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Managing Market Risk for Crypto Currencies

 

Contents

 

Overview

Asset Volatility vs Asset Sensitivity to Benchmark (Beta)

Portfolio Asset Covariance

Value at Risk (VaR)

Bitcoin Futures: Basis and Proxies

Intraday Value at Risk (VaR)

Risk-Based Limits

VaR Validation (Bayesian Approach)

Scenario Analysis

Conclusion


Overview

Crypto currencies have now become part of institutional investment strategies. According to CoinShares, assets held under management by crypto managers reached $57B at the end of Q1 2021.  

Like any other financial asset, crypto investments are subject to market risk monitoring with several approaches evolving. Crypto currencies exhibit no obvious correlation to other assets classes, risk factors  or economic variables. However, crypto currencies have exhibited high price volatility and have enough historical data to implement a robust market risk process. 

In this paper we discuss approaches to implementing market risk analytics for a portfolio of crypto assets. We will look at betas to benchmarks, correlations, Value at Risk (VaR) and historical event scenarios. 

Value at Risk allows risk managers to implement risk-based limits structures, instead of relying on traditional notional measures. The methodology we propose enables consolidation of risk for crypto assets with the rest of the portfolio. We will also discuss the use of granular time horizons for intraday limit monitoring. 

Asset Volatility vs Asset Sensitivity to Benchmark (Beta)

For exchange-traded instruments, beta measures the sensitivity of asset price returns relative to a benchmark. For US-listed large cap stocks, beta is generally computed relative to the S&P 500 index. For crypto currencies, several eligible benchmark indices have emerged that represent the performance of the overall crypto currency market.

We analyzed several currencies against S&P’s Bitcoin Index (SPBTC). SPBTC is designed to track the performance of the original crypto asset, Bitcoin. As market capitalization for other currencies grows, it would be more appropriate to switch to a dynamic multi-currency index such as Nasdaq’s NCI. At the time of this paper, Bitcoin constituted 62.4% of NCI.

Traditionally, beta is calculated over a variable time frame using least squares fit on a linear regression of benchmark return and asset return. One of the issues with calculating betas is the variability of the beta itself. In order to overcome that, especially given the volatility of crypto currencies, we recommend using a rolling beta.

Due to the varying levels of volatility and liquidity of various crypto currencies, a regression model may not always be a good fit. In addition to tracking fit through R-squared, it is important to track confidence level for the computed betas.

Figure 1 History of Beta to S&P Bitcoin Index with Confidence Intervals

The chart above shows rolling betas and confidence intervals for four crypto currencies between January 2019 and July 2021. Beta and confidence interval both vary over time and periods of high volatility (stress) cause a larger dislocation in the value of beta.

Rolling betas can be used to generate a hierarchical distribution of expected asset values.

Portfolio Asset Covariance

Beta is a useful measure to track an asset’s volatility relative to a single benchmark. In order to numerically analyze the risk exposure (variance) of a portfolio with multiple crypto assets, we need to compute a covariance matrix. Portfolio risk is a function not only of each asset’s volatility but also of the cross-correlation among them.

Figure 2 Correlations for 11 currencies (calculated using observations from 2021)

The table above shows a correlation matrix across 11 crypto assets, including Bitcoin.

Like betas, correlations among assets change over time. But correlation matrices are more unwieldy to track over time than betas are. For this reason, hierarchical models provide a good, practical framework for time-varying covariance matrices.

Value at Risk (VaR)

The VaR for a position or portfolio can be defined as some threshold Τ (in dollars) where the existing position, when faced with market conditions resembling some given historical period, will have P/L greater than Τ with probability k. Typically, k  is chosen to be 99% or 95%.

To compute this threshold Τ, we need to:

  1. Set a significance percentile k, a market observation period, and holding period n.
  2. Generate a set of future market conditions (scenarios) from today to period n.
  3. Compute a P/L on the position for each scenario

After computing each position’s P/L, we sum the P/L for each scenario and then rank the scenarios’ P/Ls to find the the k th percentile (worst) loss. This loss defines our VaR Τ at the the k th percentile for observation-period length n.

Determining what significance percentile k and observation length n to use is straightforward and often dictated by regulatory rules. For example, 99th percentile 10-day VaR is used for risk-based capital under the Market Risk Rule. Generating the scenarios and computing P/L under these scenarios is open to interpretation. We cover each of these, along with the advantages and drawbacks of each, in the next two sections.

To compute VaR, we first need to generate projective scenarios of market conditions. Broadly speaking, there are two ways to derive this set of scenarios:

  1. Project future market conditions using historical (actual) changes in market conditions
  2. Project future market conditions using a Monte Carlo simulation framework

In this paper, we consider a historical simulation approach.

