User:Sentriclecub/change in Enthalpy aka Heat of Reaction

Systemic Risk, in economics, is that risk which is common to an entire market system and effects any individual entity or component therein. It can be defined as "that risk that still remains even after a prudent investor diversies, i.e. the lingering risk that is attributable to marketwide risk sources". Systemic risk sometimes imprecisely refers to the underlying movements of the whole economic foundation which all of the system's comprising assets are rooted into. Systemic risk is also called nondiversifiable risk or systematic risk.

History
Ever since the beginning of the earliest stock markets, much research has gone into the study of measurements of risk and the formulation of various risk assessment models, in efforts to devise safer and more prudent investment strategies. Systemic risk can only be measured indirectly and requires extensive combing through years of market data. These limitations can be profound, but nonetheless critical understandings of systemic risk were bore out in the foundations and concepts in, and are vital to, the fields of banking, insurance, and investing.

Much of the theory of systemic risk was centralized in William Sharpe's work in the early 1960's in developing econometric models for determining the theoretically appropriate required rate of return for an asset. Expanding on his early research for several years, and while working as a college professor, Sharpe would later finalize his theories, which lead to his winning of the 1990 Nobel Prize in economics, shared jointly with Harry Markowitz and Merton Miller, for their combined contributions to the field of financial economics.

Explanation
When generic sources of risk are common to an entire system, then any strategy of selecting assets to invest in from that system will inexorably include a baseline level of risk, even before the addition and considerations of firm-specific risks, and unique risks. Systemic risk is the only risk investors are compensated for in econometric models which measure the risk verses return tradeoff, such as in the capital asset pricing model.

Systemic risk should not be confused with liquidity risk as the latter is specific to the security being bought or sold and the effects of liquidity risk are isolated to the securities dealers of that specific financial asset. Liquidity risk can be mitigated by hedging, or other commonly utilized financial instruments. Given the definition that systemic risk is the collection of risk exposures that affect all assets of the system and can't be diversified away, liquidity risk is therefore a specific risk belonging to an individual component of the system because liquidity risk is not necessarily common to all other financial assets in the system.

Examples
Consider an exclusive portfolio of optimally hedged investments in Latin American small-cap bonds, we can say that the non-systemic risk of this portfolio is eliminated. Yet, if there is a recession in the economy caused by drought and the market as a whole slides, the hedges would be of diminished practical benefit. This is due to the all-encompassing nature of systemic risk. By definition should a hazardous systemic event occur, then every asset will respond by an identical uniform decrease in value which is only proportional the severity of the drought.

In insurance it is unusual to obtain financial protection against systemic risks because of the inability of any insurer or reinsurer to afford to accept the risk at a price which is worthwhile to its purchaser. For example it is difficult to obtain insurance for life or property in the event of nuclear war. The essence of systemic risk is therefore the correlation of losses. Any insurance company which offered insurance against systemic risks would become insolvent when and if it ever came time to settle mass claims and make payouts. This was the case for AIG because they sold financial protection to lenders in case of home mortgagers being unable to make their loan payments timely. While initially this was a good idea (based on analysis of historical data spanning two decades) because it seemed to meet the criteria of an insurable risk, further analysis and deeper scrutiny revealed it was an avoidable mistake. .

Feasibility Issues
While econometric research of the business cycle led to considerable improvements in forecasting recessions, data on systemic risk is of questionable benefit. Commercial use and application of econometric prediction models of systemic risk have been delayed for both practical reasons, and safety/conflict of interest reasons. First of all, predictions can be accurate, but at the tradeoff for a very short time horizon, and by the time the information is of reasonable certainty to act on, it is too late to be of any use to achieve real benefit. Furthermore, the usefulness of research of systemic risks is confounded by the indeterminacy of market forces acting in a negative expectation of a hazardous systemic event. Such a reaction from a firm divesting a large share of its holdings in a particular asset can cause a market panic and a plummet in price for whichever asset was expected to fall, which in turn can easily lead to a liquidity crisis, or even market failure. In 2008, systemic risk has been one of the two most important topics discussed at meetings by members of the federal reserve. .

