Fixed Income Built on Volatile Yield — Simulating a Novel Class of DeFi Protocols

An analysis of 88mph protocol dynamics using radCAD

27 min readDec 6, 2021

By Giulio Trichilo and Jonathan Gabler

Disclaimer: All content provided herein is for general information only. No part of this content constitutes financial or legal advice. Any use or reliance on this content is solely at your own risk and discretion.


  • 88mph and CADLabs have worked together to create a radCAD agent-based model to simulate liquidity and network revenue dynamics for the 88mph v3 protocol.
  • The model is set up to cover scenarios based on configurations of pool depositor and yield token purchaser agents, and how their behavior affects protocol liquidity and network revenue.
  • 6 main experiments are performed. Two on depositor agent deposit size and duration, two on depositor agent premature withdrawal behavior, one on yield token purchaser agent behavior, a last one indicative of the effect of a sudden interest rate shock, in a toy example scenario.
  • Many of the simulation results indicate good decision making in protocol construction. We also show how existing liquidity backstops can mitigate negative scenarios.

Protocol development in the blockchain space, particularly in decentralized finance, or DeFi, is an end-to-end process that results in the construction of a cryptoeconomic ecosystem within which agent participation often gives rise to complex monetary dynamics. Simulation of these complex dynamics is slowly becoming standard practice for projects either at the protocol development stage or after deployment. The present case study is performed as a joint initiative between 88mph, a Swiss-based DeFi fixed income protocol, taking a proactive approach in modeling the complex dynamics which arise from the usage of its fixed and variable yield products, and CADLabs. We create an extensible radCAD dynamical systems and agent-based model centered around 88mph’s protocol liquidity dynamics and interaction with a selected underlying money market protocol — Compound. We perform a set of five experiments where depositor and yield token agent behavior are parameterized to enact a range of scenarios, as well as an additional experiment which gauges the effect of an instantaneous variable yield rate shock on accumulated protocol surplus.

We find, in accordance with intuition, that when depositor agents make larger or longer deposits on average, more liquidity is available to the protocol and its stakeholders; the effect of deposit size on liquidity is more pronounced than that of deposit duration. We also find that when depositor agents are constrained to more intensive premature withdrawal behavior, this adversely affects liquidity; however, the subsequent increase in protocol fees out of withdrawals allows to mitigate the effect. We find that higher selectivity in terms of yield token ROI expectations positively rewards agents, but at the cost of lower total purchases made, hence debt secured. Finally, we show that an instantaneous shock to the underlying variable yield rate has important short term effects on liquidity availability for the protocol. We show how the radCAD modelling framework is flexible enough to simulate core dynamics related to protocol liquidity for any variable-yield-dependent fixed income protocol. We conclude by providing 88mph with a set of qualitative recommendations regarding the agent scenarios analyzed.

Fixed Income in TradFi and DeFi

In traditional finance (“TradFi”), fixed income broadly refers to the class of securities that pay investors fixed interest or dividend payments until its maturity, where investors are repaid the principal amount they had invested. Government and corporate bonds are the most common types of fixed income products — both forms of securitized debt. Unlike variable-income securities, where payments change based on some underlying measure — such as short-term interest rates — the payments of a fixed income security are known in advance.

Why does fixed yield matter? Anyone familiar with modern portfolio theory will have heard of the ‘60/40 portfolio’, where 60% of the total portfolio allocation is in variable yield securities, typically equities, and the remaining 40% is in fixed income instruments, such as treasuries or low yield (safe) corporate bonds. The portion of the investment in fixed income broadly speaking hedges against the potential volatility of the variable (but potentially higher return) portion of the allocation, as well as against inflation¹.

In decentralized finance (“DeFi”), we’ve seen a “Cambrian explosion” of products and protocols offering various ways to earn a variable yield on cryptoassets, but much less so for fixed yield. Given cryptocurrencies are by nature very volatile and this characteristic broadly carries over to protocols offering variable yield (even when the yield generating asset is a stablecoin), this gives the investors the option to diversify their portfolios by allocating a portion of their strategy to a ‘fixed income money legos’², presents a much-needed opportunity.

