# P2.T5.22.11 Correlation Basics

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Describe financial correlation risk and the areas in which it appears in finance. Explain how correlation contributed to the global financial crisis of 2007-2009. Describe the structure, uses, and payoffs of a correlation swap. Estimate the impact of different correlations between assets in the trading book on the VaR capital charge. Explain the role of correlation risk in market risk and credit risk. Relate correlation risk to systemic and concentration risk.

Questions:

22.11.1. Bertha has a view about correlation, and she is evaluating several rainbow (aka, multi-asset) options. Her view is that correlation is going to decrease. Among the following trades, which best expresses her view?

b. Buy (aka, long position in) better-of-two where payoff = max(S1, S2)
c. Buy correlation (aka, pay the fixed rate) in a correlation swap
d. Short position in an exchange option where payoff = max(0, S2 - S1)

22.11.2. Consider a loan portfolio of two loans extended to Company X and Company Y. Their respective default probabilities are PD(X) = 10.0% and PD(Y) = 4.0%. The joint default probability is PD(X∩Y) = 3.930%. Which is nearest to the implied default correlation?

a. Zero
b. 0.30
c. 0.15
d. 0.60

22.11.3. According to Meissner, it is important to study correlations because they are prevalent in finance. This includes investments, trading, risk management, the global financial crisis, and regulation. In regard to correlation, each of the following statements is TRUE, except which is false?

a. Wrong-way risk is a type of (aka, special case of) correlation risk
b. Statistical independence between two variables (or vectors) implies their Pearson's correlation coefficient is zero
c. Correlation risk only refers to financial variables and excludes non-financial variables (e.g., economic events, geopolitical events) because they are impossible to parameterize
d. The typical creditor's worst-case scenario is reduced by either a lower concentration ratio and/or a lower default correlation coefficient