DeFi Investment Return Calculation — An NAV-based Approach
By Dr. David Zou, Chief Economist at HashKey Group and Wanxiang Blockchain
This research report was published on 16 February 2021.
1. Introduction
Investment return calculation is an important topic in DeFi. Not only to compare the performance between different DeFi projects or strategies, but also to allocate assets or arbitrage among them, we need to understand their returns. Compared with the mainstream financial investment, DeFi investment return calculation is still unstandardized and inaccurate. Business opportunities in this field are worth exploring, such as developing data services for DeFi investors and providing arbitrage strategies among DeFi projects.
There are a variety of approaches to allocate assets flexibly for DeFi investors, including 1) savings and staking; 2) lending (incl. margin trading); 3) being liquidity providers in AMM; and 4) liquidity mining. In these activities, investor’s own assets and borrowed assets, as well as collateralized assets and tradable assets are mixed together. Also, the prices of crypto assets move differently, making it challenging to calculate DeFi investment return.
In this article, we propose a calculation method based on net asset value (NAV). Note that to calculate NAV rigorously, accounting standard needs to be taken into consideration, especially the accrued investment return and the payable financing cost. For the convenience of our analysis, we skip complex balance sheet analysis, and adopt the cash-basis approach instead of the accrual one for investment return and financing cost. It is reasonable as the payment cycle of DeFi investment return and financing cost is typically short and valued in the block generation time. Hence, the cash-basis model will not result in significant error and is less complicated for calculation. However, if the investment return and financing cost are accumulated for a while before payment, we can use the analysis approach proposed in DeFi’s Theory of Interest.
We will, first, illustrate the NAV calculation of basic DeFi modules and then the NAV for AMM liquidity providers participating in liquidity mining. Next, we discuss how to calculate the annual percentage yield (APY) based on NAV before the summary.
2. NAV Calculation of Basic DeFi Modules
1) Savings and Staking
Assume that an investor deposits x units of crypto asset X (or puts x units of X in staking). The interest or staking yield from each unit of X at:
and the reinvestment return is not considered here (reinvestment return calculation involves compounded interest computation, which is not complex.
Assuming that at time t, the price of crypto asset X is px(t) , NAV at this time point is:
Similar logic applies to the investment return of liquidity mining.
2) Lending (incl. Margin Trading)
As introduced in DeFi Modules — From the Perspective of Investor Demand (Issue No. 94/2020), a typical leveraged long operation is:
1. At the initial moment (“t=0”, hereinafter the same), the investor uses x amount of X as collateral to borrow y amount of Y and converts all Y to X.
2. At future time T, the investor repays y amount of Y (there might be interest payments) and unlocks x amount of collateralized X.
Assume that the prices of X and Y are px(.) and py(.) at different time points.
Then, after step 1, the investor holds:
units of X (including x units as collateral).
Assume that every unit of borrowed Y incurs a financing cost of
at time ti (i = 1,2, …).
Hence, NAV at time t equals to ( t ≤ T):
When t= T, the net return of leveraged long is included in NAV:
In (3), x . px(T) represents the principal (that is, x units of X as collateral) and
represents the net return of the leveraged long position.
The prerequisite for (2) and (3) to hold true is that the leveraged long position always fulfils the collateral adequacy requirement. Otherwise, if collateral liquidation is triggered, NAV needs to be adjusted based on actual collateral liquidation and repayment. In the extreme situation where the liquidated collateral value is not sufficient to repay the debt, NAV becomes 0 (it will not be negative under the limited liability system).
In the above analysis, if X is ETH and Y is Dai, it explains how to long ETH via MakerDAO.
DeFi Modules — From the Perspective of Investor Demand (No. 94/2020) also explains other leveraged long and short strategies. We do not repeat here as the analysis is similar. In summary, the following formula needs to be fulfilled:
NAV of the leveraged trading position = principal value as collateral + asset value associated with leveraged trading — liability value (4)
The net return from the leveraged trading strategy is the return from the assets minus the cost associated with the liabilities.