An introduction to 88mph

88mph aims to be a leader in fixed yield DeFi composability, offering fixed yield products to its users, in addition to variable yield products for less risk-averse users wishing to capitalize on the potential upside of the money market protocols 88mph leverages to finance its fixed yield product offering. The typical 88mph user leverages the protocol to hedge against volatility in money market rates and earn rewards in the form of MPH tokens, which in turn allow for earning protocol revenues and gaining voting rights.

The 88mph fixed yield product

As of writing 88mph V3, which hit mainnet on September 7th 2021³, offers a fixed yield rate with a custom or preset maturity for the following supplied assets: DAI, USDC, USDT, LINK, UNI, and CRV:RENWBTC. When users (or other protocols) supply assets, 88mph acts as a non-custodial, fully on-chain intermediary between them and third-party variable yield rate money market protocols — Aave, Compound, and Harvest — to offer the best fixed yield rate on their capital.

How it works

  1. Deposits assets: deposit any amount of assets with a maturity between 1 and 365 days to get a predetermined fixed yield rate at maturity.
  2. Deposit generates variable APY: the deposit generates a yield at a variable rate on third-party protocols until it reaches its maturity.
  3. Withdraw: withdraw (incl. early withdrawal), top-up, roll over your deposit + fixed-rate yield at any time.

For example, a 12-month deposit of 100 DAI will deliver a fixed-rate yield after 12 months of variable yield generation on a third-party protocol. If the fixed yield rate at the time of deposit is 10%, then 10 DAI of yield is obtained when the deposit reaches its maturity one year later⁴.

88mph determines a deposit’s fixed yield rate based on the 30-day exponential moving average (EMA) of the variable yield rate of the underlying yield protocol. 88mph offers between 37.5% and 75% of the EMA as the fixed yield rate based on the length of deposit, with longer deposits earning a lower rate.

For example, if at the time of deposit the 88mph’s 30-day EMA of the Fixed APR asset is 10%, a 7-day deposit of 100 DAI will earn a 7.5% fixed yield. A 12-month deposit of 100 DAI will earn a 3.75% fixed-rate yield⁴.

When deposits are made, additional mechanisms kick in such as NFT minting for deposit control, vested MPH token reward generation, and the ability to stake MPH to earn protocol revenues and voting rights. We refer the reader to the documentation⁵ for a detailed discussion of these additional mechanisms, as they do not fall within the modelling scope discussed in this article.

88mph Yield Tokens

88mph Yield Tokens (YT) are fungible ERC-20/ERC-1155 tokens that allow speculators to profit from the rise in the yield rate of the underlying variable-rate yield protocols used for financing the fixed yield product. Alternatively, YT may be used as a hedge against borrowing costs for users who borrow stablecoins on the underlying protocols directly. For example, a borrower of DAI on the Compound protocol could purchase 88mph’s cDAI YT on 88mph as a hedge⁶.

YT are made available when a user makes a fixed yield rate deposit on 88mph. The YT are tied to the specific deposit made and can be purchased by a third party. YT give holders the right to earn all the future variable-rate yield generated by the corresponding deposit, plus the purchase cost of the YT.

Purchasing YT corresponds to purchasing debt due on a deposit, therefore when buying YT the insolvency risk of the associated fixed yield rate deposit is decreased since the amount of fixed-rate yield that is not backed by real assets is decreased. If all YT’s tied to a specific deposit are purchased, the yield on the deposit in question becomes riskless, as it is instantly and entirely financed by the associated YT purchase.

For instance, let’s imagine that the 30-day EMA for the DAI-Compound fixed APR asset is at 10%. So, for a 12-month 100 DAI deposit, the fixed APR offered would be 3.75% (37.5% of the 30-day EMA) before fees. Cf Fixed interest rate model section.

The corresponding 103.75 YTs would cost 3.75 DAI to purchase (learn more about YT token pricing below). The YTs entitle the holders to the variable-rate yield earned by the 100 DAI principal + 3.75 DAI over the deposit’s term. If the average Compound variable APY stays at 10% over the deposit duration, then the YT delivers 10.375 DAI to its holders.

Suppose you bought all 103.75 YTs. Your final balance will be 10.375 DAI. Thus, you earn a 6.625 DAI profit on your investment of 3.75 DAI, a 176.67% return on investment.