RiskSpan projects future market conditions using actual (observed) n-period changes in market conditions over the lookback period. For example, if we are computing 1-day VaR for regulatory capital usage under the Market Risk Rule, RiskSpan takes actual daily changes in risk factors. This approach allows our VaR scenarios to account for natural changes in correlation under extreme market moves. RiskSpan finds this to be a more natural way of capturing changing correlations without the arbitrary overlay of how to change correlations in extreme market moves. This, in turn, will more accurately capture VaR. Please note that newer crypto currencies may not have enough data to generate a meaningful set of historical scenarios. In these cases, using a benchmark adjusted by a short-term beta may be used as an alternative.

One key consideration for the historical simulation approach is the selection of the observation window or lookback period. Most regulatory guidelines require at least a one-year window. However, practitioners also recommend a shorter lookback period for highly volatile assets. In the chart below we illustrate how VaR for our portfolio of crypto currencies changes for a range of lookback periods and confidence intervals. Please note that VaR is expressed as a percentage of portfolio market value.

Use of an exponentially weighted moving average methodology can be used to overcome the challenges associated with using a shorter lookback period. This approach emphasizes recent observations by using exponentially weighted moving averages of squared deviations. In contrast to equally weighted approaches, these approaches attach different weights to the past observations contained in the observation period. Because the weights decline exponentially, the most recent observations receive much more weight than earlier observations.

Figure 3 Daily VaR as % of Market Value calculated using various historical observation periods

VaR as a single number does not represent the distribution of P/L outcomes. In addition to computing VaR under various confidence intervals, we also compute expected shortfall, worst loss, and standard deviation of simulated P/L vectors. Worst loss and standard deviation are self-explanatory while the calculation of expected shortfall is described below.

Expected shortfall is the average of all the P/L figures to the left of the VaR figure. If we have 1,000 simulated P/L vectors, and the VaR is the 950th worst case observation, the expected shortfall is the average of P/Ls from 951 to 1000. 

The table below presents VaR-related metrics as a percentage of portfolio market value under various lookback periods.

Figure 4 VaR for a portfolio of crypto assets computed for various lookback periods and confidence intervals

Bitcoin Futures: Basis and Proxies

One of the most popular trades for commodity futures is the basis trade. This is when traders build a strategy around the difference between the spot price and futures contract price of a commodity. This exists in corn, soybean, oil and of course Bitcoin. 

For the purpose of calculating VaR, specific contracts may not provide enough history and risk systems use continuous contracts. Continuous contracts introduce additional basis as seen in the chart below. Risk managers need to work with the front office to align risk factor selection with trading strategies, without compromising independence of the risk process.

Figure 5 BTC/Futures basis difference between generic and active contracts

Intraday Value

The highly volatile nature of crypto currencies requires another consideration for VaR calculations. A typical risk process is run at the end of the day and VaR is calculated for a one-day or longer forecasting period. But Crypto currencies, especially Bitcoin, can also show significant intraday price movements. 

We obtained intraday prices for Bitcoin (BTC) from Gemini, which is ranked third by volume. This data was normalized to create time series to generate historical simulations. The chart below shows VaR as a percentage of market value for Bitcoin (BTC) for one-minute, one-hour and one-day forecasting periods. Our analysis shows that a Bitcoin position can lose as much as 3.5% of its value in one hour (99th percentile VaR).

 

Risk-Based Limits 

Right from the inception of Value at Risk as a concept it has been used by companies to manage limits for a trading unit. VaR serves as a single risk-based limit metric with several advantages and a few challenges:

Pros of using VaR for risk-based limit:

  • VaR can be applied across all levels of portfolio aggregation.
  • Aggregations can be applied across varying exposures and strategies.
  • Today’s cloud scale makes it easy to calculate VaR using granular risk factor data.

VaR can be subject to model risk and manipulation. Transparency and use of market risk factors can avoid this pitfall.

Ability to calculate intra-day VaR is key for a risk-based limit implementation for crypto assets. Risk managers should consider at least an hourly VaR limit in addition to the traditional daily limits.

VaR Validation (Bayesian Approach)

Standard approaches for back-testing VaR are applicable to portfolios of crypto assets as well.

Given the volatile nature of this asset class, we also explored an approach to validating the confidence interval and percentiles implied from historical simulations. Although this is a topic that deserves its own document, we present a high-level explanation and results of our analysis.

Building an approach first proposed in the Pyfolio library, we generated a posterior distribution using the Pymc3 package from our historically observed VaR simulations.

Sampling routines from Pymc3 were used to generate 10,000 simulations of the 3-year lookback case. A distribution of percentiles (VaR) was then computed across these simulations.

The distribution shows that the mean 95th percentile VaR would be 7.3% vs 8.9% calculated using the historical simulation approach. However, the tail of the distribution indicates a VaR closer to the historical simulation approach. One could conclude that the test indicates that the original calculation still represents the extreme case, which is the motivation behind VaR.

