Asset Pricing Models CHAPTER 8

What are we going to learn in this chaper?

Why are we interested in these models?

Capital Market Theory Determination of the returns for risky assets Assumptions: All investors are efficient investors (points on the efficient frontier) (importance of utility function) Investors can borrow or lend any amount of money at the risk-free rate of return (RFR) (ease of lending, difficulty in borrowing) All investors have homogeneous expectations (identical probability distributions for future returns)

Capital Market Theory All investors have the same one-period time horizon All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio (investment alternatives as continuous curves) There are no taxes or transaction costs involved in buying or selling assets There is no inflation or any change in interest rates, or inflation is fully anticipated Capital markets are in equilibrium (all investments properly priced in line with their risk levels)

Risk Free Asset Development of Capital Market Theory What would be a risk free asset? Why would it be considered risk free?

Risk Free Asset What is the formula of covariance? If the return for the risk free assets are certain, what does this mean in terms of standard deviation? How does this affect covariance of the risk free asset with a risky asset? What is the formula of correlation? The effects on correlation?

Risk Free Asset What happens to the average rate of return when you combine a risk-free asset with a portfolio of risky assets such as those that exist on the Markowitz efficient frontier? What happens to the standard deviation of returns when you combine a risk-free asset with a portfolio of risky assets such as those that exist on the Markowitz efficient frontier?

Utilizing Risk Free Asset RFR-A RFR-B Tangent line to the efficient frontier Point M

Utilizing Risk Free Asset

Incorporating Leverage How could an investor attain a higher expected return than is available at Point M? What effect would adding leverage have on the return and risk for your portfolio if you borrow an amount equal to 50 percent of your original wealth at the risk-free rate? Assume that E(RFR) = 0.06 and E(RM) = 0.12 The return on your leveraged portfolio and its risk would be:

Incorporating Leverage

New efficient frontier: the straight line from the RFR tangent to Point M. Capital market line (CML) You either invest part of your portfolio in the risk-free asset and the rest in the risky asset Portfolio M, or you borrow at the risk free rate and invest these funds in the risky asset portfolio. In either case, all the variability comes from the risky asset M portfolio.

Market Portfolio What is special about portfolio M? What should be the weight of each asset in this portfolio? Market portfolio What would be some assets included in this portfolio? Completely diversified portfolio

Market Portfolio Completely diversified portfolio: all the risk unique to individual assets in the portfolio is diversified away. Unsystematic risk Systematic risk

Diversification What is diversification? What is the purpose of diversification? How many securities must be included to arrive at a completely diversified portfolio? Can reduce the overall standard deviation of the portfolio but you cannot eliminate variability by adding stocks to the portfolio?

Diversification

CAPM Capital asset pricing model (CAPM) What is CAPM used for? Security market line (SML)

SML The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Cov i,M ) Slope of SML Restatement using Beta

SML

Beta What does Beta measure? Standardized measure of risk What is the beta of the market portfolio? What does a beta higher/lower than 1 mean?

Beta

Beta & Expected Returns StockBetaRFRRME(Ri) A B C D E

Beta In equilibrium, all assets and all portfolios of assets should plot on the SML. What if the estimated rate of return lies above the SML? What if the estimated rate of return lies below the SML? In an efficient market in equilibrium, you would not expect any assets to plot off the SML because. If there are deviations, what would be the source?

Identifying Undervalued and Overvalued Assets How do we identify whether a stock is under or over valued? What tools to use for estimations of returns? Which action to take when a stock is under/over valued?

Identifying Undervalued and Overvalued Assets StockCur. PriceExp. PriceExp. Div.Est. Fut. Ret. A B C D E5054- StockBetaReq. Ret.Est. Ret.Diff.Evaluation A %10.00 % B %6.20 % C %21.20 % D %3.30 % E %8.00 %

Identifying Undervalued and Overvalued Assets

Calculating Systematic Risk How do we calculate the systematic risk? What is the characteristic line?

Calculating Systematic Risk

END OF CHAPTER