# Market risk

Market risk is the risk taken on by banks, companies or investors that results from their performed operations and activities aimed at making profits. For example for banks and investors, the portfolio’s market risk is the result market making, dealing or taken positions with a bullish or bearish view in the underlying. Companies are exposed to market risk for example due to the fluctuations in oil prices or interest rates. Market risk in itself is not bad, however it should be managed thoroughly. If not, excessive risk taking can result in severe loss or even bankruptcy.

## Market risk outline

Market risk can be measured as the fluctuation in asset values and income streams from assets. In what follows, we discuss concepts on value-at-risk, the optimal hedge ratio, the greeks, dynamic hedging, duration and convexity and show how they can be used to measure and manage market risk.

• #### Value-at-risk

Value-at-risk, also know as VaR, is a metric introduced by JP Morgan indicating the total risk of a portfolio in a single number. In technical terms, value-at-risk indicates that with a certain probability, over a given period of time, the loss of a portfolio will not be greater than x.

• #### Parametric value-at-risk

The parametric value-at-risk model is the best starting point to the get insight in the methodology.  The parametric value-at-risk model is build on the normal distribution which requires an estimate of volatility (and the mean return) to indicate a portfolio’s market riskiness.

• #### Historical value-at-risk

The second approach in calculating the value-at-risk metric doesn’t rely on an underlying model. Instead it’s based on historical data from which the risk metric can be constructed.

• #### Monte Carlo value-at-risk

The third approach in estimating the value-at-risk metric applies the Monte Carlo technique. In Monte Carlo value-at-risk, the simulation process is based on 2 ingredients: an underlying stock price process, and an assumed distribution.

• #### Optimal hedge ratio

Companies and the portfolio of investors are exposed to various amounts of risk factors. They can opt to reduce their exposure to a certain risk factor.

• #### The greeks

Managing the risk of an option can be quite difficult especially due to its nonlinear payoff profile. Price or interest rate changes, time accrual, volatility jumps can both have a high and peculiar impact on the option value.

• #### Dynamic hedging

In contrast to forwards, option deltas change with respect to the underlying price. This is because the gamma which changes the delta of options. As a result of the gamma, the portfolio can become over or underhedged.

• #### Duration

Duration is an important concept for fixed income securities. It is a time-weighted average of the future cash flows. Duration is used as a measure of interest rate risk.

• #### Convexity

Changes in bond values can be approximated by using duration. However, when interest rate changes are quite large, the quality of this approximation deteriorates. In case of severe changes, the approximation in bond value changes can be improved by using convexity.