Stable Aggregate Currencies
Summary
- A Stable Aggregate Currency (SAC) is a weighted basket of underlying currencies constructed to reduce volatility and increase value preservation.
- Backtests (from 2003 to the present) of periodically reweighted mean-variance optimized (MVO) and equal-weighted portfolios indicate SAC baskets demonstrate less historical volatility (HV) than a majority of the world’s major hard currencies.
- SACs can be implemented on-chain, using a combination of three components: 1) weights computation, 2) Balancer Pool, and 3) Smart contracts for user on/off ramp.
Introduction
Volatile exchange rates and currency devaluation can erode the economic security and purchasing power of affected citizens. Governments may exacerbate the softening of their native currency through poor fiscal and monetary policy.
Cryptocurrencies can make marked financial improvements to citizens whose native currency has historically exhibited relative instability and devaluation. An example where they have already had a significant impact is cross-border remittances, which are cheaper to process using cryptocurrencies such as Bitcoin than traditional channels like Western Union [1]. Similarly, innovations in cryptocurrencies, such as stablecoins, have the potential to make a similar, positive impact.
Stablecoins are a class of cryptocurrency whose value is usually pegged to a single underlying asset’s value (typically a hard currency). Examples include Tether, USDC, and Maker’s DAI, all pegged to the US Dollar. The composability of stablecoins can be leveraged to construct a Stable Aggregate Currency (SAC). This note explores avenues to implement an SAC and backtests the value preservation and volatility attributes of a SAC, constructed two ways, against various individual currencies over the past twenty years.
Stable Aggregate Currency (SAC)
A stable aggregate currency (SAC) is a weighted basket of underlying currencies in circulation. An example could be a currency that is backed by equal portions of USD, GBP, and EUR. SACs can be advantageous in the following ways: a) reducing idiosyncratic risks, b) reducing exchange rate volatility, and c) preserving purchasing power. The primary reason for these benefits comes from the diversification property of the SAC. Idiosyncratic risks are reduced because the aggregate currency diversifies unique risks associated with a single currency related to the fiscal and economic policies of the issuing government. Exchange rate volatility is reduced, again, because of diversification. Guidici et al [2] explore the economic implications in more detail.
The weights of an individual currency in a SAC must be computed by some procedure. Since the SAC is a portfolio of currencies, portfolio optimization algorithms can optimally assign weights to different currencies based on a particular optimization criterion. Common portfolio optimization methods include mean-variance optimization (MVO) [3] and Hierarchical Risk Parity (HRP) [4].
On-Chain Implementation
A potential architecture for implementing a SAC on-chain consists of three high-level components:
- Weights computation
- Index implementation
- Smart contracts.
Weights computation uses a chosen algorithm (MVO, HRP, etc …) to assign weights to individual currencies in the currency basket. This is typically a computationally intensive process, so it can be done off-chain. The design choices and hyperparameters that need to be tuned here are the same for any actively managed portfolio, such as how often to rebalance, how much lookback data to use when computing forward-looking weights, and so on. Simpler algorithms can also be employed, such as equal weighting of currencies.
Once the weights are computed, a Balancer ManagedPool can implement the computed currency index and create a SAC. Each currency in the pool would be a stablecoin representing a hard currency, such as USD, EUR, CNY, JPY, and GBP. The SAC management team is responsible for updating the pool weights — this could be set up with a governance structure similar to Maker’s DAI, which has an interest rate-setting governance process. The pool’s LP token then represents the SAC.
Smart contracts would provide an interface to exchange the SAC token for local currencies, to provide on/off ramps for users.
A question to investigate further is whether it is possible to combine Balancer’s ManagedPool with Composable Stable Pools. This is a consideration because Composable StablePools are designed to be more capital-efficient for pegged assets such as stablecoins. However, StablePools don’t allow active management of weights, so this may only be possible for simpler implementations of the SAC (such as an equally weighted SAC).
Backtesting
To backtest the volatility and value preservation attributes of a SAC, we downloaded FOREX data from 2003 onwards. Eight hard currencies (indicated in the legend in Fig. 1) were combined in two ways ( a) equally weighted, b) mean-variance optimization (MVO)) to create two hypothetical SAC currencies. When using MVO to compute portfolio weights, currencies were first converted to a “reduced normalized value in exchange,” (RNVAL) given by Eq 1. This was done to remove the portfolio’s dependence on a base currency (USD in our simulations). Further details are provided in Guidici et al [2].
Where t is the time index, c_ij(t) is the exchange rate between currencies i and j, respectively, at time t. After converting each currency index to an RNVAL, the MVO optimization problem, given by Eq 2, was solved to compute the weights of each currency. The MVO portfolio was rebalanced every 90 days, using 90 days of historical data to compute the covariance matrix in Eq 2.
where cov(i,j)) is the covariance matrix of the time-series RNVALi(t) and RNVALj(t), respectively. Fig.1 shows both the SAC’s value backed by the portfolio of currencies and the individual currencies that make up the portfolio.
For each currency, we compute an unnormalized historical volatility (HV) index. HV measures the dispersion of returns and is computed as HV = std(log_returns).
Several points of comparison originate from Fig 1:
- The HV of the SAC currencies is lower than the volatility of any individual currency (except CNY). USD is the reference, and with this perspective, has an artificial HV=0.
- The MVO-based SAC and equally weighted SAC portfolios exhibit similar historic volatility and value preservation.
The backtesting suggests that the primary advantages an indexed currency provides are reduced volatility and maintenance of purchasing power relative to other currencies.
Conclusion & Next Steps
This note uses a portfolio construction approach to simulate a stable aggregate currency (SAC) that is not referenced to a single currency and proposes a way to implement this with existing crypto primitives: stablecoins and Balancer pools. Backtesting indicates that SACs have desirable attributes, including increased value preservation and lower volatility than individual currencies. This implicitly considers the effect of interest rates, monetary policy, and other factors that influenced the relative valuation of currencies but does not disentangle the relative contribution of those factors.
Future work will investigate in more detail whether cryptocurrencies are well suited for this purpose beyond the initial considerations stated, the potential effects of implementing such a currency in a nation-state, and how monetary policy can work if an SAC is adopted in a nation-state. Additional open questions include ways to track currency performance relative to other measures of interest, such as purchasing power.
References
- https://www.coingecko.com/learn/bitcoin-vs-western-union-low-fees
- Giudici, Paolo, Thomas Leach, and Paolo Pagnottoni. “Libra or Librae? Basket based stablecoins to mitigate foreign exchange volatility spillovers.” Finance Research Letters 44 (2022): 102054.
- Kim, Jang Ho, et al. “Mean–variance optimization for asset allocation.” The Journal of Portfolio Management 47.5 (2021): 24–40.
- Burggraf, Tobias. “Beyond risk parity–A machine learning-based hierarchical risk parity approach on cryptocurrencies.” Finance Research Letters 38 (2021): 101523.
