# Correlation Risk

Correlation risk refers to the risk of a financial loss when correlation in the market changes. It plays a central role in risk management and the pricing of basket derivatives.

Risk Management

In risk management, correlation risk refers to the risk of a loss in a financial position occurring due to a difference between anticipated correlation and realized correlation. In particular, this occurs when the estimate of correlation was wrong or the correlation in the market changed.

The risk management of a ptf heavily depends on the used correlation. This is illustrated by the following example:

Assume a financial position is given by ptf weights w1, ..., wd and the distribution of the assets X is multivariate normal.

Then the P&L of the position is:  and is hence normally distributed with mean:  and variance:  which equals   if the positions are uncorrelated.

Otherwise, the VaR depends on the correlations of all assets and therefore a change in the correlation may significantly alter the risk of the position.

If the pricing of basket derivatives is considered, the value of the derivative itself depends on the unknown correlation.

In this case, correlation risk refers to the change in the value of the derivative with changing correlation (cega).

By analyzing prices of options on single names and on market indices, Driessen et al show that correlation risk is priced in the options markets.

Practitioners trade priced correlation risk by using short positions in index options and long positions in individual options (dispersion trading). A similar position can be taken with a correlation swap.

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