between the asset returns in the corresponding row and column over the historical period.
Table ([fig:VVV-Weights-Comparison]) — The columns represent the following information respectively: Annualized volatility of the assets calculated on a 90 day moving internal; vvvFactor calculated on a 90-day moving interval; The VVV adjusted volatility; weights calculated using VVV volatility; weights using mean variance optimization (MVO); weights using MVO and no shorting constraint. The last three rows show the portfolio expected return calculated based on the annualized average return over the data set horizon; the portfolio volatility; the sharpe ratio given by the portfolio expected return minus benchmark rate of 10% divided by the portfolio volatility.
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