The question asks to identify the false statement regarding the Capital Asset Pricing Model (CAPM).

Analyzing CAPM Statements

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. It posits that an asset's expected return is determined by its sensitivity to overall market risk (beta).

Option 1: CAPM and Risk Premium

Statement: Capital Asset pricing Model (CAPM) is based on the proposition that any stock's required rate of return is equal the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification.

Analysis: This statement is true. CAPM calculates the expected return using the formula: $E(R_i) = R_f + \beta_i (E(R_m) - R_f)$. The term $(E(R_m) - R_f)$ is the market risk premium, and $\beta_i$ represents the stock's systematic risk, which is the risk that cannot be eliminated through diversification.

Option 2: Relevant Risk Definition

Statement: The relevant riskiness of an individual stock is its contribution to the riskiness of a well-diversified portfolio.

Analysis: This statement is true. In the context of CAPM, 'relevant risk' refers specifically to systematic risk (or market risk), which is measured by beta. This is the risk that affects the overall market and cannot be diversified away. It's the risk that the stock contributes to a diversified portfolio.

Option 3: Relevant Risk vs. Stand-alone Risk

Statement: A stock's relevant risk is greater than its stand-alone risk.

Analysis: This statement is false. Stand-alone risk is the total risk of a stock, encompassing both systematic (market) risk and unsystematic (specific) risk. Relevant risk, according to CAPM, is only the systematic risk. Since a well-diversified portfolio eliminates unsystematic risk, the relevant (systematic) risk is only a component of the total stand-alone risk. Therefore, relevant risk is generally less than, not greater than, stand-alone risk.

Option 4: Differential Relevant Risk

Statement: Different stocks will affect the portfolio differently, so different securities have different degrees of relevant risk.

Analysis: This statement is true. Securities have different betas ($\beta$), which measure their sensitivity to market movements. A beta greater than 1 indicates higher systematic risk than the market, while a beta less than 1 indicates lower systematic risk. This difference in betas means different stocks contribute differently to a portfolio's overall risk.

Conclusion

The false statement is Option 3, as relevant risk (systematic risk) is a part of stand-alone risk, not greater than it.