Risk mitigation

The main risk which the 88mph protocol may incur is the risk of insolvency: the situation where 88mph does not have enough funds to return the deposited funds plus fixed yield to a user. 88mph relies on four lines of defense to mitigate the risk of insolvency⁷:

  1. An oracle that can accurately price (not necessarily predict) future yield. This ensures that YTs get sold most of the time.
  2. Frequent early withdrawals, which allow 88mph depositors to accumulate the forfeited yield to build up a surplus that acts as a backstop.
  3. Volatile floating yield rates in the underlying yield protocols, which allows 88mph to use the surplus yield from deposits that were offered low fixed yield rates to subsidize the deficit caused by the deposits that were offered high fixed yield rates.
  4. A security module (not yet deployed), which acts as the ultimate backstop; similar to Aave’s safety module with capped double liability.

In collaboration with the 88mph team, CADLabs has created a radCAD “digital twin” dynamical systems model to simulate 88mph protocol dynamics, gauge insolvency risk through the lens of protocol liquidity, and quantify the minimum levels of depositor engagement/activity and external variable yield which are required for the protocol to remain solvent.

radCAD — a performant alternative to cadCAD

Open-source modelling software flexible enough for the broad use case of cryptoeconomic simulations is, as of this day, still a niche resource. Fortunately for the Web 3 space, in 2018, the San Francisco-based engineering firm BlockScience open-sourcedcadCAD, a python-based modelling framework for research, validation, and Computer-Aided Design of complex systems. It is currently the go-to python software package for simulation of complex systems in the Web 3 space.

In 2021, the CADLabs team created radCAD, an open-source cadCAD alternative for professional use cases requiring higher simulation performance across backends. It also features a simplified developer API, is fully backward compatible with cadCAD, and has seen adoption by high-profile Web 3 projects (e.g. Ethereum Foundation). A full suite of beginner and advanced educational materials around cadCAD and radCAD is available from CADLabs’ online educational project, cadCAD Edu.

An analysis of 88mph’s protocol dynamics

The main risk associated with the 88mph protocol is that of protocol-wide insolvency — the inability to pay out the fixed yield that all fixed income product holders must be paid at each maturation date. In order to mitigate this risk, 88mph has multiple lines of defense in accurate oracle pricing for future yield, protocol fees for early deposit withdrawals which can be reinjected into overall liquidity, fixed income de-risking through third party YT purchases, and in case of a long term rise in underlying variable yield, simply yield capture at the level of overall deposits being made.

It is therefore evident that where the creation of a radCAD model creates the most impact for 88mph is in modelling agent behavior around making deposits, making early withdrawals, purchasing YTs, and having a plausible model of the underlying protocol’s money market rates — the variable yields. Hence, the radCAD model leverages parameterization of the aforementioned agent behaviors to provide 88mph with scenario analysis, and the ability to qualitatively and quantitatively assess protocol liquidity. While the 88mph v3 protocol is a lot richer in terms of user incentivization with the MPH, xMPH tokens, and deposit management via NFT minting, for the purposes of the model construction, these are either abstracted or scoped out. The radCAD framework is flexible enough that these additional dynamics can be included in subsequent system specifications.

radCAD “digital twin” model scope and key assumptions

In order to effectively model the relationship between agents (depositors, YT buyers), 88mph deposit pools, and the underlying money market protocols and their variable rates, we make several simplifying assumptions that enable modular model construction and scenario analysis, and which additionally showcase radCAD’s flexibility with respect to the strictness of assumptions and modelling granularity.

In practical terms, we restrict our analysis to a ternary relationship between one 88mph asset pool (corresponding to the interest contract for a particular money market), its underlying money market, and two agent types: depositors (withdrawers) and YT purchasers. We believe this ternary relationship to be the fulcrum of protocol solvency and hence consider this system in isolation from other asset pools and their respective underlying money market protocols. In particular, the asset pool — the money market pair which is considered is the most liquid out of those offered (at the time of writing) — is the DAI pool on the Compound lending protocol.

This specification, namely an intermediary asset pool linked with a single underlying variable rate money market, interacted upon by multiple stakeholders using the intermediary’s product, can be generally applied not just in the case of 88mph, but to model any protocol which provides fixed income financed through proceeds earned from variable yield above the offered fixed rate. However, as will be discussed, the way in which we adapt this set of assumptions is unique to 88mph’s protocol dynamics and was the fruit of close collaboration.

