Financial Risk Manager Part 1

Explanation

This is the most likely to be linear among the given options. According to the Capital Asset Pricing Model (CAPM), there is a linear relationship between a stock's beta and its expected return. The formula is:

$E(R_i) = R_f + \beta_i(E(R_m) - R_f)$

Where:

• $E(R_i)$ is the expected return on the asset
• $R_f$ is the risk-free rate
• $\beta_i$ is the beta of the asset
• $E(R_m)$ is the expected return of the market

This equation describes a straight line, with beta as the independent variable and expected return as the dependent variable.

Why other options are incorrect:

• A: The relationship between default probability and credit rating is typically not linear. Credit ratings are ordinal categories, and the increase in default probability is often not uniform between rating steps.

• B: Due to the nature of option pricing models like the Black-Scholes, the delta (rate of change of the option price with respect to changes in the underlying asset price) changes as the underlying's price changes, resulting in a curved relationship.

• D: The relationship between expected return and standard deviation of returns is typically represented by a curved efficient frontier in modern portfolio theory, not a straight line._