Placeholder Fund Partner Chris Burniske is the most well-known researcher in the field of cryptographic asset valuation. On April 26, 2019, he published the blog "Value Capture and Quantification: Cryptocapital vs Cryptocommodities", "On Value Capture and Valuation: Encryption Capital and Encrypted Commodities, the PoS Pass is proposed to be capital in some cases and commodities in some cases, which should be separately analyzed and aggregated. Inspired by Chris's article, combined with Random Capital's research on the valuation method of the certificate, I proposed the three-pool analysis model of PoS.

The basis of the Sanchi model is that people have different purposes for holding the cryptographic certificate, and the crypto-pass is also involved in economic activities in different ways, thus presenting different asset properties. Think of each asset class as a reservoir, which is like a water in a reservoir. At the same time, the cryptocurrency market is a unified market with close ties, and the exchanges share a consistent market price. The holder of the pass can choose to buy or sell the pass according to his or her financial situation, price expectations and risk preferences, and can also change the asset type of the pass. Therefore, the pools of assets are connected, as if they are connected to each other, the water surface (price) is always the same, and the water (pass) can flow between the pools. If the demand for a certain type of asset certificate rises and the asset pool capacity becomes larger, the inflow of the certificate will be absorbed from other asset pools, and the price of the certificate will be pushed up if the capacity of other pools remains unchanged. Conversely, if the demand for a certain type of asset clearance declines and the asset pool capacity becomes smaller, it will overflow the certificate. If the other pools have the same capacity, the pass price is pulled down. Note: The water level and the currency price are opposite. The higher the water level, the lower the currency price, which is inconsistent with intuition.

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Long-term investors of PoS Pass will act as verifiers or principals to earn income through Staking. Staking's certificate is directly involved in production (participation in the consensus process) and is therefore capital. The certificates held by short-term investors for speculative purposes are usually deposited on the exchange, ready to be traded, and the asset class is a commodity. Price speculation for the certificate is very similar to speculating bulk commodities, and compared to crude oil, soybeans, copper and other commodities, the supply of the certificate is inelastic (not growing with demand), which is more conducive to price speculation and price manipulation. The asset class of the certificate held for the purpose of use is currency, and the certificate of the currency attribute is generally stored in the user's wallet, ready for payment and other purposes.

**The capital pool, commodity pool and currency pool are connected, that is, the pass is continuously transformed between the three asset types.** If short-term investors are optimistic about the long-term price trend, they will use all or part of the pass for Staking. Long-term investors may also choose to unlock the pass of the Staking status at any time and place it on the exchange. If the user's demand for the use of the pass increases, he or she will buy or withdraw from the exchange. When there is an unnecessary need for a pass, one option is to convert Staking into a long-term investment or transfer it to the exchange for sale.

Capital pools, commodity pools, and money pools have different internal dynamics that should be analyzed separately. The purpose of the analysis is to find out the influencing factors affecting the capacity of an asset pool, or under what circumstances the capacity of the pool increases, and under what circumstances the capacity of the pool decreases, that is, understand the impact of the internal dynamics of the Sanchi on the price of the certificate.

From the perspective of asset classes, PoS Pass is very similar to real estate. Self-occupied property is a consumer product for homeowners; rental properties are capital for homeowners; properties sold are commodities. The basic function of the property is to satisfy the people's living needs. On the premise, the property can be used for renting or selling, and has the asset value. Everyone knows that domestic housing prices are high. In fact, there are also places with low housing prices. In some small cities with poor economic prospects and population loss, housing prices are very low. When the consumer demand for real estate is shrinking, the rental price will not go up, and there will be no speculative funds to enter the real estate market. Similarly, in the three-pool model, the long-term increase in the price of the pass can only come from the currency pool. Only by continuously expanding the use of the pass and expanding the scale of use can we push the price of coins up for a long time. Some people think that Staking is a demand for the certificate and can create value. I don't agree. The Staking mechanism is designed to maintain cryptographic protocol security, but security is not an end in itself. Encryption protocols must be "useful", have transaction cost advantages, and can carry value exchanges. The world does not need a secure but useless encryption protocol.

