Foundations of Finance: CAPM and Portfolio Risk

A measure of the spread of possible outcomes for an investment, quantifying the level of uncertainty associated with returns.

A simplified strategy where an investor divides their wealth equally among all available assets.

A measure of the degree to which two variables move together. In finance, it can indicate the level of correlation between the returns of two investments.

A general measure of systemic risk, which is the risk associated with the overall market or economy.

A measure of specific risk, which is the risk that is unique to a particular asset or investment and not shared by other assets.

The relationship between the return of an individual asset and the return of a market index, measured by Beta (𝛽).

A type of statistical analysis that examines the linear relationship between two variables. In finance, it can be used to assess the relationship between an individual asset's returns and the market's returns, thereby pinpointing systematic risk (Beta).

A model that captures the relationship between the returns of an individual asset and the returns of a broader market index.

The variance of a portfolio with many uncorrelated assets approaches zero as the number of assets increases infinitely. This is because the diversification effect eliminates unsystematic risk.

A risk that affects only one asset or a small group of assets. It's not correlated with the overall market. This risk can be reduced by adding many uncorrelated assets.

The risk that affects the entire market or a large number of assets simultaneously. This risk cannot be eliminated through diversification.

In a portfolio with many assets, the portfolio variance is the sum of squared weights times the variance of each asset.

The relationship between the risk of an asset and its expected return. It provides a framework for understanding how investors should be compensated for taking on risk.

The relationship between the risk of an individual asset and its expected return, as determined by the Capital Asset Pricing Model (CAPM). It depicts a line that represents the expected return for any asset based on its systematic risk.

The expected return on a security is determined by its beta, a measure of its systematic risk, and the risk-free rate. It is the expected return of a security adjusted for its systematic risk.

A statistical method developed by Fama and MacBeth used to test asset pricing models, including CAPM. It involves estimating the relationship between expected returns and risk factors across many time periods.

A measure of how much an asset's return changes in relation to changes in the market portfolio. It represents the systematic risk of an individual asset, reflecting its sensitivity to overall market movements.

The expected excess return an investor should demand for holding an asset with a one-hundred percent exposure to a particular risk factor.

A statistical method used to estimate the market price of a risk factor and the exposure of an asset to that factor.

A measure of how much an asset's return changes in response to changes in a specific risk factor.

The excess return that an investor expects to earn for holding a risky asset compared to a risk-free asset.

A model that explains asset returns based on their sensitivity to systematic risk.

The return that can be earned from a risk-free investment such as a government bond.

A measure of how much the portfolio's overall volatility changes when you slightly adjust the weight of a specific asset. It essentially quantifies the risk contribution of that individual asset to the portfolio's total risk.

The risk contribution of a specific asset depends on its covariance with every other asset in the portfolio.

The risk contribution of an asset is determined by its covariance with other assets in the portfolio. Covariance measures the relationship between assets, indicating how they move together.

The portfolio's risk contribution is calculated by taking the partial derivative of the portfolio's standard deviation with respect to the asset's weight.

Only systematic risk, the market-wide risk that cannot be diversified away, matters in a portfolio. Covariance captures this systematic risk.

The derivative of the portfolio variance is twice the standard deviation multiplied by the derivative of the standard deviation.

The portfolio variance is a measure of its overall risk and is calculated by a sum of weighted covariances.

The partial derivative of the portfolio variance with respect to an asset's weight is calculated as twice the weighted sum of covariances.

CAPM (Capital Asset Pricing Model) is a model that explains the relationship between a stock's expected return and its systematic risk, measured by beta.

Beta (β) represents a stock's sensitivity to market movements. A beta of 1 means the stock's price moves in line with the market, while a beta greater than 1 indicates higher volatility.

The Fama-MacBeth (FM) procedure is a statistical technique used to test the validity of the CAPM. It involves two steps: time-series regressions to estimate betas for each stock and cross-sectional regressions to examine the relationship between beta and expected returns.

The time-series regression step of the FM procedure uses historical data to estimate the beta of each individual stock. This is done by regressing the stock's excess returns against the market excess returns.

In the cross-sectional regression step of the FM procedure, the estimated betas are used as independent variables to explain the variation in stock returns across different stocks at a specific point in time.

The FM procedure tests whether higher beta stocks have significantly higher expected returns, as predicted by CAPM. If the relationship is statistically significant, it provides evidence supporting CAPM.

The FM procedure helps to identify the validity of the CAPM in explaining stock returns using historical data. It determines whether there is a significant relationship between systematic risk (beta) and expected returns across multiple stocks.

The FM procedure can provide valuable insights into the relationship between risk and return in financial markets. This can help investors to understand the factors that drive stock returns and make informed investment decisions.

A factor model that expands upon the CAPM by incorporating two additional factors: SMB (size) and HML (value). It seeks to better explain the variation in stock returns.

Represents the risk that is unique to a particular asset or investment and is not shared by other assets; it can be diversified away by building a portfolio.

A factor that captures the difference in returns between small-cap stocks and large-cap stocks, suggesting that small-cap stocks tend to outperform.

A factor that captures the difference in returns between high book-to-market (value) stocks and low book-to-market (growth) stocks, suggesting that value stocks tend to outperform.

A portfolio construction strategy aiming to reduce idiosyncratic risk by holding diverse assets; it mitigates the impact of specific risks associated with individual investments.