Deep Down Rabbit Hole #2

Why is Asteria’s Impermanent Loss Hedger supported by two cutting-edge quantitative models — is the best solution for hedging Impermanent loss?

In the current AMM landscape, solutions that help mitigate impermanent loss mainly consist of token compensation, which often impairs long-term token holders’ interest, making it difficult to provide IL protection for all pools.

In today’s blog, we will try to analyze certain parameters/solutions, including increasing slippage, dynamic fees, or even oracle can help address the age-old problem of impermanent loss.

As we go through these analyses, it will become increasingly apparent why Asteria’s impermanent loss Hedger engineered on the European option portfolio and reinforced by two novel quantitative models is the best solution to the impermanent loss.

Analysis #1 — Are oracles solely effective in reducing Impermanent loss?

The key reason behind impermanent loss is the fact that AMM pools are obliged to sell low and buy at a higher price to continue to supply liquidity whenever a price movement occurs. Can oracles be tasked with selling high and buying low?

It is imperative to note that oracles are not a prediction tool and any oracles are usually feedback on the historical prices of an asset. A casual relationship between the upcoming/future market trends and the oracle itself does not exist.

An oracle’s pricing is mainly derived from CEXs and traders, and this pricing moves much faster than constant product market-making-based AMMs. An oracle cannot predict/forecast the future market, and hence it cannot sell high and buy low.

❌ Conclusion: To that end, an oracle cannot solely reduce impermanent loss.

However, an oracle integration coupled with intelligent risk management and a specialized options pricing model can certainly be a very potent solution to IL, as already seen from years of Backtesting of Asteria’s Impermanent loss hedger.

Analysis #2 — Can dynamically adjusting token weight reduce impermanent loss?

In theory, dampening impermanent loss by dynamically adjusting token weight was first put forward by Bancor. However, at a later stage, Bancor dropped this solution only to provide impermanent loss compensation by inflating their token supply.

Why did Bancor drop this solution? The reasoning is relatively simple — in practice, dynamically adjusting the token weight can indeed reduce impermanent loss. The tradeoff — doing so will also increase the slippage for traders that can severely impede market action.

Other AMMs that have native dynamic weights attempted to increase the max. Slippage from 1.5% to 4.5%. This leads to a dramatic increase in trading costs, which can severely dampen trading activity. On record, backtesting data for these AMM will suggest an increase in LP returns, but the real issue is that the majority of traders will simply not pick a trade unless it is arbitrability profitable.

On the other hand, if the AMM promotes more arbitrage, then the market activity will still be negatively affected since LP return will reduce significantly.

❌ Conclusion: dynamically adjusting token weight to reduce impermanent loss is a strategy that works in theory. It is simply not an efficient or long-term solution for IL, as it increases trading slippage and reduces LP return.

Analysis #3 — Can dynamic trading fees reduce impermanent loss?

According to the formula for impermanent loss mentioned above or using the derivation for the IL formula in our previous blog post, we can easily understand that impermanent loss is only related to starting price P and the price movement P’ = Pk, but is not associated with trading fees.

This means dynamically adjusting trading fees will do little to no good in reducing impermanent loss.

If we increase the trading fees to reduce IL? In this case, it is observed that the rate of return increases when trading fees is decreased, which means increasing trading fees cannot recompense for impermanent loss.

❌ Conclusion: Dynamically adjusting trading fees does little to no good for reducing impermanent loss, as there is no direct correlation between the two factors.

Analysis #4 — Can we reduce impermanent loss using Asteria’s time selection strategy?

We all know by now that the majority of impermanent losses occur during periods of high volatility or intense price movement. At Asteria, we believe that exiting/departing from these high-volatility market timeframes according to a set of condition triggers can work effectively in reducing impermanent loss.

Asteria’s bespoke time strategy — exits position during periods of extreme volatility and re-enters the market after assessing certain factors, including price fluctuation, volatility, and waiting time.

The strategy triggers an exit when the price fluctuation exceeds a certain level. This exit is reinforced until price fluctuation decreases and volatility begins to dampen as well.

Conclusion: By implementing optimal parameters and algorithms, the time strategy effectively protects LPs from impermanent loss, as there is little to no exposure to LP position during periods of extreme price fluctuations or high volatility.

Analysis #5 — Can we reduce impermanent loss by using Carr-Madan Formula & European Option Portfolio

Asteria has developed and back-tested an IL Euporian option portfolio hedging product for the X*Y=K algorithm on DEXs.

According to the Carr-Madan formula,

For any return structure f(ξT) with respect to ξT that expires at time T, it can be realized by constructing a European Option portfolio with ξT as the target and expiration date T, under the condition of f(ξT) as second-order derivable, which is essentially a static investment strategy:

Among them, i0 is a constant the system determines when constructing the investment portfolio (current period). The portfolio here includes:

Which is the interest rate,

which is the quantity of the underlying asset,

which is the quantity of European options, where i < i0 as put option; i > i0 as call option.

By dampening the IL, we can see that the automated spot market maker is equivalent to “free,” providing the market with a set of call-options and put-option combinations with different strike prices (that is, the source of IL is the same as using Limit orders traded on centralized exchanges).

For hedging IL, we need to create an options portfolio to generate the following income:

exactly the opposite of IL.

Assuming ξ0=1

We get the curve of f, f’, and f’’:

Conclusion: By implementing the European options portfolio, and the Carr-Madam formula, Asteria is able to hedge the LP position by 98%.

And that will be it for this blog post, folks. Hope you enjoyed reading the different analyses. We’ll be back with another curious case of Impermanent loss and how Asteria fights it to provide LPs with sustainable and high yields across all market cycles.

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Asteria

Asteria, committed to be DeFi infrastructure, defines decentralized protocol of option pricing, trading and hedging of AMM mechanism