The macro analysis of the currency pool is based on the Fisher exchange equation, which is also the basis for most current cryptocurrency valuation methods. The Fisher exchange equation is a classic formula of economics on commodity exchange. MV = PQ, where M is the amount of money, V is the velocity of money, P is the average price level of the commodity, and Q is the total amount of the commodity. The right side of the equation, P*Q, is the total transaction amount over a period of time. On the left side, M is the amount of money in the economy. V is the average number of transfers of the money over a period of time. M*V is also the total transaction amount for a period of time. For example, in an economy, there is a 10 billion yuan transaction within one year, and the economy has issued a total of 1 billion yuan of currency. On average, all currencies have changed hands 10 times in a year, that is, V equals 10. The Fisher exchange equation is an axiom and does not require proof. Because both sides of this equation are the total amount of commodity transactions over a period of time, only the right side of the commodity, the left side is the currency, can be said to be synonymous, so the Fisher equation is an identity.

When used for cryptocurrency, the Fisher's equation M is the cryptocurrency circulation market value; V is the currency circulation speed; P is the commodity price supplied by the blockchain economy; Q is the number of commodities traded by the economy. The Fisher-Frequency equation is a cryptocurrency valuation that focuses on cryptocurrency prices. The currency price is included in the M variable, M is the circulated market value of the cryptocurrency, equal to the unit price of the cryptocurrency multiplied by the tradable currency, the PC represents the cryptocurrency unit price, and the CS represents the cryptocurrency flux. Then the Fisher equation becomes PC*CS*V = P*Q. Then P*Q is equal to the total amount of commodity exchange over a period of time, that is, GDP, with GDP representing P*Q, and the equation becomes PC*CS*V = GDP, so PC = GDP/(CS * V). So far, the Fisher equation has been transformed into a form that the valuation model can be used directly. That is, the cryptocurrency price is equal to the product of GDP divided by the tradable currency circulation and the circulation speed.

After the Fisher's formula is deformed, it is very clear that the hints on the fundamentals of the encryption pass are clear. Assuming V is constant, GDP growth can increase money demand (liquidity) without changing currency prices, or push up currency prices if liquidity does not change. This is consistent with the investor's intuition, that is, the blockchain should be grounded and useful, and the pass is valuable. Moreover, the more economic activities in which the pass is the currency, the greater the amount, and the stronger the incentive for the price of the currency to rise.

The upper section uses the Fisher formula to analyze the currency pool and assumes that the currency velocity V is constant. This assumption is basically true for hard currency currency. For example, in the past half century, the dollar M1 fluctuated between 5-10, and the rate of change was very slow. But for "unreliable" currencies, circulation is much faster. Everyone knows that during the War of Liberation, there was a serious inflation under the rule of the National Government. It was said that when people got their wages, they would go to the store all the way to buy the necessities of life, and the price would become higher when they ran slower. The owner will get the currency and will find the supplier to purchase the goods as soon as possible. The circulation of money will become very high. The circulation of banknotes is subject to physical restrictions such as running speed, but for cryptocurrencies circulating on the Internet, it can be done instantaneously from obtaining the currency to spending money. With the decentralized exchange DEX and automatic market-making AMM mechanisms becoming more and more perfect, if users are not willing to hold certain certificates, V will become extremely high.

In general, the velocity V of the cryptocurrency can vary over a large range, and the decisive factor of V is the willingness of people to hold a pass. Due to personal choices, the analysis of V can only be done at the micro level. Suppose an economy (analogous to PoS) has only two assets, one is cash, and the other is a perpetual bond that can be realized at face value, fixed interest, and payable on a daily basis. If consumers do not hold cash on a daily basis, but only use bonds to exchange them when they need to use cash, and the merchants buy bonds as soon as they get cash, then the cash flow rate V approaches infinity, and the demand for cash tends to Near infinity. However, this is unlikely to happen because there is transaction cost for redeeming cash with bonds, such as handling fees, and it takes time and effort to redeem. So how much cash should people hold? This is the problem solved by the Baumol-Tobin model.

The basic idea of the Baumol-Tobin model is that people hold cash in a dilemma: the more cash they hold, the more interest they lose; but if they only keep a small amount of cash, they have to withstand the daily consumption needs. Transaction costs associated with frequent conversion of bonds into cash. Thus, the problem of maintaining cash stocks translates into the problem of minimizing the sum of the two costs of loss of interest income and transaction costs.