We further formalize the following assumptions for all analyses performed:

  • The model employs an additive interest rate model as opposed to one in which per-block compounding is present, as the timestep frequency is days. We believe this provides correct directional guidance on results without overcomplicating the logic. Refinement of the interest rate model (based by default on the compound protocol formula) can be made in the future.
  • The user agents relative to deposit making and YT purchase employ logic which pertains to a certain degree of realism with regards to the distributional models used (gamma distributions). The policy functions do not calibrate distribution (and other) parameters based on historical data on deposits and YT purchase behavior, yet can be extended to so. As such, there is no guarantee that the agents, as implemented, will reflect actual user behaviour.
  • We assume that the system is composed of a single 88mph pool asset pool (DAI), its underlying money market pool (Compound), depositor and YT purchaser agents exist in isolation with regards to the external ecosystem, which implies that the only interaction between users and the money market pool happens through usage of the 88mph protocol.

Scenario analysis simulation results

In this section we discuss the main findings from the radCAD simulations performed on the 88mph “digital twin”. We performed a set of five main sensitivity analyses via parameter sweeps and an additional one via A/B testing, where we gauged the effect of depositor and YT agent behavior on protocol liquidity and 88mph network revenue (protocol fees).

We find that when depositor agent behavior is constrained to making larger principal and longer duration deposits that underlying money market liquidity and network revenue captured by the protocol are increased. We also find that constraining depositor agent behavior with regards to the magnitude of premature withdrawals that network revenue increases at the cost of decreased underlying money market liquidity. From our analysis on YT agent behavior we find that increasing the expected YT ROI purchasing constraint results in greater yield capture at the expense of a lower volume of YT sold. In our final analysis, where we replace the stochastic interest rate derived from the Compound money market formula with a deterministic step function, we find that a sudden drop in money market rate has severe short term consequences on the protocol’s accumulated interest surplus. We summarize these findings below.

Overview of performed analysis (“What-if Matrix”)

In the following sections, we present the results for each of the main analyses performed. We group the six experiments performed into four distinct sections, as indicated in the section labels above. In each analysis section, we then reiterate on the relevant what-if questions.

Analysis 1: Effects of Agent deposit-making behavior on pool liquidity and network revenue

Analysis 1 covers the findings from the first two experiments, with particular focus on Experiment 1. Since experiment 2 is conceptually similar, findings are compared in the section’s conclusion.

In Experiment 1, we take a look at the what if question: How does the depositor agents’ deposit magnitude profile affect available liquidity and protocol revenue?

This analysis allows the exploration of underlying money market liquidity and its multiple constituents as affected by agent interaction with the 88mph protocol.

We perform a parameter sweep over the deposit amount gamma distributions’ shape parameter, which controls agent behavior with regards to the sizes of deposit principals made on the 88mph protocol, which are then invested in the underlying Compound market. A higher shape parameter means that more of the distribution’s probability mass is centered towards bigger deposits, away from zero. The analysis provides the overall intuitive result that larger deposits on average lead to more available liquidity in the underlying money market.

NOTE: One may additionally work with the distribution’s scale and location parameters, however it is easier to produce more distinguishable agent behavior when working with the shape parameter, and keeping location and scale constant. Parameter effect can be understood here:

We present the results below:

Distribution of Deposit sizes for Agent Behavior shape parameter settings

In the plot above, we show the resulting empirical distributions of agent deposit sizes over the entire simulation. We see how a higher shape parameter leads to larger deposit sizes by agents on average. The effects of this are then presented on overall liquidity.

Overall liquidity over simulation duration for shape parameter settings

Intuitively, we see that there is more available liquidity when agents make larger deposits. More available liquidity also implies higher volatility of the corresponding time series evolution.

Pool accumulated surplus over simulation duration for shape parameter settings

Here we see the accumulated interest surplus for 88mph in asset units (in this case DAI), whilst we can broadly discern a trend with larger deposit making agents resulting in higher surplus accumulation, YT purchaser agents also come into play here making this dynamic less trivial than in the previous cases.

