# aToken Valuation

How does the market and economic theory value aTokens?

aTokens are deposit certificates of an underlying token that accrues interests from being borrowed on Aave. aTokens are redeemable at any time at a 1-to-1 rate with their underlying asset, on the Aave 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 than the current risk-free rate, the discount is offset by value accrual.

aTokens are also available on alternative protocols such as decentralised 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 = 1.01 DAI. 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 price above DAI.

This valuation implies aDAI holders have access to alternative sources of liquidity with some profit margin on the price. At the moment external liquidity is only available for aDAI while all aToken would benefit from alternative sources of liquidity.

# Intrinsic Value

The intrinsic value of an asset generating passive income comes from future cashflows, actualised to assess the present value.

• On Aave: $APY(aDAI) = 9.75\%$ 30-day average

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

For a fixed time return:

For 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.

$\hspace{1cm} Present Value (aDAI) = Payout / Risk \hspace{1mm} free \hspace{1mm} rate \\$

Aave is constantly pushing the boundaries of innovation offering new decentralised 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.

This contrasts with the unusual global rate environment where nominal rates have fallen to their lowest, with many countries dropping their rates below 0%, penalising savings.

# Results

The aToken valuation analysis shows that both economic theory and the markets place aDAI's value above DAI's. Users have strong incentives to hold aToken, that is prices higher and accrues interests, rather than the underlying Token.

Overall, aDAI trades on median 1% above DAI, giving a 1% cushion if a user needs to liquidate aTokens and there is no liquidity on Aave. There is no liquidity discount on the price of aDAI. 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, the intrinsic value of aTokens is greater than that of the underlying Token.