Talking about the constant mixing strategy and Uniswap, how does the CPPI strategy integrate into DeFi


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Author: Kevin Sekniqi,

Compilation: free and easy

Note: The original author is Dr. Kevin Sekniqi from Cornell University. In this article, he uses a constant-mix strategy to explain the principle of Uniswap’s asset pool, and proposes this strategy in a volatile and mean-returning market China is profitable. In addition, he also mentioned the constant ratio portfolio insurance (CPPI) strategy, which performs better than the constant mixed strategy (ie Uniswap) in the differentiated (depreciation or appreciation) market, and the combination of the two strategies may Will become a trend of DeFi in the future.

Recently, an interesting tweet appeared in the field of encrypted Twitter (which seems to be missing now), which discusses the constant-mix strategy in the context of Uniswap and impermanence loss, which is a well-known and simplified dynamic Portfolio management technology.

To my surprise, people don’t seem to realize the constant mixing strategy. In fact, people have known and used the constant mixing strategy since 1985, maybe even much earlier. Yes, you are not mistaken! Since then, Perold and others have written great journals on this topic. In fact, part of this article is derived from those papers.

Here, I want to spend some time discussing portfolio management strategies through Uniswap.

The interesting thing about Uniswap is that it is not an exchange, and people don’t seem to realize it! Well, at least, the exchange side is a second-order effect. In fact, it is a smart contract that implements a specific type of dynamic portfolio management strategy, the so-called constant-mix. This strategy can be simply interpreted as “buy when it falls and sell when it rises.” This, in turn, has a concave expenditure structure. We will discuss all of these soon.

However, if someone insists that Uniswap is an exchange, then he is technically right as soon as possible, but in fact Uniswap is only an exchange presented through a second-order effect.

This is like saying that mayonnaise can be used as food. Yes, food is indeed the second function of mayonnaise, but its main purpose is as a condiment.

The goal I want to achieve in this article is to explain everything in the simplest language, so that even laymen can understand it. Many people in this industry tend to rename the basic things that have been known for decades, including impermanence loss (IL), automated market maker (AMM), etc., and we will make all of this simple.


First of all, in the rest of this article, I will ask you to forget “Impermanence Loss”, “Automated Market Maker” or other Uniswap related terms. This is completely a renaming of an existing thing, and it can be confusing.

We will try to learn these things through appropriate terminology, so that you can easily and independently read the relevant literature of the financial industry without relying on bad crypto blog posts… such as this one.

Now, let’s get started. To understand why Uniswap does this, let us first state our goal: we want to understand Alice, a savvy investor, how she allocates assets between stocks and cash in a way that best suits her risk profile. Of course, the market maker’s behavior will inform her of her risk status to a certain extent.

For simplicity, Alice can only hold assets in cash or by buying stocks. In other words, Alice needs to decide how to “balance” and “rebalance” her portfolio between these two assets. This looks like an asset pool of Uniswap. We enforce this simplified restriction because we can infer the total value of Alice’s assets through a one-dimensional variable (ie the value of the stock). Cash remains constant. If we want to use two assets, such as stocks and bonds, we need to visualize a three-dimensional surface. This is not too bad, but to make it easier for us to understand, you only need to consider an input variable x (stock value) and its relationship to y (total portfolio value in USD). All the analysis here can be simply extended to any number of variables.

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If Alice is very risk averse, she will choose all the cash. If she is more adventurous, then she will buy stocks. However, please note that I did not ask a few questions, including “Which stocks should Alice buy?” This is a question that has nothing to do with portfolio management. Instead, the most important thing for Alice is “when should she buy or sell stocks” and “how much to sell.”

In the rest of this article, we will discuss three strategies:

  • Buy and hold strategy: do nothing;
  • Constant mixed strategy: buy when falling, sell when rising;
  • Constant ratio investment portfolio insurance (CPPI) strategy: sell when the stock price drops and buy when it rises;

The interesting thing between the three is that they will get different benefits based on how the market behaves over time. The first strategy is linear, which means that it only depends on the current market conditions (that is, how the stock is performing), while the latter two will have two ways of bumps, which means that if there is a mean reversal (that is, a concave The maximum amount is in the middle), the second type will perform well, and if there is a deviation from the mean (that is, the maximum value is a sharp rise or fall of stocks), the third type will perform well. We will describe all of these in detail later.

Portfolio Strategy #1: Buy and hold, that is, do nothing


The strategy of doing nothing, or commonly referred to as “buy and hold”, is very easy to understand. At the beginning, Alice will choose a certain cash/stock allocation and then go with the flow. The better the stock, the better the outcome of the portfolio, as shown in the figure above. Obviously, net expenditure is a linear function, the slope of which depends on the original distribution between stocks and cash. The more stock, the higher the slope, as shown below.


When Alice holds all cash, her net portfolio performance has nothing to do with stock performance. The slope is zero at this time, which is straightforward.

Portfolio Strategy #2: Constantly mixed strategy, or buy when falling and sell when rising


At this time the strategy becomes more interesting. As the name implies, these strategies are designed to maintain constant stock exposure proportional to the stock portfolio. This is exactly how Uniswap works. After creating a new asset pool, the protocol aims to keep the ratio between the two assets y and x unchanged (ie x*y=k, and k is some constant).