For the sake of understanding, let's take a simple example. A consumer consumes 1 yuan a day. He can use the bonds to exchange the cash needed for the whole year on the first day of the year, which is 365 yuan, which will be spent by the end of the year. The average cash he held this year was 365/2, equal to 182.5 yuan. If the bond's annual interest rate is 10%, then the consumer's interest income from holding cash losses is 18.25 yuan. Assume that each time you convert from a bond to cash, the exchange cost is $2. Then the transaction cost + interest loss = 20.25 yuan. If he exchanges cash for each year at the beginning of the year and the middle of the year, each time he converts 182.5 yuan, his interest loss is 182.5 divided by 2 times the interest rate of 10% = 9.125 yuan. But he exchanged two cash and needed to pay twice the transaction cost, which is 4 yuan. At this time, the total cost of cash held by consumers is 9.125+4=13.125, which saves more than 7 yuan more than one year. So is it a small number of conversations? No, if consumers choose to exchange 10 times, the interest loss is really less, but it costs 20 yuan for the transaction fee, which is obviously not optimal. Therefore, knowing the total amount of cash required for one year, assuming that the cost is uniform, and then knowing the deposit interest rate and the exchange transaction fee, the number of exchanges with the lowest cost and the amount of cash exchanged each time can be calculated.

The formula of the Bowmore-Tobin model is that the optimal exchange amount MD is equal to the root number (b*T0/2*i). Where T0 is the total amount of cash required, b is the exchange cost, and i is the interest rate. The problem was just applied to the formula: T0 = 365, b = 2, i = 10%, and MD = 60 is calculated. That is, consumers exchange 120 yuan in cash each time, and then use it to change, and holding an average of 60 yuan in cash is the optimal solution.

The micro-analysis of the currency pool concludes that the higher the per capita consumption, the higher the cost of the exchange, and the lower the Staking interest rate, the higher the per capita currency balance and the larger the currency pool. The two variables that need to be noted are the exchange rate b and the interest rate i of Staking. In order to encourage users to hold cash, the lower the Staking rate, the better. However, the opposite requirement is that in order to protect network security and increase the proportion of Staking, it is necessary to set a relatively high Staking rate. The best of both worlds is to provide a high rate of return when the Staking ratio is too low. After the Staking ratio is high enough to ensure system security, the yield is reduced, ie dynamically adjusted.

In the PoS system, the exchange cost b is the interest to unlock the Staking loss, determined by the interest rate and the unlock period. Bringing this condition to the Baumol-Tobin model, the conclusion is that the best average balance is half the amount of money consumed by the user during an unlock period. This conclusion is completely intuitive and does not require mathematical derivation. Still assuming that you spend 1 yuan a day, there is no fee for redeeming from bonds to cash, but a 30-day unlock period is required. The best way is obviously to exchange 30 yuan each time. When the 30 yuan arrives, the last redemption money will be spent, and then the next redemption request will be initiated immediately. So the optimal average cash balance is 30/2 = 15 yuan.

PoS Passes unlock the redemption of the pass from Staking, and can design a longer unlock period to increase the exchange cost. But in the real world, of course, there are not only two asset types. Users can choose to hold other cryptocurrencies (such as BTC or stable currency) for a long time and redeem the PoS Pass only when needed. Therefore, the unlocking cycle is not too long, but there should be a reasonable range. The current PoS system design is simply considering the unlocking cycle from the perspective of consensus security. It is incomplete and needs to be considered in the design of economic mechanism.

Let's analyze the product pool below. The first thing to be clear is that the game of the commodity pool directly determines the price of the currency, but the analysis of the speculative pool in this paper is not intended to predict short-term price movements. Value investors believe that short-term price movements are unpredictable or even important. The analysis of commodity pool dynamics aims to understand the impact of price changes on the PoS economic system.

Statistics on the price history data of encrypted assets can be found that the correlation between the short-term trend of the price of encrypted assets is very high, or that there is a clear phenomenon of inflation and decline. In 2018, the top 200 cryptocurrencies with a market value of more than 75% were more than 75%. Therefore, the short-term rise and fall of the pass price is not related to its own fundamentals, but depends on the overall direction of the cryptocurrency market. But if you put the time to a few years, the correlation of the cryptocurrency price can become very low. The most typical example is the top ten cryptocurrency in January 2014. By now (August 2019), there have been six zeros, but in the same period Bitcoin has risen more than 70 times.

The price movement of cryptocurrencies is a superposition of basic trends and reversal price volatility. As shown in the long-term price chart of Bitcoin, as shown in the index price coordinate system, the long-term price trend of BTC continues to rise, and the price of the currency fluctuates around the long-term trend. Reflexivity is a theory about the deviation of asset prices from equilibrium, which is self-enhancement (positive feedback) of price trends. The phenomenon is that the rate of decline in the bear market and the increase in the bull market are large, and bears and cattle will continue for a long time. It is beyond the scope of this article to discuss why cryptocurrency price volatility is reflexive.