Cumulative liquidity contributions over simulation duration for shape parameter settings

In the plots above, we decompose the overall liquidity above into cumulative contributions of deposits made, withdrawn prematurely, and withdrawn at maturation. We assume there are no deposits rolled over, which the 88mph protocol in practice does enable. We see a clear cut effect of liquidity addition and withdrawal magnitude based on depositor agent deposit sizes. Since both maturation and premature withdrawal are subject to protocol fees, this directly impacts the magnitude of network revenue obtained.

Analysis Results

In this analysis we have explored the effect of changing the shape parameter of the gamma distribution which dictates agent deposit making behavior in terms of average deposit size. Increasing the parameter skews average deposits to higher values, which has the effect of increasing overall money market pool liquidity, and hence greater amounts to be reaped as protocol / network fees. A greater interest surplus is obtained with larger deposits on average.

In Experiment 2, we take a look at the similar what-if question: “How does the depositor agents’ deposit duration profile affect available liquidity and protocol revenue?”

Here, we instead perform a parameter sweep over the deposit durations that agents make. These are also controlled by an appropriately parameterized gamma distribution, and where we once again sweep over the shape parameter. We obtain results which are qualitatively similar to the experiment 1, however we note that the effect is less clear cut in terms of overall differences in liquidity for different parameter settings, especially with regards to premature withdrawals.

Analysis 2: Effects of Agent withdrawal-making behavior on pool liquidity and network revenue

Analysis 2 covers the findings from Experiments 3 and 4, with particular focus on Experiment 3. Since experiment 4 is conceptually similar, findings are compared in the section’s conclusion.

In Experiment 3, we take a look at the what if question: How does the amount of depositor agents which engage in premature withdrawals affect available liquidity and protocol revenue?

In the presented analysis we take a look at changing the percentage of agent deposit actions which have an associated premature withdrawals event series. A higher percentage means that more agents which make a deposit are likely to withdraw the amount prematurely. We include the edge cases of 0% (no agent) and 100% (all agents) performing premature withdrawals, with two intermediate cases of 30% and 70% of agents respectively. We let agents which do engage in premature withdrawal to make anywhere between 0 and 5 premature withdrawals over the duration of their deposit.

We constrain this analysis to an edge case where, if an agent engages in premature withdrawal, they perform a full premature withdrawal over the upto 5 times. This means that at maturity, there is nothing left to withdraw in all cases.

Example: 1000 DAI is deposited today (time t) for 100 days. The agent decides to make 4 premature withdrawals at timesteps and amounts t10: 250DAI, t+20: 250DAI, t+30: 250DAI, and t+50: 250DAI. In this case, all the principal has been withdrawn prematurely, by day 50.

Experiment results:

Overall liquidity over simulation duration for premature withdrawal engagement parameter setting

In the plot above we show overall liquidity over the duration of the simulation. Intuitively, we find that the case where 0% of agents engage in full premature withdrawal yields more overall liquidity than when 100% of agents are constrained to full premature withdrawals only.

Pool accumulated surplus over simulation duration for premature withdrawal engagement parameter setting

In the plot above, we see how constraining all agents to perform full premature withdrawals (purple series) vs none of them (pink series) has a noticeable effect on the accumulated interest surplus in asset units, and hence on network revenue that can be obtained via protocol fees.

Cumulative liquidity contributions over simulation duration for premature withdrawal engagement parameter setting

The first row of plots above show how much liquidity is cumulatively removed from premature withdrawals or maturation respectively. By construction, we see that the edge cases where 0% or 100% of agents engage in full premature withdrawals, then 100% of liquidity is removed from the pool exclusively due to premature withdrawals, and vice versa with natural maturation. In the 70% and 30% setting this has the effect of balancing the total liquidity removed between premature and maturation, based on the set percentages.

In the bottom left plot above we see liquidity removed from YT agent profit taking, naturally, less is possible to be removed in cases where a greater percentage of agents are constrained to full premature withdrawals only.

In the bottom right plot above we see liquidity added from YT agent purchase. More liquidity is added in cases where a greater percentage of agents are constrained to larger amounts of premature withdrawals. Given the protocol’s early withdrawal fee, this implies a greater accumulation of the forfeited yield used to build up a surplus. This is consistent with the 88mph protocol’s risk mitigation measure.