Major studies have shown that hedge funds may often increase systemic risk for the markets that they trade in, through their customary use of financial leverage to turn small amounts of capital into large and controlling stakes in assets, for a given system. Ordinary markets whereby static investors participate in the trading of component assets under the normal guidance of price, supply, and demand have a much more proven track record. In general, this simplified ideal scenario has an alignment of the participents with the market's best interests, providing the system long term price stability and ample liquidity. Dynamic investors are a relatively new class of market participants and much research is being done, and analysis is focused on whether or not excess returns are generated by a process that indirectly injects systemic risk into the system. Much of current research is exploring the potential fragility of the global system comprising banks.

Relation to Total Risk
The total risk of any asset comes from two sources. The risk of the system in which it belongs is the first source, plus the asset-specific risks (risks which don't affect the whole system). As an example, in the global system of aluminum producers in which the firm Alcoa belongs to, the risks that involve the global free market uninterrupted trade and availability of bauxite would be a systemic risk whereas its future negotiations with a labor union threatening to strike is an idiosyncratic risk. To solve for the firm's total specific risk $$ \sigma_{specific}^2 $$ one would have to consider the statistical sum of all those risks which both affect Alcoa and do not necessarily affect the entire system.

To solve for the systemic risk, specific risk is subtracted from total risk $$ \sigma_{systemic}^2 = \sigma_{total}^2 - \sigma_{specific}^2 $$ and in theory can be derived from data of just one component studied in isolation from the rest of the system. Total risk is easily measured, however specific risk and systemic risk require extensive review of all the available data, and is only accurate within the model's margin of error.

Proof of the Equivalence of Definitions
For a two asset portfolio:- where $$w_i$$ is the weighting of component asset $$ i $$, and the weight of all the components sum to 1.
 * Portfolio variance: $$ \sigma_p^2 = w_A^2 \sigma_A^2  + w_B^2 \sigma_B^2 + 2w_Aw_B  \sigma_{A} \sigma_{B} \rho_{AB}$$
 * Variance of a Portfolio of $$ n $$ assets in a system of $$ n $$ objects and $$ w_i $$ is the weighting of component asset $$ i $$.


 * $$ \sigma_p^2 = \sum_{i=1}^n w_i^2 \sigma_{i}^2 + \sum_{i=1}^n \sum_{j=1}^n w_i w_j \sigma_i \sigma_j \rho_{ij} $$,

where i≠j. Alternatively the expression can be written as:


 * $$ \sigma_p^2 = \sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{ij} $$

where the covariance term $$ \rho_{ij} = 1 $$ for i=j and the derivative of the Implicit function $ \sigma_p^2 $ with respect to $$ w_i $$ for all $$ n $$ assets is

$$D_{v}{\sigma_p^2}{(w_i)} = \sum_{i=1}^n \sum_{j=1}^n v_j \frac{\partial \sigma_p^2}{\partial w_j}$$ where i≠j and where v is the direction of the function (in one dimension) if the derivative exists.


 * This derivative exists and is zero when the sum of all the $$n(n-1)$$ covariance terms are minimized and $$ \sigma_{p,min}^2 = \sigma_{systemic}^2 $$.

In layman's terms, if one considers every possible pairing of assets of a given system, and makes an infinitely small adjustment (in the direction from asset i to asset j) of the relative weighting between any two assets in the portfolio then under every possible scenario the investor significantly increases risk if the risk of the portfolio already equals the risk of the system.

Econometric Modeling of Systemic Risk
As it turns out, a value-weighted portfolio is the one which minimizes the sum of the covariance terms (which is negative) and the portfolio is optimal. This optimal portfolio has the least amount of risk and has the market-value weighted average expected return. Although the proof suggests that the systemic risk can be observed experimentally, simply by constructing a market weighted portfolio, this is not true. Observing the portfolio's variance and interpreting it as the systemic risk is not valid because the weightings are a function of this process, and this test only confirms what it predicts. Only a model which is based on this mathematical idea has any predictive value, and is vastly more complicated.

Regulation
One of the main reasons for regulation in the marketplace is to reduce systemic risk. However, regulation arbitrage - the transfer of commerce from a regulated sector to a less regulated or unregulated sector - brings markets a full circle and restores systemic risk. For example, the banking sector was brought under regulations in order to reduce systemic risks. Since the banks themselves could not give credit where the risk (and therefore returns) were high, it was primarily the insurance sector which took over such deals. Thus the systemic risk migrated from one sector to another and proves that regulation cannot be the sole protection against systemic risks. Ways to regulate systemic risk, can be through legislation, or through various market factors.