In the face of price reflexivity, long-term investors can have two options. The first is very simple and effective. It is to ignore the fluctuations and only earn the basic trend of the money, that is, the long-term coins. Most investors who make a lot of money in the cryptocurrency market are using the strategy of using the currency. The second type is very difficult but very tempting, that is, predicting reflexivity, and the big band is high and low. This involves very complicated and difficult trading timing methods and is beyond the scope of this article. Regardless of the strategy, the basic condition for long-term investment success is that cryptocurrencies have an upward trend. This is the problem to be solved by fundamental analysis, and I believe that the long-term fundamentals are only related to the money pool, and have nothing to do with the commodity pool. The capital pool only provides guarantee for the development of the encryption economy and cannot provide motivation. This has created a very interesting situation. The commodity pool directly determines the price of the currency. If you make short-term investments, you can focus only on the commodity pool, and only the capital pool and the currency pool will affect the external factors of the supply of the certificate. For long-term investments, commodity pools become less important.

The most important conclusion of the commodity pool analysis is that the short-term surge in the price of the pass is an import, and the encryption economy cannot control and can only adapt. Therefore, the mechanism design should consider how to use speculative power to push up the network effect. On the other hand, it is necessary to control the negative impact of price plunging on the internal trading activities of the encryption economy.

The primary purpose of the PoS capital pool is to ensure network security. In theory, a malicious verifier can control the network by mastering more than 33% of Staking. But in fact, because modern PoS has a mechanism for random grouping of certifiers and random assignment of blocks, the cost of the attack is much higher than the theoretical value. For networks with very dispersed currencies, obtaining such a huge amount of certificates requires extremely high costs. According to Ethereum researcher Justin Drake, Ethereum 2.0 requires only 30% pledge, which is enough to maintain system security. The cost of the entire system for safe payment, that is, the certifier's income, security cost = total market value * additional rate + transaction fee. Starting from the principle of economics, under the premise of ensuring system security, the cost should be as low as possible, that is, the lower the issuance, the better.

It is generally believed that the value of Staking is composed of two parts: the right to income and the right to governance. In April 2019, Jake Brukhman and CoinFund published the A relative value model for governance tokens. The highlight of the study is the definition of the decisiveness of the right to governance, that is, the probability that a weighted voting right will have a decisive influence on the outcome of the vote. If someone has 50% of the voting rights, they can decide 100% of the voting results. If the pass is held by an average of four people, 25% per person, the probability of one person's voting rights determining the result of the vote is 37.5%. If the system has 25 people with equal currency, the probability that one of them will vote for the voting rights is about 5%. The conclusion is that the small amount of voting rights is very decisive, almost zero, and decisively increases with the voting rights exponentially. It can be seen that in the case of dispersing the currency, the marginal value of the governance power is basically zero and can be ignored.

Next, analyze the value of the income right, Staking's actual rate of return = Staking yield – node operating cost + pass price increment. It can be seen that under the same conditions, in order to provide attractive benefits, the lower the cost of node operation, the better, including the configuration of the node host, availability requirements and IT operation and maintenance costs. There is a view that the calculation of the actual rate of return is not a deduction of exchange rate losses, but should be deducted from the rate of increase. This involves the issue of the currency standard, and my assumption is based on the French currency (or BTC). If the PoS pass is the basis, it should be deducted from the increase rate, but this situation is rare. I have not encountered an investor who is based on the PoS pass.

Then Staking's actual rate of return, if it exceeds the risk-free rate of legal currency (Staking's default risk is low, can be considered risk-free), is a reasonable investment. At present, the large-capacity PoS certificate (such as Tezos/Cosmos) has an annual turnover rate of 5%-10%, and the annual volatility of the certificate price is much higher than this level. Therefore, the most variable variable of actual income is the exchange rate (the legal currency price of the certificate). The inference is that it is unreasonable for short-term investors to do Staking because the short-term exchange rate cannot be predicted. Only long-term investors who are optimistic about the appreciation of the certificate (at least able to maintain value) should do Staking.

In summary, the capital pool's certificate is first to ensure the safety of the blockchain. From the perspective of economic principles, the safety cost of the entire economy (number of nodes * single node cost) should be reduced as much as possible under the premise of ensuring safety. The core pool of demand for the pass is not the interest rate and governance rights, but the expectation of long-term preservation and appreciation.

