Risk metrics, by definition, is a set of financial models used by investors to gauge portfolio risk. Measurement of portfolio risk may be done in several steps. One is to model the market that creates changes in the value of the portfolio. The market model should be adequately specified in order for the portfolio to be revalued with the use of information taken from the market model. Then, the risk measurements are taken from change in portfolio value’s probability distribution. This change in portfolio value is more commonly known as profit and loss.

Systems for risk management are taken from models that indicate possible changes in factors that influence portfolio value. These risk factors are very important when pricing. Generally the factors that drive the prices of financial securities include commodity prices, correlation, equity prices, interest rates, foreign exchange rates and volatility. Driving future scenarios for every risk factor can help you make changes in the value of your portfolio and re-price it as well.

There are different kinds of portfolio risk management. An example is standard deviation. This measure is the first to be widely used when gauging portfolio risk. Although standard deviation is relatively simple to calculate, it may not be an ideal risk metric because it penalizes profits and losses.

Value at risk (VaR) is another measure that is preferred among many investment banks that are looking to gauge portfolio risk for banking regulators. This measure typically leans more on losses, which is why it is considered as a downside risk measure. Another commonly used portfolio risk measure is expected shortfall, which is also known in different terms such as conditional value at risk, expected tail loss or Xloss.

In addition, marginal value at risk may be considered as the amount of risk added to the portfolio. Simply put, it is the difference between the value at risk of the total portfolio and the portfolio sans the position.

Moreover, incremental risk gives information with regard to the sensitivity of the portfolio risk to adjustments in the portfolio’s position holding sizes. Sub-additivity is an important element of incremental risk. This is where the sum of the incremental risk of the portfolio’s positions is equal to the total portfolio risk. Sub-additivity has useful applications in terms of allocating risk to various units, in which the goals is to maintain the sum of the risks equal with the total risk.

Sub-additivity is necessary with regard to risk aggregation across accounts, business units, desks or subsidiary companies. It is essential when various business units independently calculate risks and want to know the total risks involved. This property may also matter for regulators who want to meet capital requirements by breaking down into affiliates.

Because there are three major risk measures in risk metrics, there are also three incremental risk measures namely the incremental value at risk; incremental expected shortfall and incremental standard deviation.

In addition, incremental risk statistics have applications for optimizing portfolio. A portfolio with lesser risk will most likely have an incremental risk that is equal to zero in all positions. On the other hand, if all positions have an incremental risk of zero, then the portfolio is sure to have a minimum risk if and only if the risk measure is sub-additive.