Analysis Results

In this analysis we took a look at changing the percentage of agents which decide to engage in premature withdrawal of deposits they make, including edge cases. We perform this analysis in the edge case where agents are constrained to full premature withdrawals only, regardless of which percentage engages in it. We intuitively find that constraining 100% of agents to engage in full premature withdrawals adversely affects total pool liquidity, but enables a higher amount of protocol / network fees to be taken, compared to cases in which less agents engage in full withdrawals.

In Experiment 4, we take a look at the similar what-if question: How does the amount of depositor agents which engage in premature withdrawals affect available liquidity and protocol revenue?

This experiment consisted in changing the minimum percentage of principal which can be withdrawn prematurely by agents who engage in premature withdrawals. We fix agents which withdraw prematurely at 50%.

Example: 1000 DAI is deposited today (time t) for 100 days. At a minimum of 50%, in the case where the agent decides to make 4 premature withdrawals at timesteps and amounts t+10: 125DAI, t+20: 125DAI, t+30: 125DAI, and t+50: 125DAI. In this case, 50% of the principal has been withdrawn prematurely, by day 50. The remaining 50%, or 500DAI will be removed at maturity: t+100.

Experiments 3 and 4 yield qualitatively similar results. However, we observe that the effect of varying the parameter for percent premature in experiment 4 is more subtle than directly varying the percentage of agents who engage in premature withdrawals, as in experiment 3. Relaxing the edge case constraint in the main analysis makes both of these experiments yield more commensurate results.

Analysis 3: Effects of Agent Yield Token ROI Selectivity on liquidity and network revenue

In this analysis on YT agents, the what-if question asked is — “How does yield token purchase agents’ selectivity profile with regards to Yield Token ROI affect available liquidity?”

This analysis allows the exploration of Accumulated Surplus as Percentage of Current Deposits Amount over time depending on the YT ROI expectation purchase threshold.

We perform a parameter sweep over four different values of the minimum expected ROI threshold Yield Token agents are willing to purchase YT for — 50%, 90%, 150%, and 200%. This models the selectivity profile of YT buyer agents, choosing only the most lucrative YT. YT agent logic with regards to purchasing is based on expected ROI at the current variable yield rate to remain constant over the underlying deposits’ duration.

Experiment Results:

Accumulated surplus (as a percentage of Current Deposits Amount) over simulation duration for YT buyer agent selectivity parameter settings

Each series in the plot above is relative to a parameter value for the selectivity threshold. The higher the threshold, the higher the likelihood of YT buyer agents engaging only in more lucrative deals, as a consequence there is less influence of them on the overall accumulated interest surplus, expressed here as a percentage of current deposits.

Additionally, we notice that agents which settle for lower ROIs (pink and blue series) seem to have higher accumulated surplus in accordance with the overall accumulation phase in the pool, but then lose out to agents which are more selective. The low engagement of high ROI seeking agents is motivated below.

Minimal and maximal ROI over simulation duration for YT buyer agent selectivity parameter settings

In the plots above we see the corresponding minimum and maximum ROI for YT, which agents engage in at their selectivity level with the expectation that the observed variable APY at the time of purchase will persist for the duration of the underlying deposit.

Cumulative count of YT sold over simulation duration for YT buyer agent selectivity parameter settings

As expected, the higher the ROI selectivity, the less YT’s are being bought by agents with that preference — hence addition to liquidity is lower.

Analysis Results

The higher the YT agent selectivity threshold, the higher the likelihood of selecting only more lucrative deals, which leads to less overall influence on the accumulated interest surplus. If real world YT buyers were to employ higher fidelity ROI prediction methods, the effect on 88mph surplus would be accordingly greater.

This shows the importance of modelling the YT demand side in consideration of accurately modelling underlying money market rate behavior and the derivative Oracle Rate, as they drive the financial dynamics.

Analysis 4: Effect of a yield rate shock on total interest surplus

In this final analysis, the what-if question asked is — How does an instantaneous shock to the underlying money market rate affect protocol accumulated surplus?

