Ch. 11: Optimal Portfolio Choice and the CAPM

How does the correlation between two stocks affect the risk and return of portfolios that combine them?

- Correlation has NO EFFECT on the expected return of the portfolios combining them - The volatility, however, will differ depending on correlation: the lower the correlation, the lower the volatility of the portfolios

Capital Asset Pricing Model Assumptions

1. Investors can trade all securities at competitive market prices without incurring taxes or transaction costs, and can borrow and lend at the same risk-free interest rate. 2. Investors hold only efficient portfolios of traded securities - portfolios that yield the maximum expected return for a given level of volatility. 3. Investors have homogeneous expectations regarding the volatilities, correlations and expected returns of securities.

Given the CAPM equation E(ri)=r(f)+(beta i)(E(Rmkt)-r(f)), what is the market risk premium?

E(Rmkt)-r(f)

Efficient Portfolio

Offers investors the highest possible expected return for a given level of risk.

Security Market Line (SML)

The line that goes through the risk-free investment (beta=0) and the market (beta=1). (SML=price that a security should be) - The equation implied by the CAPM, and shows the linear relationship between E[R] and systematic risk, as measured by beta

What is the optimal risky portfolio, and how would you invest in it?

The market portfolio - Can invest in an index tracker fund or an ETF

Efficient Frontier

The set of efficient portfolios for different levels of risk.

How does the efficient frontier change when we use more stocks to construct portfolios?

As investors add stocks to a portfolio, the efficient frontier improves

Why is the market portfolio efficient according to the CAPM?

Since every investor is holding the tangent portfolio, the combined portfolio of risky securities of all investors must also equal the tangent portfolio. Furthermore, because every security is owned by someone, the sum of all investors' portfolios must equal the portfolio of all risky securities available in the market

Why is the market portfolio efficient according to CAPM?

Since every investor is holding the tangent portfolio, the combined portfolio of risky securities of all investors must also equal the tangent portfolio. Furthermore, because every security is owned by someone, the sum of all investors' portfolios must equal the portfolio of all risky securities available in the market. Therefore, the efficient tangent portfolio of risky securities (portfolio that all investors hold) must equal the market portfolio.

Correlation

The covariance of two assets' returns divided by the product of the standard deviations of the assets' returns. - The closer to 1, the more the returns tend to move together - 0 means assets move independently - Assets with -1 move in opposite directions

Covariance

The expected product of the deviation of each return from its mean, which can be measured from historical data

Tangent Portfolio

The portfolio with the highest Sharpe ratio; provides the biggest reward per unit of volatility of any portfolio available.

Sharpe Ratio

The ratio of a portfolio's excess return to the portfolio's standard deviation (volatility). The efficient portfolio is the one with the highest Sharpe ratio.

Capital Market Line (CML)

The set of portfolios with the highest possible expected return for a level of standard deviation (volatility). Under CAPM assumptions, it is the line through the risk-free security and the market portfolio.

How does the volatility of a portfolio compare with the weighted average volatility of the stocks within it?

The weighted average volatility of the stocks within a portfolio is greater than the volatility of the portfolio, unless the stocks are perfectly correlated

Meaning of the CAPM equation E[Ri]

Yields the return that investors will require to add the asset to their portfolio - i.e. the investment's cost of capital. Buying shares of a security improves the performance of a portfolio if its expected return exceeds the required return based on its beta with the portfolio.