Ch.7 Investments

2 paths to positive risk premium:

1. If the stock has a +B, it will inherit some market risk premium

   1. Cost: exposure to systematic risk

2. If the stock has +A, it is a cost-free benefit (higher ER without risk inc)

Always assume alpha is 0.

The equilibrium risk premium is determined by systematic risk(beta)

Capital Asset Pricing Model(CAPM): a model that relates the required rate of return on a security to its systematic risk measured by beta.

• Based on two assumptions:

  • Investors are all mean-variance optimizers

  • Markets are well-functioning with few impediments to trading

Economy Equilibrium implications:

• (refer to all assets as stocks) proportion = market value[price * # of shares]/total market value

• Market portfolio is optimal risky and on the efficient frontier

  • CML is the best attainable in this scenario

• The risk premium on the market portfolio will be proportional to the variance of the portfolio and amount of risk aversion.

• Risk prem(indiv) = risk premium(port) * beta coefficient of the security

Mutual Fund Theorem: All investors desire the same portfolio of risky assets and can be satisfied by a single mutual fund composed of that portfolio.

Separation of Portfolio Selection:

1. Technical - an efficient mutual fund is created by prof. managers

2. Personal - an investor's risk aversion determines the allocation of the complete portfolio

When investor's purchase stocks, their demand drives up prices which reduces ER and risk prem.

The risk premium DOES NOT depend on the total volatility of the stock

Security Market Line(SML): a graph of the ER - Beta relationship of the CAPM

Limitations of CAPM:

• Reliance of the theoretical market portfolio

• Applies to expected returns as opposed to actual returns

Central Prediction of CAPM - the market portfolio is mean-variance efficient (tested by an index model)

In a two-factor economy the expected return on a security would be the sum of three terms:

• The risk-free of return

• The security's sensitivity to the market index * the risk premium of the index

• The security's sensitivity to interest rate risk * the risk premium of the T-bond

Three aspects of successful specification:

1. Higher adjusted R-square

2. Lower residual SD

3. Smaller value of alpha

Arbitrage: Relatively mispricing creates riskless profit

Arbitrage Pricing Theory(APT): Risk-return relationships from no-arbitrage considerations in large capital markets

A well-diversified portfolio:

• Nonsystematic risk is negligible

• Arbitrage portfolio

• Positive Return

• Sero net-investment

• Risk-free

Multifactor Generalization of APT and CAPM:

• Factor portfolio

  • Well-diversified portfolio constructed to have a beta of 1.0 on one factor and beta of zero on any other factor