In addition, as mentioned earlier, from the perspective of system cost, the Staking ratio should be as low as possible, so that the lower increase rate can be converted into an attractive Staking yield. The Staking ratio can also affect the volatility of currency fluctuations, and a high percentage of Staking may become an amplifier for currency fluctuations. When the price of the currency falls, due to the expected exchange rate loss, investors will unlock the Staking Pass and transfer to the commodity pool to sell, which will further lower the currency price and form positive feedback. Conversely, when the price of the currency rises, due to the expectation of exchange rate gains, there will be investors buying the pass, raising Staking and further pushing up the price of the currency, or positive feedback. In order to stabilize the PoS economic system and suppress positive feedback, especially to prevent the collapse of the coin price, the PoS economic system collapses, and the curve of the increase rate with the Staking ratio should be designed. Before the Staking ratio is reduced to a level that affects system safety, the increase in the rate of increase and the decrease in the Staking ratio form a “double click”, which greatly increases the Staking yield and attracts investors to buy and increase the Stake. Conversely, when the Staking ratio is much higher than the reasonable level of maintenance safety, the increase rate should be reduced and the system safety expenditure should be reduced. Refer to Polkadot's DOT issuance curve design.

Trend investors believe that market games determine asset prices, and value investments believe that the value of assets determines the long-term direction of market games. So why study the so-called value that affects prices for a long time and indirectly, instead of studying the market game that directly determines prices? The reason is that a large number of studies have shown that trying to predict prices based on market games is futile and cannot obtain long-term market-average returns. The Sanchi model reflects the basic idea of value investing. The commodity pool transaction directly determines the pass price, and the capital pool guarantee agreement is safe, but the long-term basis for pricing is the ability of the currency pool to absorb the pass.

Starting from the Sanchi model, a relative valuation method for PoS pass can be obtained. Market Rate = Circulation Market Value / User Wallet Address Market Value. That is, the ratio of the market value of circulation and the market value of the currency pool. The market value of the currency pool can be obtained by subtracting the market value of Staking (capital pool) from the market value of the circulation and subtracting the market value of the exchange wallet address (speculative pool). The current market rate is very similar to the P/E ratio, reflecting the valuation level of the PoS Pass. Compared with the absolute valuation, the advantage of the relative valuation method is that it does not need to make predictions, and based on the existing data, it can provide information with investment reference value. But relative valuations can be established and depend on the effectiveness of the market. In an efficient market, assets of the same type and quality should be comparable in valuation. If there is a difference in valuation levels, there is an opportunity for arbitrage. The crypto-asset market has only a 10-year history, and it can be said that a baby is a very inefficient market. In such a market environment, the valuation level of horizontally compared encrypted assets is of little significance. A more meaningful approach is to compare the valuation of an asset at different points in time, but it also requires a long history of crypto assets, so basically all research on bitcoin. Compared with Bitcoin, the current history of PoS chain is too short, and the relative valuation index is invalid. But I believe that after 5-10 years, the market rate will become an important investment indicator for PoS.

The Sanchi model can also develop an absolute valuation model, but like other existing absolute valuation models, it needs to be based on some obviously unreliable assumptions. In fact, the process of thinking about valuation is much more important than the final result. The future is uncertain, and the input to any valuation model comes from predictions, so it is impossible to be completely accurate, so the results of the valuation are not likely to be accurate. The basics of analyzing the encryption certificate should be as comprehensive and detailed as possible. As for the specificity of the valuation, it is enough to look at it, and it is not necessary to be blinded by itself. Charlie Munger said: "Some of the worst business decisions I have seen are based on detailed analysis. Advanced mathematics is the illusion of precision. They do this in business schools because they have to do something. Buffett often Talking about the discounted cash flow method to estimate the stock value, but I have never seen Buffett take the calculator to calculate the stock value.” I hope readers understand the true meaning of the valuation, and the need to know the vagueness is far better than the precise mistake. And the vagueness is right enough to support outstanding investment.

**The conclusion of this article is:** All models are wrong, but some are useful. Why are all models wrong? Because the model is always oversimplified compared to the real world. For example, the Baumol-Tobin model cannot quantify human irrationality. In the real world, it is possible to obtain higher low-risk yields with a little manipulation, and many people still put money in bank current accounts. The real capital market is a complex, non-linear system, and no model can completely depict even one aspect of the capital market. But some models are useful to help us think more effectively.

**This article first appeared in the carbon chain value** , according to the speech of the second anniversary of the establishment of the carbon chain value, the original title is "the development direction of the public chain and investment opportunities – thinking about the value of PoS public chain"

*Author: Liu Yi, Cdot Network founder, Random Capital Partners, Web3, Block Chaining encryption technology and money market senior researcher, Bitcoin early investors.*