Editing Decentralized underwriting (section)

== Capital reserves ==
A ''capital reserve'' in a traditional insurance company<ref>A capital reserve is also known as an ''actuarial reserve'', AKA ''technical reserve'', AKA ''insurance reserve'', AKA ''reserve holdings'', AKA ''capital'', AKA ''treasury'', AKA ''surplus.''</ref> is a treasury of capital (equity, cash, bonds, etc.) set aside for future insurance liabilities, to cover risk beyond the present period’s premia collection. The size of an iDAO's capital reserve holdings is an important issue. If the reserve is too small, there is greater risk of iDAO insolvency and ruin. If the reserve is too high, the holding costs of the liquid cash increases the costs of insurance. The negotiation between these two negative inevitabilities is illuminated by analyzing an iDAO's [[wikipedia:Value_at_risk#VaR_risk_management|value at risk]] (VaR). 

For an iDAO insurance contract, when a claim is made, money to cover the claim can be taken from two sources:

# iDAO treasury of capital reserves
# REP-to-BOND market. (The encumbered REP tokens are burned and equivalent BONDs are minted and sold at market for immediate cash to cover the claim. If enough REP was encumbered at the point the contract was sold and validated by the DAO, then there is no problem. If it wasn’t enough, then the treasury is necessary, or more BONDs needs to be minted, which diminishes all members’ REP value.)

This second source of coverage for claims gives a new twist on classical ruin theory<ref>Dickson (2005), Chapters 7 & 8.</ref>: The reserve treasury is unnecessary if there are enough fees coming in to guarantee that the future value of REP is sufficient for the REP-to-BOND market to cover claims. The uncertainty of future fees, however, leads to the necessity of calculating the probability of ruin for any given reserve level.

In an iDAO, reserve holdings can be dynamically and algorithmically governed to optimize for security and premium cost. For example, when the value of REP tokens decreases, the iDAO can automatically stipulate a percentage of premia are earmarked to build the reserve. When the value of REP tokens increases, the reserve can be diminished and paid out to REP holders. This mechanism gives iDAOs another tool for increasing their efficiency, but it is a positive feedback loop (which is bad from an engineering perspective) which should be governed carefully.

An economic analysis of the need for capital reserves requires the analyst to specify what utility they are optimizing for. In insurance the question is how much risk is tolerated compared with how much insurance premiums cost. Under the assumption of infinite tolerance for risk, an argument exists concluding no capital reserves are always optimal for maximizing profit.<ref name=":1">Dickson (2005), Chapter 3.5, e.g., concludes the only optimal solutions are full coverage or none, under their particular assumptions.</ref> Under those values, even though the underwriters risk periodic iDAO bankruptcy and default, it can be more profitable in the long run to function without the holding costs of liquid reserves. However, a more nuanced approach is to calculate the estimated relationship between risk of insolvency and cost of insurance. This allows an iDAO to disclose the danger of ruin and calculate the difference in premia between 0 chance of ruin but higher premia (complete coverage of risk with reserve holdings) versus positive chance of ruin but lower premia.

Capital reserve holdings are a contentious issue in traditional economics. In the example of banking, regulatory agencies such as the BIS, the IMF, the Fed, and the World Bank have had differing regulatory standards at different times in history ([[wikipedia:Bretton_Woods_system|Bretton Woods Agreement]], [[wikipedia:Basel_III|Basel III]], e.g.) to manage different types of lending risk. After a global meltdown, regulation tightens. After a decade of security, regulations loosen. This leads to cycles of security crises. Economists don't have any complete model for authoritatively answering how large a capital reserve should be, since there are many competing variables which hold differing explanatory capacity in differing market circumstances.<ref name=":0" /> But traditional economies enjoy the advantage of regulators with asymmetric information and power. A central bank can manipulate their interest rates or reserve holdings standards with greater freedom than a DAO. Those regulators do not need to justify or publish their reasoning with complete models.

Web3 [[DAO#Primary DAOs|primary DAOs]], on the other hand, demand far more explicit and rigorous regulatory rules than traditional firms, because of their openness to pseudonymous members, their open source operating procedures, and their transparent financial transactions. Fortunately, these very weaknesses to attacks are also sources of potential strengths. Algorithmic execution of smart contracts in open decentralized platforms gives an unprecedented level of transparency which leads to more [[wikipedia:Perfect_competition|perfect markets]], which leads to greater predictability. Information asymmetry is minimized. Further, transaction costs are diminished with electronic self-execution of smart contracts. Further, decentralization encourages diversity, which promotes deep and fluid markets, leading to greater stability.

In an iDAO, the size of the capital reserves does not always need to cover 100% of estimated risk<ref>For a quantitative treatment of risk see, e.g., Robin J. Cunningham, Thomas N. Herzog, Richard L. London (2006) ''Models for Quantifying Risk'' (2nd ed.), ACTEX Publications.</ref> to prevent the threat of agency ruin, because there is also value in the equity stock of the company and in market inertia (i.e., a DAO's history of fair business even after temporary random setbacks is valuable). This is part of the reason for a common gulf between theoreticians and practicing financiers. Researchers often require an insurance firm to cover 100% of risk with capital reserves in their models, but in practice, laws in certain insurance realms only require 8-12% of the risk to be covered with the reserve. The value of the company in some cases, will itself cover the other ~90% risk. We know the company would refinance in case of temporary difficulties. The company would be willing to take a loan to cover debt for the opportunity to continue working and insuring people after a temporary setback. The proof that the company is willing and capable of covering claims, even when they are temporarily in debt, improves the company's reputation, giving them greater promise of future cash flows, which usually outweighs the debt, justifying the continuance of the insurance agency.

