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Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst q % {\displaystyle q\%} of cases.
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve.The purpose of this reserve is to make the risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator.
In general, the factors driving the prices of financial securities are equity prices, foreign exchange rates, commodity prices, interest rates, correlation and volatility. By generating future scenarios for each risk factor, we can infer changes in portfolio value and reprice the portfolio for different "states of the world".
The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital.It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
The expected rate of return for the second investment is (.45 * .2) + (.55 * -1) = -46%; The expected rate of return for the third investment is (.8 * .5) + (.2 * -1) = 20%; These calculations show that in our scenario the third investment is expected to be the most profitable of the three. The second one even has a negative ROR.
The IRB approach relies on a bank's own assessment of its counterparties and exposures to calculate capital requirements for credit risk. The Basel Committee on Banking Supervision explained the rationale for adopting this approach in a consultative paper issued in 2001. [3] Such an approach has two primary objectives -
Risk-neutral investors will be indifferent among the available interest rates in two countries because the exchange rate between those countries is expected to adjust such that the dollar return on dollar deposits is equal to the dollar return on euro deposits, thereby eliminating the potential for uncovered interest arbitrage profits.
A higher volatility stock, with the same expected return of 7% but with annual volatility of 20%, would indicate returns from approximately negative 33% to positive 47% most of the time (19 times out of 20, or 95%). These estimates assume a normal distribution; in reality stock price movements are found to be leptokurtotic (fat-tailed).