This analysis allows the exploration of accumulated interest surplus over time when a step function is used to model the underlying money market rate, instead of the stochastic process which arises when modelling the interest rate on the Compound protocol. The step function is such that the initially high (constant) APY of 10% instantaneously drops to 1%, and remains constant thereafter.

In order to gauge the effect of the rate shock independently of other factors, we impose the constraint of absence of YT buyer agents, effectively removing the agent’s contribution to the experiment.

Experiment results:

Simulated money market rate based on the Compound interest rate model for DAI (v2) and 30-Day EMA oracle rate

By default, the Variable APY series is generated from the compound money market formula, and parameterized with the default values. It decreases over time due to the increase in the Pool Supply coming from the 88MPH Deposits. The Oracle Rate series is obtained as a result of exponential smoothing — it is the 30 Days EMA.

In this experiment, it is replaced with the step function outlined above, which produces an associated lag in the oracle rate.

Rate shock modeled with a Step Function, and corresponding Oracle Rate

Here we see that the accumulated interest surplus, as percentage of current deposits, falls sharply after the instantaneous rate drop as a result of an overly optimistic oracle rate. Since the interest rate is thereafter a positive constant (1%), the interest surplus slowly starts to recuperate as the deposits made with that rate mature and new ones start to dominate in the pool.

Accumulated Suplus as percentage of Current Deposit Amounts over the simulation duration

Analysis Results

The simulated Variable APY instantaneous shock, in the absence of YT buyer agents, causes a sharp fall in the accumulated interest surplus, thus demonstrating the dangers of pool illiquidity and the inefficiency of an oracle rate which is not constructed to be reactionary enough. This dynamic underlines the need for risk mitigating provisions for the protocol, which 88mph is addressing and actively improving upon. Specifically, these are a fourfold line of defense which includes⁷:

  • A reactive oracle rate, lower than the market rate for security benefits,
  • Yield surplus taken as early withdrawal and forfeited yield, amply discussed in this study,
  • Yield surplus rebalancing between 88mph liquidity pools — which can dynamically address liquidity shortage,
  • And finally an in-development security module similar to Aave’s safety module, with capped double liability, subject to deposit incentivization dynamics via MPH rewards.

Insights, Recommendations for 88mph

Through the creation of a radCAD “digital twin” for the core money market agent interaction scope of the 88mph protocol we performed an in depth scenario analysis which covers various behaviors of depositor and YT purchaser agents, whose experiments have provided valuable insights on the effects that the protocol’s user base may have on liquidity and network revenue.

In Experiment 1, depositor agent behavior was parameterized in order to enact different scenarios with regards to the average size deposit principal amounts. In Experiment 2, this was repeated for deposit duration. In accordance with intuition, when depositor agents make larger or longer deposits on average, more liquidity is available to the protocol and its stakeholders in terms of network revenue capture; the effect of deposit size on liquidity is more pronounced than in the case of deposit duration. These results are in line with expectations, and in order to achieve such interaction, it is necessary for the 88mph protocol to grow its user base and provide great incentives for them to stay, which will allow the protocol to stay liquid.

In Experiments 3 and 4, depositor agent behavior was parameterized in order to enact different scenarios with regards to premature withdrawal intensity. We find that when depositor agents are constrained to more intensive premature withdrawal behavior, this adversely affects liquidity; however, the subsequent increase in protocol fees out of withdrawals allows to mitigate the effect. 88mph’s decision to enact network fee accrual for penalizing premature withdrawals and abandoning the liquidity ecosystem is an effective risk mitigator. We believe 88mph could create additional disincentives to penalize such actors, whether through a basic fee increase or via novel mechanisms which complement MPH token rewards.

In Experiment 5 From our analysis on YT agent behavior we find that increasing the selectivity profile with regards to ROI results in greater yield capture at the expense of a lower volume of YT sold. While it is true that the logic for ROI expectation is simplistic as of this iteration, this experiment is useful in shedding light on the need to find a good tradeoff between the ROI the platform offers and the incentives to actually purchase YT en masse, contributing to liquidity.