Conceptually, the constant mixing strategy aims to increase the asset’s exposure as the value of the asset decreases. This is a classic example of stock-to-bills. Suppose Alice invests $60 in stocks and $40 in cash, thus creating a 60/40 constant mixed pool. Then suppose that the stock drops by 10%, so the value of the stock drops from $60 to $54, and the portfolio value drops from $100 to $94. At this time, the ratio will be 54 USD/94 USD, or 57.4%, which is lower than the expected 60%. At this time, the agreement stipulates that Alice must purchase more stocks (because she needs to purchase depreciated assets), thereby increasing her stock exposure to 60%. Alice will need to take out $2.40 from her cash position to buy the stock, thereby bringing the stock position to $56.40 and reducing the cash position to $37.60. Now, the new percentage is 60/40 again (that is, 56.4/94=60; 37.6/94=40). Let me reiterate: this works the same as the Uniswap asset pool, but one thing to note is that anyone can deposit funds into a specific token pool, not just Alice. Of course, Uniswap no longer involves stocks and cash, but tokens, such as AVAX and ETH.

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Now, let us figure out one thing: this is a very strange concept. Why the savvy investor Alice will buy more depreciated assets. The answer is naturally not because Alice did not know. Instead, this is because Alice believes that the market where she is implementing this strategy is unstable and regressive. Of course, if this is the case, then it makes sense for Alice to continue to buy more depreciated assets because it will soon return to a higher value. In this case, it doesn’t matter how much the asset drops, you just continue Buy in.

“The constant mix strategy (i.e. Uniswap) is profitable in a volatile but reverting market.”

Since Uniswap is only a constant mixed market, this means that as long as the target fund pool only contains the mean reversion market, it will always be profitable as a liquidity provider. On the other hand, if you provide liquidity to the market, and these markets are very different (ie permanent depreciation or permanent appreciation), then the profitability of joining Uniswap as an LP is better than simply buying and holding The strategy is much lower. Or, as we will soon see CPPI strategy. The chart below shows the comparison between the constant mixed strategy and the buy and hold strategy.


This effect is also shown more accurately in the figure below. As people have seen, if you just buy and hold when the market is differentiated, the profit margin of a constant mixed strategy is very low in the long run. why? Scenario 1: If the value of the stock market drops sharply (and stays at that level), then continued mixing will buy more and more worthless assets. Scenario 2: If the value of the stock market rises sharply (and stays at that level), the constant mix will sell more and more shares instead of other relatively depreciated assets (in this case, cash).


Therefore, all in all, if the assets return to the usual average level, it is worth it to become an LP of Uniswap. Otherwise, this will definitely cause losses, and it should not be a strategy adopted by Alice.

Portfolio Strategy 3: Constant Ratio Investment Portfolio Insurance (CPPI), or sell when stocks fall and buy when they rise


What if the market does not return to its average value? On the contrary, what happens if the market deviates significantly from the entry point, that is, the underlying depreciation or appreciation? Of course, as mentioned above, for Alice, implementing a constant mixing strategy (ie becoming a Uniswap LP) is not the best choice. Instead, Alice should sell when assets depreciate and then buy assets that appreciate. This makes sense: if Alice knows the stock will continue to depreciate, she should sell it as much as possible, and if she knows the stock will continue to appreciate, then she should buy as much as possible. This type of strategy is called a constant ratio portfolio insurance (CPPI) strategy, and it takes the form: USD in stocks = m (Assets-Floor), where m is a fixed multiplier, which is Alice Part of risk tolerance. As shown in the figure above, these strategies perform well when the market diverges instead of returning, which makes them convex.

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The following is the working principle of CPPI: Suppose Alice chooses m=2 and the floor is 75 USD (the latter floor is Alice’s lower tolerance for losses caused by depreciation of total equity). According to these figures, the value of Alice’s stock = 2*($100 – $75) = US$50. Therefore, Alice allocates stock and cash at a 50/50 ratio. The following figure shows the chart of this venture portfolio:


Given that Alice chose m=2 and the floor is $75, the following is the performance of her portfolio during the downturn. Suppose the stock drops by 10%, then her stock depreciates from $50 to $45, and the total investment portfolio depreciates from $100 to $95. Since the CPPI rules force the stock position to become 2∗($95−$75)=40 USD, Alice must sell an additional USD 5 worth of stock and further reduce his exposure. In other words, a 10% drop in the stock forces Alice to sell $5 worth of stock. Now, her risk assets have become “light”.

“Constant ratio portfolio insurance (CPPI) outperforms the constant mix strategy (ie Uniswap) in differentiated (depreciation or appreciation) markets.”

CPPI implements stock options in a roundabout way, instead of using standard option techniques. Alice’s loss is capped at $25 (because the floor is $75), and she can also enjoy a high upside (though not unlimited). All in all, in a bear market, the CPPI strategy will protect Alice, and in a bull market, the CPPI strategy will perform well. However, if there are frequent reversals, its performance will be under the constant mixing strategy (ie Uniswap). The figure below shows a comparison of the CPPI strategy and two different buying and holding strategies.


Final thoughts

Uniswap is an interesting experiment. It is the first successful deployment of portfolio management based on constant hybrid smart contracts between any two pairs of ERC-20 tokens on Ethereum. Its second-order effect is as an exchange, although it is safe to say that the exchange of assets through this method is far inferior to a standard exchange based on an order book.

In any case, it will be interesting to see some on-chain protocols that provide CPPI strategies. Then it will be very interesting to see how they can be used with the constant mixing strategy protocol. I expect traders will frequently adjust their positions to Uniswap and CPPISwap based on market conditions. However, it is obvious that we are too early to discuss these, many of which have yet to be implemented.

Related information: Perold, Andre and Sharpe, William. Dynamic Strategies for Asset Allocation. Accessed 2020.