CFA Level I - Reading 51

The assumptions of capital market theory are:

• Markowitz investors: All investors use the Markowitz mean-variance framework to select securities. This means they want to select portfolios that lie along the efficient frontier, based on their utility functions.
• Unlimited risk-free lending and borrowing: Investors can borrow or lend any amount of money at the risk-free rate.
• Homogeneous expectations: This means that when investors look at a stock, they all see the same risk/return distribution.
• One-period horizon: All investors have the same one-period time horizon.
• Divisible assets: All investments are infinitely divisible.
• Frictionless markets: There are no taxes or transaction costs.
• No inflation and constant interest: There is no inflation, and interest rates do not change.
• Equilibrium: The capital markets are in equilibrium. 

The market portfolio is the portfolio consisting of every risky asset; the weights on each asset are equal to the percentage of the market value of the asset to the market value of the entire market portfolio. For example, if the market value of a stock is $100 million and the market value of the market portfolio is $5 billion, that stock’s weight in the market portfolio is 2 percent ($100 million / $5 billion).

Since the market portfolio contains all risky assets, it must represent the ultimate in diversification. All the risk that can be diversified away must be gone.

Beta is a standardized measure of systematic risk. Beta measures the sensitivity of a security's returns to changes in the market return.

Relaxing the CAPM assumptions changes the model’s implications.

• Different borrowing and lending rates: The CAPM cannot be derived without equal borrowing and lending rates, unless investors can create a zero-beta portfolio. This puts a kink in the CML.
• Transaction costs: The existence of transactions costs means that the SML is a band (with fairly tight upper and lower bounds on prices) rather than a line.
• Heterogeneous expectations and planning periods: The impact of heterogeneous expectations and multiple planning periods on the CAPM is similar to the impact of transactions costs—the SML becomes a band rather than a line.
• Taxes: Individual investors facing different marginal tax rates will have different after-tax return expectations, so their SMLs and CMLs will be quite different. 

Combining the CML (risk-free rate and efficient frontier) with an investor’s indifference curve map separates out the decision to invest from what to invest in and is called the separation theorem. The investment selection process is thus simplified from stock picking to efficient portfolio construction through diversification.