In Experiment 6, where we replace Compound interest rate with a step function, we find that a sudden drop in money market rate has severe short term consequences on the protocol’s accumulated interest surplus. While external shocks of this sort are, looking at historical data, inevitable and will lead to short term illiquidity, we believe it is opportune for 88mph to complement the very low rates which will immediately follow the shock with whatever liquidity was accumulated over the protocol’s operating lifetime, as a monetary counterbalance. To this effect, the 88mph v3 protocol is constructed such that the surplus generated in a particular 88mph v3 pool is kept in the pool; this surplus continuously compounds based on the underlying money market rate. In the event of a liquidity shortage in any 88mph pool, liquidity surplus can be transferred from any liquid pool to one in need of liquidity. These dynamics are beyond the scope of the current model, however provisions to the effect are already in place.

Modelling flexibility and extensibility

We have touched upon the fact that the radCAD model’s scope is flexible enough to cover a class of variable yield dependent fixed income protocols, yet granular enough for the presented implementation to be unique to 88mph. This is a key advantage of the radCAD modelling approach, as potential extensions range from parameter calibration based on real data, to extending the model to protocol functionality so far out of scope, such as MPH token rewards and incentives.

On the conservative end, a relatively straightforward extension would be to leverage blockchain data APIs to query and process historical deposit principal amounts and respective durations into the DAI on Compound money market via 88mph to fit the gamma distributions’ parameters, to have higher fidelity depositor agent behavior. On the same note, one could calibrate YT agent ROI selectivity via examining which expected ROI users actually purchased, or adopt purchasing logic based on what was observed.

Higher profile extensions would include modelling token incentives such as MPH token rewards, and gauging feedback effects from the staking or liquidity mining programs on protocol liquidity, in essence extending the system specification from an ‘isolated’ environment of agents-protocol-money market pool to a more complex environment. It is easy to see that while multiple protocols of the same class can be represented with the same initial environment model, that extending this to incorporate the protocol’s unique incentives can create a truly high fidelity model and unique asset for the protocol team.


We have covered and motivated the need for protocols such as 88mph in the Web 3 space — fixed income, which investors in the traditional financial space have used for many years as a means to hedge against risk and diversify their portfolios, is a DeFi novelty, whose adoption is being spearheaded by protocols like 88mph. The innovation here is in the creation of unique fixed income products which are new DeFi primitives as opposed to a reimplementation of traditional instruments, built with protocol composability in mind.

We proceeded to use the constructed agent-based radCAD “digital twin” to provide prescriptive insights with regards to user behavior and potential protocol measures to keep the protocol liquid and keep the ecosystem in good health. Our experiments confirmed the intuition that maintaining and growing the user base and incentivizing the creation of larger, longer-term deposits helps with underlying money market liquidity, network revenue in the form of protocol fees, and yield capture. We also confirmed the intuition that heavy engagement in premature withdrawals could hurt liquidity in the long term and should be disincentivized. We find that when yield token purchase agents are parameterized to enact higher selectivity in terms of yield token ROI expectations that they are positively rewarded, at the cost of lower total purchases made, hence debt secured. The yield token agent behavior used in the experiment relies upon agents being effectively able to systematically estimate expected ROI, which is a non-trivial assumption, and can be more accurately modelled via data-driven insights.

Finally, we saw how an instantaneous shock to the underlying variable yield rate could negatively affect accumulated interest and should be followed up via an expansionary token policy, to maintain platform engagement high despite offering lower rates in the short term. It is to be noted that this experiment is performed in absence of YT buyer agents to exemplify the nature of this effect. In principle, the presence of YT buyer agents can act to mitigate the negative effects of the rate shock.

Rigorous simulation of scenarios in the hyper fast-growing space that is DeFi, where composability and great talent are making innovation skyrocket, will soon become a must.

Successful Web 3 protocols have today managed to retain users via solid foundations and incentive engineering the same way successful construction enterprises built great roads, bridges, and waterways back before there was such a thing as a degree in civil engineering. We hope modeling initiatives such as the one described in the present article will inspire both existing protocol teams and aspiring ones to strive towards the possible understanding of their systems, thereby contributing to a well-engineered Web 3 future.

About CADLabs

CADLabs is a Web 3 research and token engineering firm specializing in Computer-aided Design (CAD) of decentralized protocols. We enable informed decision-making through professional research, design, simulation, and validation services. Email:


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CADLabs is a Web 3 systems engineering firm specializing in Computer-aided Design (CAD) of decentralized protocols.