Optimal Portfolio Choice and CAPM

Optimal Portfolio Choice and the Capital Asset Pricing Model

• Investors can choose efficient portfolios by understanding mean-variance portfolio optimization.
• This technique is used routinely by professional investors and financial institutions.
• The Capital Asset Pricing Model (CAPM) is the most important model for the relationship between risk and return.
• In CAPM, the efficient portfolio is the market portfolio of all stocks and securities.
• Expected returns of securities depend on their beta with the market portfolio.
• Volatility of a portfolio is measured by standard deviation.
• Calculating portfolio return involves weighting average returns of investments in the portfolio with their respective weights.
• Diversification reduces risk in a portfolio.
• Covariance is the expected product of deviations from the means of two returns.
• Correlation measures the relationship between two returns, and values range from -1 to +1.
• Calculating a portfolio's variance involves weighted averages of the variances of individual stocks and covariances between pairs.
• Efficient portfolios maximize expected return for a given level of volatility.
• Portfolios with 20% or more in stock Intel are efficient options.
• By combining stocks into a portfolio, risk is reduced through diversification.
• Stocks that tend to move together have a higher correlation.
• Risk is lessened when investments have less tendency to move together.
• Adding more stocks diversifies further, lessening risk.
• Diversification is most beneficial with a small number of stocks.
• Short sales (selling a security one does not own) are possible and can increase investment return but also increase overall portfolio volatility.
• The Sharpe ratio is a measure of a portfolio's risk-return tradeoff.
• The portfolio with the highest Sharpe ratio is called the tangent portfolio or efficient portfolio.
• Investors choosing the most efficient portfolio depend on their risk tolerance.
• The efficient portfolio depends on the market portfolio.
• Determining which securities to sell or buy is based on their expected returns in relation to their required return.

The Volatility of a Large Portfolio

• The return of a portfolio of n stocks is equal to the weighted average of the returns of individual stocks.
• When portfolios of many stocks are considered, the variance is determined primarily by the average covariance of component stocks.
• Volatility decreases as more stocks are included in portfolios.

Risk-Free Saving and Borrowing

• Investing in risk-free securities, such as Treasury bills, reduces overall portfolio volatility.
• Investing in stocks via margin may increase expected portfolio return (but also volatility).
• Expected return of a portfolio with risk-free securities is the weighted average of the risk-free investment and the risky portfolio.
• Volatility of a portfolio holding a combination of risk-free investments and a risky portfolio is lower than the variance of the risky portfolio as a percentage.

The Capital Asset Pricing Model (CAPM)

• The market portfolio is the efficient portfolio in the market.
• Investors with homogeneous expectations identify the market portfolio as the portfolio of highest Sharpe ratio regardless of their risk preferences.
• In the CAPM, the risk premium of a security is proportional to its beta.
• The risk premium for a security is its market risk multiplied by the market risk premium.
• The Capital Market Line (CML) describes the relationship between risk and return for efficient portfolios, combined with risk-free return.