This gap has not been investigated exhaustively in the economic literature. Older companies may deserve to enjoy the gap in full coverage. But younger companies with less track record and less talent and inertia will not deserve the same gap—nascent companies should ideally be collateralized 100%. In the case of new Web3 insurance companies, with zero track record and little accountability, such regulation should explicitly include that valuation of the company to give continuous formulas for determining the required reserves, not with discrete jump standards imposed by the existing governmental bureaucracies which are not responsive to the market.


In our case, REP in an iDAO is a hybrid financial tool with 3 functions: 

# REP is equity since it gives claims on future iDAO profits through the REP salary.
# REP is also a utility token, because it is required to participate in new underwriting.
# REP tokens are essential to the process of covering claims, so they are constantly revaluated through the REP market.

The amount of reserves necessary for mitigating risk of ruin in an iDAO is dependent on incoming fees (as usual) and future value of existing REP tokens as equity (based primarily on existing contracts and secondarily on the history of the DAO) and as utility. So, as long as underwriters are doing their jobs, there is then less need for reserves. How much less?

It depends on the existing contracts relative to the quantity of active REP and the risk of those contracts being claimed or defaulting. That depends on many factors, such as the current health of the systems being insured as measured by actuarial statistics and historical inertia. The short answer is: we don’t know. We cannot precisely know how much an insurance company is worth because of the large amount of risk it covers. It has a high variation, depending on how many premia the iDAO will earn in the future. 

However, if we can get a good estimate on the future premia the iDAO will collect, then we can have more confidence in the precise relation between the size of reserve and the risk of iDAO ruin. We make this relation clear below, by formulating the explicit dependence on the increase or decrease of premia.

So we need to trust the estimate of the future direction of the rate of premia in the DAO. If the market does not have enough inertia and decentralization to diversify the risk, giving enough stability to value the company above 0 for a long enough time to cover its contracts, then an iDAO will require a reserve which guarantees full coverage. 

In general, if the fees are stable or increasing faster than interest/inflation <math>r</math>, and faster than the valuation at the initiation of a contract, then the tokens are worth more than the estimate and no reserve is necessary, assuming the DAO is policing the contracts properly (i.e., the proper amount of REP was encumbered in all contracts to cover the risk). Conversely, if fees are decreasing, then a reserve may be necessary to prevent a death spiral. So the amount of capital reserves necessary is greater when fees are decreasing faster than predicted at the moment the contracts were valuated. In sum, the size of the reserve required is smaller when the rate of fees are increasing and larger when the rate decreases. This is partially a positive feedback cycle, because if you drop the reserve in good times, then need to save in bad times, that is difficult. Building the reserve when REP is losing its value might lead to the increased perception that REP loses its value. However, that is not correct, because a REP token is a claim on the reserve they are building. So existing REP doesn’t really lose value by building a reserve. It just delays the reward, and loses the relatively minor opportunity cost of holding the liquid cash in reserve for future claims during down periods.


Perhaps counterintuitively, if some of the public loses confidence in the particular iDAO and stops paying premia, then the overall risk of overminting BONDs to cover under-encumbered contracts may actually decrease. For example, if premia are decreasing, and so REP is losing value, then some under-encumbered contracts default, which decreases the risk exposure of the DAO to dilution of REP with BONDs, which increases the value of REP. This negative feedback mechanism naturally helps the stability of an iDAO. Any new contracts underwritten with REP after the market adjustment can be achieved with the usual procedure for valuating REP at the initiation of the contract. 

Nevertheless, when premia are decreasing, that shrinks the basic valuation of REP as calculated by its function as an annuity. To remain completely covered against risk of iDAO ruin, the amount of value that the REP loses by fair valuation according to the tokenomics formulas, times the amount of REP encumbered in risky contracts, should be covered by depositing the remaining premia in reserve, to the degree that all existing contracts are covered. Then the iDAO will die if all future fees are assigned to the reserve and yet to reserve is not sufficient to cover all actual future claims. In that case the underwriters will lose all their REP value, but the customers would all be covered until the reserve is drained. That is fair, because that would mean every single contract was claimed, which means the underwriters did a terrible job and deserve to lose their REP. However, that is statistically unlikely in a large DAO. Whoever didn’t have a customer claim on the contracts the underwriter wrote, then the underwriter still has REP and so still has a claim on the remaining reserve, and can still underwrite new contracts or cash out. So the iDAO will continue to live as long as a single underwriter is still doing their job.

This all assumes the market is predictable, which relies partially on the present value formula being predictable. The reserve needs to build when the fees are decreasing and the reserve can shrink and reward underwriters through the REP salary when fees increase. (E.g., increased claims can sometimes decrease the fees, if the insured cancel their policies, or if they are dropped by underwriters who don’t want to continue to insure them, or if underwriters increase their fees.)

So the 0th order state is if the DAO values the contracts properly based on the evidence they have for REP value, then it the DAO remains sound. If they underestimate or overestimate the value, the DAO should build or shrink the reserve—1st order adjustments. 2nd order adjustments may eventually be merited if the DAO become large and stable enough for the measurements to be accurate enough to overcome stochastic errors.

What happens if everyone claims their policy at the same time when a reserve is gone? Then the DAO defaults on the claims, because no one will be getting fees, so the REP will be worthless. So we need to assume the REP market is valuable.


There are more issues that can be explored. For example, if there is an increased demand for insurance, as measured by an increase in contracts, which is reflected in an increase in premia and therefore an increase in the REP salary, then the DAO profits increase which means the salary increases. However, since more REP will be minted, a single REP token may not increase in value. [??check against tokenomics formulas.] Based on this, existing contracts may be over-encumbered (or under-encumbered if premia decrease or the market dips). How should we respond? Governance can be made to adjust the requirements based on those market forces.