Figure 6 Distribution of percentiles generated from posterior simulations

Scenario Analysis

In addition to standard shock scenarios, we recommend using the volatility of Bitcoin to construct a simulation of outcomes. The chart below shows the change in Bitcoin (BTC) volatility for select events in the last two years. Outside of standard macro events, crypto assets respond to cyber security events and media effects, including social media.

Figure 7 Weekly observed volatility for Bitcoin  

Conclusion

Given the volatility of crypto assets, we recommend, to the extent possible, a probability distribution approach. At the very least, risk managers should monitor changes in relationship (beta) of assets.

For most financial institutions, crypto assets are part of portfolios that include other traditional asset classes. A standard approach must be used across all asset classes, which may make it challenging to apply shorter lookback windows for computing VaR. Use of the exponentially weighted moving approach (described above) may be considered.

Intraday VaR for this asset class can be significant and risk managers should set appropriate limits to manage downward risk.

Idiosyncratic risks associated with this asset class have created a need for monitoring scenarios not necessarily applicable to other asset classes. For this reason, more scenarios pertaining to cyber risk are beginning to be applied across other asset classes.  

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Related Article

Calculating VaR: A Review of Methods


COVID-19 and the Cloud

COVID-19 creates a need for analytics in real time

Regarding the COVID-19 pandemic, Warren Buffet has observed that we haven’t faced anything that quite resembles this problem” and the fallout is “still hard to evaluate. 

The pandemic has created unprecedented shock to economies and asset performance. The recent unemployment  data, although encouraging , has only added to the uncertaintyFurthermore, impact and recovery are unevenoften varying considerably from county to county and city to city. Consider: 

  1. COVID-19 cases and fatalities were initially concentrated in just a few cities and counties resulting in almost a total shutdown of these regions. 
  2. Certain sectors, such as travel and leisure, have been affected worse than others while other sectors such as oil and gas have additional issues. Regions with exposure to these sectors have higher unemployment rates even with fewer COVID-19 cases. 
  3. Timing of reopening and recoveries has also varied due to regional and political factors. 

Regional employment, business activity, consumer spending and several other macro factors are changing in real time. This information is available through several non-traditional data sources. 

Legacy models are not working, and several known correlations are broken. 

Determining value and risk in this environment is requiring unprecedented quantities of analytics and on-demand computational bandwidth. 

COVID-19 in the Cloud

Need for on-demand computation and storage across the organization 

I don’t need a hard disk in my computer if I can get to the server faster… carrying around these non-connected computers is byzantine by comparison.” ~ Steve Jobs 


Front office, risk management, quants and model risk management – every aspect of the analytics ecosystem requires the ability to run large number of scenarios quickly. 

Portfolio managers need to recalibrate asset valuation, manage hedges and answer questions from senior management, all while looking for opportunities to find cheap assets. Risk managers are working closely with quants and portfolio managers to better understand the impact of this unprecedented environment on assets. Quants must not only support existing risk and valuation processes but also be able to run new estimations and explain model behavior as data streams in from variety of sources. 

These activities require several processors and large storage units to be stood up on-demand. Even in normal times infrastructure teams require at least 10 to 12 weeks to procure and deploy additional hardware. With most of the financial services world now working remotely, this time lag is further exaggerated.  

No individual firm maintains enough excess capacity to accommodate such a large and urgent need for data and computation. 

The work-from-home model has proven that we have sufficient internet bandwidth to enable the fast access required to host and use data on the cloud. 

Cloud is about how you do computing

“Cloud is about how you do computing, not where you do computing.” ~ Paul Maritz, CEO of VMware 


Cloud computing is now part of everyday vocabulary and powers even the most common consumer devices. However, financial services firms are still in early stages of evaluating and transitioning to a cloud-based computing environment. 

Cloud is the only way to procure the level of surge capacity required today. At RiskSpan we are computing an average of half-million additional scenarios per client on demand. Users don’t have the luxury to wait for an overnight batch process to react to changing market conditions. End users fire off a new scenario assuming that the hardware will scale up automagically. 

When searching Google’s large dataset or using Salesforce to run analytics we expect the hardware scaling to be limitless. Unfortunately, valuation and risk management software are typically built to run on a pre-defined hardware configuration.  

Cloud native applications, in contrast, are designed and built to leverage the on-demand scaling of a cloud platform. Valuation and risk management products offered as SaaS scale on-demand, managing the integration with cloud platforms. 

Financial services firms don’t need to take on the burden of rewriting their software to work on the cloud. Platforms such as RS Edge enable clients to plug their existing data, assumptions and models into a cloudnative platform. This enables them to get all the analytics they’ve always had—just faster and cheaper.  

Serverless access can also help companies provide access to their quant groups without incurring additional IT resource expense. 

A recent survey from Flexera shows that 30% of enterprises have increased their cloud usage significantly due to COVID-19.

