Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT)

Chapter 1: Introduction

This chapter discusses capital asset pricing model and arbitrage pricing theory.
It builds upon the concepts of risk and return from Chapters 5 and 6.
The chapter covers CAPM, APT, and the Fama-French model.

CAPM is a theoretical description of how the market prices individual securities based on their risk.
It considers the risk class of an asset during pricing.
CAPM predicts the relationship between an asset's risk and its expected return.
It serves two vital functions:
- Provides a benchmark rate of return for evaluating possible investments.
- Helps to make an educated guess as to the expected return on an asset that has not yet been traded in the marketplace.
CAPM is a centerpiece of modern financial economics.
William Sharpe proposed the model and was awarded the 1990 Nobel Prize in Economics.

The price of risk is determined by two factors:
- Market price of risk.
- Quantity of risk of asset I.

CAPM is an equilibrium model derived using principles of diversification and simplified assumptions about investor behavior and market conditions.
Market equilibrium refers to a condition where market prices balance the demand of buyers and the supply of sellers.
These prices are called equilibrium prices.
CAPM relates the expected required rate of return for any security to its risk, as measured by beta.
Total risk is the sum of systematic and unsystematic risk.
Unsystematic risk can be diversified away at no cost, so the market will not reward holders of unsystematic risk.

Unsystematic risk is related to the firm and can be diversified.
Systematic risk cannot be diversified away without cost.
The market compensates for systematic risk with a risk premium.
Beta measures systematic risk, which is related to the market.
Investors have different risk tolerances and choose securities with different betas.
An aggressive investor might choose a portfolio with a beta of 2, while a conservative investor might choose a portfolio with a beta of 0.5.
Beta greater than 1 indicates higher risk, while beta less than 1 indicates lower risk.
Beta measures the sensitivity of a stock's return to the returns on the market portfolio.
Beta = \frac{Covariance(Return{security}, Return{market})}{Variance(Market)}

Expected return of a security is calculated as:
- Expected Return{security} = Risk Free Return + Covariance(Return{security}, Return_{market}) / Variance(Market) * Market Risk Premium
- Where Market Risk Premium = Expected Return_{market} - Risk Free Return
Investors need to be compensated with a risk premium for bearing systematic risk.
The market reward to risk ratio is effectively the market risk premium.
If the expected rate of return of a security is known, the theoretical price can be derived by discounting the cash flows generated from the security at this expected rate of return.
The expected return beta relationship is viewed as a kind of asset pricing model.
Assumptions and predictions of the price is based on certain assumptions, some of which are unrealistic.

Assumptions of the CAPM include:
- All investors have a single period investment horizon.
- Investors can invest in the universal set of publicly traded financial assets.
- Investors can borrow or lend at the risk free rate unlimitedly.
- No taxes or transaction costs.
- Information is costless and available to all investors.
- Investors are price takers.
- All investors have homogenous expectations about the expected values, variance, and correlation of security returns.
- All investors attempt to construct efficient frontier portfolios and are rational mean variance optimizers.
Investors are all very similar except in their initial wealth and their degree of risk aversion.
Several assumptions are unrealistic and ignore real world complexities, but they lead to powerful insights into the nature of equilibrium insecurity.