# Investing and Pool Shares ## Reserve Pool Shares Frankencoin Pool Shares (FPS) are shares in the equity reserve pool of the Frankencoin system. Being an FPS holdes is similar to being a shareholder of a bank. As the Frankencoin system makes profits through fees or liquidations, the price of the pool shares is automatically adjusted upwards. Likewise, when risks materialize and the reserve pool incurs a loss, the value declines. They can be minted at any time and redeemed again after a minimum holding period of three months. Over time, reserve pool shares that are not moved accumulate votes. Shareholders with at least 2% of the votes gain veto power. ## Usage If you want to acquire or sell some FPS, you can head over to the [Equity page](https://app.frankencoin.com/equity). Once there, you can find two sections. Let's focus on the left one first.

Buy new FPS

Here, you can buy new FPS or sell the FPS you own. In this example, the user wants to acquire 1 000 ZCHF worth of FPS. The current price of one FPS is 1 016 ZCHF, so 1 000 ZCHF would net the user 0.9812 FPS. Note that the wrapped FPS, or WFPS, can also be traded/wrapped here. Selling FPS can be done here as well. In this case, the FPS are burned and the corresponding amount of capital is sent to the redeemer. It is important to observe the minimum holding time of 3 months required to redeem FPS. Below this section, we can see that this address currently owns 7.60 FPS at a value of 7 721 ZCHF and a holding duration of 4 months. At the bottom of the page there's a link to trade WFPS on Polygon. Next, let's take a look at the right side.

FPS stats

The top of the sections displays the current price of one FPS and the current supply of all FPS. This is followed by a price chart and another section with various information: Market Cap: The total value of all the FPS in circulation, calculated by multiplying the number of FPS by the current FPS price. This shows the overall value of the governance tokens in the system. Total reserve: The total reserve in ZCHF that is held to support the system. This reserve acts as collateral to back the stability of Frankencoins and ensures the system’s solvency. Equity capital: This represents the value of the equity that FPS holders own in the system. It’s the capital available to cover potential losses within the Frankencoin system. Minter reserve: The total reserve set aside specifically for positions created by minters. This reserve acts as a safety net. Total income: The total amount of income generated by the system. Total losses: This shows the total losses incurred by the system. In this case, it’s at zero, indicating that no losses have been recorded in the system. ## Economics Anyone can create additional pool shares by depositing reserve capital at any time, or redeem them again after a minimum holding period of 90 days. Therefore, an important design consideration is the pricing mechanism for pool shares. As having a price implies having a valuation, this boils down to evaluating the Frankencoin system. ### Proportional Capital Valuation In an approach inspired by the research paper "[The Continuous Capital Corporation](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4189472)", the Frankencoin system evaluates itself at a constant multiple of its capital. This multiple is set to three. So if there is 1 million ZCHF in equity capital K, anyone can subscribe to new pool shares at a valuation of 3 million ZCHF, or also redeem old shares at that valuation. Mathematically, valuation V is:

Market cap as a function of capital

Whereas V(K) is the market cap of all Frankencoin Pool Shares (FPS) in circulation if there are K Frankencoins in equity capital. Given the number of pool shares s in circulation, the marginal price p per share is given as

Price per share

From the above constraints follow that an investment of additional capital ΔK leads to the following rules for determining the new number of shares given the old number of shares:

New number of shares after investment ΔK

Similarly, the same investment ΔK leads to a new price:

New price per share after investment ΔK

One can verify that the valuation equation still holds after that investment by multiplying the number of shares with their price in order to obtain the new valuation:

Verification

In other words: When someone invests into the Frankencoin system, two thirds of the increased market cap come from the price increase and one third comes from the increased number of shares. ### Equilibrium Consider again the example with 30 million ZCHF in outstanding mints and an interest of 5%, leading to a reserve inflow of 1.5 million per year. Under these circumstances, rational market participants will value the entire pool at 30 million ZCHF and therefore buy additional pool shares until the valuation hits 30 million ZCHF. This valuation is reached at a reserve pool size of 10 million ZCHF, leaving 20 million ZCHF in circulation that can be used for other purposes. This is at least the simple case without savings. The savings module that was later added splits the income stream into two: one to This is essentially fractional reserve banking with a reserve of one third. In contrast, the tier 1 equity capital of modern banks is usually much less than that, so the Frankencoin system has considerably higher reserves. However, unlike in the traditional banking system, this reserve requirement is not strictly enforced by a regulator, but more like a carrot that attracts the equilibrium towards the reserve target. If the effective interest at which new positions can be opened is at 5% and the reserve is below the target of one third of the outstanding balance, then it is possible to do interest arbitrage by minting additional ZCHF at an interest of 5% per year and using those to buy pool shares that yield maybe 6% per year. The opposite is the case if the reserve is higher than one third. In that case, minters should think about selling pool shares to repay their debt (if they are able to). This leads to the following rule of thumb: if the FPS market cap is higher than the market cap of ZCHF, then that means that the market participants are betting on the system to grow. If the FPS market cap is lower than the ZCHF market cap, then the market is signalling that it expects the Frankencoin system to shrink. ### Limits to Capital Efficiency What if someone creates a clone of the Frankencoin system with a reserve target of 25%? Would they be able to offer a better deal thanks to better capital efficiency? Here, one needs to be aware that there is a trade-off. It is certainly more attractive for those who mint some ZCHF to buy pool shares and sellthe remaining coins on the market. However, one needs to be aware that this implies that there is a buyer for the other 75% of the ZCHF to keep the system in equilibrium. These buyers are typically users that hold ZCHF for transactional purposes. And for them, stability is key. But stability suffers if one aims for an overly ambitious level of capital efficiency, making the clone less attractive for transactional purposes. It is hard to tell where exactly the right equilibrium is, but this is not a race to the bottom where the system with the lowest capital requirements automatically wins. We believe that aiming for a 33% reserve is a robust middle ground, that still allows for plenty of seigniorage gains. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://docs.frankencoin.com/pool-shares.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.