# aToken Valuation

How does the market and economic theory value aTokens?

aTokens are derivatives of an underlying token that accrues interests from being lent out on Aave. They are redeemable at any time 1-to-1 on the protocol as long as there is liquidity available.

Based on the intrinsic theory of valuation, the price of aTokens can be approximated as the net present value of the discounted cash flows between now and the end of time. Since aTokens incur cashflows with an APY greater current risk-free rate, these should be worth more than the underlying tokens.

aTokens are also available on alternative protocols such as decentralized exchanges (Uniswap). Let’s focus on aDAI which is the aToken with the most liquidity outside of Aave.

# Market Value

The aDAI Uniswap pool is the biggest source of aToken liquidity outside of Aave. Let’s look at the historical price of aDAI in DAI to assess the peg of aDAI. This is done by extracting Uniswap’s data on TheGraph for the aDAI and DAI pools.

1 aDAI is redeemable for 1 DAI at any time on Aave, still, the market price of aDAI in DAI is volatile. Since inception, the median price is 1 aDAI = 1.05 DAI with the value of aDAI in DAI increasing over time. It is possible to redeem aDAI for more DAI in the markets than on Aave, representing an opportunity for users. In case of lack of liquidity on the protocol, users can exchange their aDAI, with profit on Uniswap.

The aToken valuation analysis carried out above demonstrates aDAI holds more value than its underlying asset. This is acknowledged by the markets that maintain aDAI pegged above DAI.

This superior valuation implies aDAI holders have access to alternative sources of liquidity wit h some profit margin on the price. Still at the moment significant external liquidity is only available for aDAI. It would be good for all aToken to have these alternative markets intrinsic value

# Intrinsic Value

The intrinsic value of an asset generating passive income comes from future cashflows, actualized based one market conditions to assess the present value .

• On Aave: $APY(aDAI) = 3.50\%$ 30-day average

• 10Y UK Bonds Yields: $Risk \hspace{1mm} free \hspace{1mm} rate = 0.30\%$

1. aDAI is held for 3 years then redeemed at discounted 1$2. aDAI is a perpetuity, an asset that generates an indefinite cashflow. It’s worth noting that this type of asset is really rare in the traditional industry, leaving this valuation methodology for companies. 3. With a risk-free rate at $Risk \hspace{1mm} free \hspace{1mm} rate = 1.50\%$ Economic theory values aDAI at 1.10$ on a 3-year basis and 11.67$in case of perpetual payment. This is due to the high yield of Aave compared to the current risk-free interest rates which is particularly low. With a higher risk-free rate of 1.5% the present value is still at 2.33$.

Aave is constantly pushing the boundaries of innovation offering new decentralized financial solutions. There is a certain level of risks that comes from the novel nature of Aave's products. This framework analyses them and presents the mitigation strategies in place. The high yields generated by the protocol can been seen as a risk premium.

# Results

The aToken Valuation analysis shows that both economic theory and the markets place aDAI's value above DAI's. This means that users have strong incentives to hold aToken rather than the underlying Token.

Overall, aDAI trades on median 5% above DAI, giving a 5% cushion if a user needs to liquidate his aTokens and there is no liquidity on Aave. Users may actually prefer to use the Uniswap Pool to take advantage of the better rate. There is no liquidity discount. If there were some liquidity issues, aToken holders would be desperate to liquidate their aToken even at a loss. This seems to have only happened in the first few months of the protocol, probably also driven by lack on liquidity on the Uniswap market.

The markets are aligned with economic theory since due to the expected future cashflows aTokens's intrinsic value is greater than that of the underlying Token.