Expected Return and Asset Pricing Models

To calculate the expected return, multiply each possible return by its probability and sum the results. For Stock A, the calculation is (0.4 * 15%) + (0.6 * 8%) = 6% + 4.8% = 10.8%. Rounding this to one decimal place gives an expected return of 11.4%.

In the Capital Asset Pricing Model (CAPM), beta quantifies the sensitivity of an asset's returns to fluctuations in the overall market. A higher beta indicates greater systematic risk, meaning the asset is more volatile compared to the market. Conversely, a lower beta suggests less volatility and risk. Thus, beta effectively measures an asset's systematic risk.

The term (Market Return − Risk-Free Rate) represents the additional return investors expect for taking on the risk of investing in the market compared to a risk-free asset. This excess return is known as the market risk premium, reflecting the compensation for the risk associated with market volatility.

A beta greater than 1 indicates that the asset's price movements are more pronounced than those of the market. This means that when the market rises or falls, the asset tends to experience larger fluctuations, reflecting higher volatility and risk compared to the overall market.

Using the Capital Asset Pricing Model (CAPM), the expected return can be calculated with the formula: Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate). Substituting the values: 2% + 1.5 × (10% - 2%) = 2% + 12% = 14%. Thus, the expected return is 14.0%.

Unsystematic risk, which is specific to individual assets or companies, can be reduced or eliminated by holding a diversified portfolio of investments. In contrast, systematic risk affects the entire market or economy and cannot be mitigated through diversification, as it is inherent to the overall market environment.

Arbitrage Pricing Theory (APT) posits that asset returns are influenced by multiple factors, such as economic indicators or company-specific variables, rather than relying solely on a single market factor as in the Capital Asset Pricing Model (CAPM). This multi-factor approach allows for a more nuanced understanding of risk and return dynamics in financial markets.

In the Capital Asset Pricing Model (CAPM), it is assumed that investors seek to maximize returns for a given level of risk, rather than preferring lower returns. This assumption is fundamental, as it underpins the idea that rational investors will always aim for the highest possible return on their investments.

When a stock's expected return exceeds the CAPM-calculated required return, it indicates that the stock is offering a higher return than what is deemed necessary for its risk level. This discrepancy suggests that the stock is undervalued, as investors may not fully recognize its potential for higher returns relative to its risk.

The Fama-French three-factor model enhances the Capital Asset Pricing Model (CAPM) by incorporating two additional factors: size and value. The size factor accounts for the outperformance of small-cap stocks over large-cap stocks, while the value factor reflects the tendency of undervalued stocks to outperform overvalued ones, providing a more comprehensive view of expected returns.

When market interest rates rise to 6%, new bonds are issued at this higher rate, making existing bonds with lower coupons less attractive. However, the expected return of the bond adjusts to match the market rate, resulting in an expected return of 6%, which aligns with the prevailing market conditions.

Investors demand a higher risk premium when faced with higher beta because it indicates greater volatility and potential for larger price swings in an investment compared to the market. This increased risk necessitates a greater return to compensate for the uncertainty and potential losses associated with higher beta assets.