COVID-19 in the Cloud

Cloud is cost effective 

In 2000, when my partner Ben Horowitz was CEO of the first cloud computing company, Loudcloud, the cost of a customer running a basic Internet application was approximately $150,000 a month.”  ~ Marc Andreessen, Co-founder of Netscape, Board Member of Facebook 


Cloud hardware is cost effective, primarily due to the on-demand nature of the pricing model. $250B asset manager uses RS Edge to run millions of scenarios for a 45minute period every day. Analysis is performed over a thousand servers at a cost of $500 per month. The same hardware if deployed for 24 hours would cost $27,000 per month 

Cloud is not free and can be a two-edged sword. The same on-demand aspect thaenables end users to spin up servers as needed, if not monitoredcan cause the cost of such servers to accumulate to undesirable levelsOne of the benefits of a cloud-native platform is built-on procedures to drop unused servers, which minimizes the risk of paying for unused bandwidth. 

And yes, Mr. Andreeseen’s basic application can be hosted today for less than $100 per month 

The same survey from Flexera shows that organizations plan to increase public cloud spending by 47% over the next 12 months. 

COVID-19 in the Cloud

Alternate data analysis

“The temptation to form premature theories upon insufficient data is the bane of our profession.” ~ Sir Arthur Conan Doyle, Sherlock Holmes.


Alternate data sources are not always easily accessible and available within analytic applications. The effort and time required to integrate them can be wasted if the usefulness of the information cannot be determined upfront. Timing of analyzing and applying the data is key. 

Machine learning techniques offer quick and robust ways of analyzing data. Tools to run these algorithms are not readily available on a desktop computer.  

Every major cloud platform provides a wealth of tools, algorithms and pre-trained models to integrate and analyze large and messy alternate datasets. 

Join fintova’s Gary Maier and me at 1 p.m. EDT on June 24th as we discuss other important factors to consider when performing analytics in the cloud. Register now.


Chart of the Month: Tracking Mortgage Delinquency Against Non-traditional Economic Indicators by MSA

Tracking Mortgage Delinquency Against Non-traditional Economic Indicators by MSA 

Traditional economic indicators lack the timeliness and regional granularity necessary to track the impact of COVID-19 pandemic on communities across the country. Unemployment reports published by the Bureau of Labor Statistics, for example, tend to have latency issues and don’t cover all workers. As regional economies attempt to get back to a new “normal” RiskSpan has begun compiling non-traditional “alternative” data that can provide a more granular and real-time view of issues and trends. In past crises, traditional macro indicators such as home price indices and unemployment rates were sufficient to explain the trajectory of consumer credit. However, in the current crisis, mortgage delinquencies are deteriorating more rapidly with significant regional dispersion. Serious mortgage delinquencies in the New York metro region were around 1.1% by April 2009 vs 30 day delinquencies at 9.9% of UPB in April 2020.  

STACR loan–level data shows that nationwide 30–day delinquencies increased from 0.8% to 4.2% nationwide. In this chart we track the performance and state of employment of 5 large metros (MSA). 

May Chart of the Month


Indicators included in our Chart of the Month: 

Change in unemployment is the BLS measure computed from unemployment claims. Traditionally this indicator has been used to measure economic health of a region. BLS reporting typically lags by months and weeks. 

Air quality index is a measure we calculate using level PM2.5 reported by EPA’s AirNow database on a daily basis. This metric is a proxy of increased vehicular traffic in different regions. Using a nationwide network of monitoring sites, EPA has developed ambient air quality trends for particle pollution, also called Particulate Matter (PM). We compute the index as daily level of PM2.5 vs the average of the last 5 years.  For regions that are still under a shutdown air quality index should be less than 100 (e.g. New York at 75% vs Houston at 105%) 

Air pollution from traffic has increased in regions where businesses have opened in May ’20 (e.g. LA went up from 69% in April to 98% in May).  However, consumer spending has not always increased at the same level.  We look to proxies for hourly employment levels. 

New Daily COVID-19 Cases: This is a health crisis and managing the rate of new COVID-19 cases will drive decisions to open or close businesses. The chart reports the monthly peak in new cases using daily data from Opportunity Insight 

Hourly Employment and Hours Worked at small businesses is provided by Opportunity Insight using data from Homebase. Homebase is a company that provides virtual scheduling and time-tracking tools, focused on small businesses in sectors such as retail, restaurant, and leisure/accommodation. The chart shows change in level of hourly employment as compared to January 2020. We expect this is to be a leading indicator of employment levels for this sector of consumers. 


Sources of data: 

Freddie Mac’s (STACR) transaction database 

Opportunity Insight’s Recovery Tracker 

Bureau of Labor and Statistics (BLS)’ MSA level economic reports 

Environment Protection Agency (EPA)’s AirNow database. 


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