3) Liquidity Providers in AMM
The Quantification and Hedging of Impermanent Loss (No. 09/2021) discusses the gain and loss of AMM liquidity providers. If we do not consider liquidity mining, the total return of all liquidity providers is affected by three factors: 1) the trading fee, which will be directly reflected in the liquidity pool; 2) the change in the composition of the liquidity pool due to transactions, corresponding to impermanent loss; and 3) the price movement of crypto assets in the liquidity pool.
It is difficult to separate the three factors (especially, to separate impermanent loss). However, it is much easier to calculate NAV of one typical liquidity provider if we consider all factors together.
Assume that the market share of that liquidity provider in the liquidity pool is p, and the composition of the liquidity pool is (xt, yt) at time t. Then his NAV is:
3. NAV Calculation for AMM Liquidity Providers Participating in Liquidity Mining
Assume that at t=0, an investor holds x+a units of X and performs the following operation:
1. Pledge a units of X to borrow y units of Y.
2. Put the remaining x units of X and borrowed y units of Y into the AMM liquidity pool, taking a market share of .
3. Participate in liquidity mining, assuming the total amount of the liquidity token Z is z.
Assume that the composition of the liquidity pool is (xt, yt) at time t and every unit of borrowed Y incurs a financing cost of
Hence, the investor’s NAV at time t is:
In (6),
represents the investor’s return from the AMM liquidity pool and liquidity mining (incl. impermanent loss); a . px (T) represents the principal value of collateralized assets; and
represents the liabilities from borrowing crypto assets. (6) shows that we can calculate NAV as a collective investment for AMM liquidity providers participating in liquidity mining.
Investors can also become AMM liquidity providers and participate in liquidity mining through other means. The analysis method is similar, so we do not repeat it here.
4. APY Calculation Based on NAV
Assume that NAV (T1) and NAV (T2) are NAV for the investor investing in DeFi at two different time points T1 <T2 . Then, the investment return within this time period is:
Note that the prerequisite for (7) is that no additional investment or capital withdrawal by the investor within this time period. Hence, the NAV growth rate reflects the investment return. If there is additional investment or capital withdrawal, we need to adopt the weighted average capital approach (e.g. internal rate of return or modified Dietz method) or the weighted average time approach. There have been a lot of research in the mainstream financial industry on this topic. We can refer to the Global Investment Performance Standards (GIPS) by CFA Institute.
If we use n = (T2-T1)/365 to represent the number of years for the investment period, the annualized APY is:
5. Summary
As revealed by our analysis, although there are many new challenges in calculating DeFi investment return, we can still adopt the mainstream financial methods to a large extent as long as key concepts are clear. In addition, as DeFi scales, investment return calculation will converge to GIPS. The following key concepts are involved in DeFi investment return.
1. Capital investment, capital withdrawal and NAV. In short, capital investment and withdrawal correspond to the cash flow of DeFi investment, which is a concept of flow. NAV is the stock of DeFi investment at a specific time point, equal to the net value of investment assets minus associated liabilities.
2. Collateral and leverage. To record the leveraged trading activities in the balance sheet, collaterals, which is the principal, belong to the equity section, and leverage corresponds to liabilities. The risk exposure created by the two items is an asset. The net return from leveraged trading is part of the equity section too.
3. Collective investment tool. This simplifies the analysis on AMM liquidity provider + liquidity mining.
About the Author
Dr. David Zou is the Chief Economist at HashKey Group and Wanxiang Blockchain. He is a research fellow at the Research Bureau of the People’s Bank of China and an associate research fellow and visiting scholar at the Financial Institute of the People’s Bank of China. Dr. Zou has years of extensive experience in top Chinese financial institutes including Central Huijin Investment, China Investment Corporation (CIC), where he worked as the Vice President in Risk Management Department, Senior Vice President and Chief of Staff to the Deputy Chief Investment Officer, and Nanhu Financial Corporation (NFC), where he is the founding partner who has helped the city of Nanhu near to Shanghai to develop its financial district and financial regulatory framework. Before joining Wanxiang Blockchain, Dr.Zou worked for Bitmain, a leading blockchain and AI firm, as the Chief Economist.
About HashKey Group
HashKey Group is Asia’s leading end-to-end digital asset management and finance house. HashKey empowers institutional investors to capture high-potential investment opportunities in digital assets and blockchain technology.
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