Financial Markets | Coursera (free for auditing)

Instructor: Robert Shiller

Author of this notes: Ziyu Chen (with help from Chatgpt, investopedia.com, and Khan Academy)

Reach me at [email protected] for any comment and advice

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Module 1&2

CAPM

The Capital Asset Pricing Model (CAPM) is a financial model used to determine the expected return on an investment based on its risk relative to the market.

$\text{Expected Return}=R_f+β×(R_m−R_f)$

• Risk-Free Rate $R_f$: The return on a risk-free asset, typically government bonds. It represents the minimum return an investor expects for taking on any risk.
• Beta β: A measure of an asset’s volatility compared to the market.
• Market Return $R_m$: The overall return expected from the market.

CAPM assumes that investors need to be compensated in two ways for taking on risk:

1. Time Value of Money: Represented by the risk-free rate, this is the return they could earn with no risk.
2. Risk Premium: Represented by the β factor, this is the extra return investors expect for the additional risk of the asset compared to the market.

Decomposition of Variance in Stock Return

We often separate the total risk of a stock's return into two components: systematic risk and idiosyncratic risk.

• Systematic Risk (Market-related): The portion of a stock's return that moves with the overall market. In CAPM, this is represented by $\beta^2 \times \sigma^2_m$, where:
  • $\beta$: The stock’s beta, measuring its sensitivity to market movements.
  • $\sigma^2_m$: The variance of the market return, capturing the volatility of the market.
• Idiosyncratic Risk (Stock-specific): The portion of the stock’s return due to unique, stock-specific factors. It is captured by the variance of the residual in the regression, denoted as $\sigma^2_\epsilon$

Covariance in CAPM: