Transcript Chapter 11
Chapter 11 • • • • • Measuring Market Risk and beta Portfolio Betas CAPM and Expected Return Security Market Line Capital Budgeting and Project Risk Measuring Market Risk • Market risk: Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” Market risk of an individual stock represents part of its total risk. • – – – Total risk = market risk + unique risk Total risk is measured by variance (or Std.Dev.) For well-diversified investors, only market risk matters, since unique risk has been eliminated through diversification. Total Risk, Unique Risk and Market Risk Measuring Market Risk • Beta: Sensitivity of a stock's return to fluctuations in returns on the market portfolio. – Market Portfolio – An ultimate well-diversified portfolio with all assets (stocks) in the economy. In practice a broad stock market index, is used to represent the market. – In terms of numbers, beta gives the size and sign of change in the return of an investment when there is one unit change in return on market portfolio. • Beta describes the size of an investment’s market risk relative to that of market portfolio, but it does not give us the exact size of the market risk. Measuring Market Risk More on Beta • Market portfolio’s beta is 1.0 – A portfolio that replicates a market index has beta of 1.0 • Beta for a riskless investment is zero – Treasury bills • Most stocks have betas in the range of 0.5 to 1.5. – If beta = 1.0, stock has as much market risk as the market portfolio. – If beta > 1.0, stock has larger market risk than the market. – If beta < 1.0, stock has less market risk than the market. – Most stocks have betas in the range of 0.5 to 1.5. • Beta can be negative, but very unlikely. Estimating Beta • Beta can be estimated using past return data cov(ri , rm ) betai i var(rm ) • Regression analysis – Find the fitted line for the plot of a stock’s returns against market portfolio’s returns. ri ˆi ˆi rm – The slope is the estimate of beta. Estimating Beta Portfolio Betas • Diversification decreases unique risk, but not market risk. • The beta of your portfolio will be an weighted average of the betas of the securities in the portfolio. n portfolio i wi 1 w1 2 w2 i i n wn Example: Portfolio beta Calculate beta for a portfolio with 50% HP and 50% Wal-Mart. Assume beta for HP and Wal-Mart are 1.29 and 0.61, respectively Capital Asset Pricing Model ri rf i Risk premium i i Market risk premium rm rf m Expected Re turn ri rf i (rm rf ) – Expected risk premium on a stock/portfolio is proportional to its beta. – Expected return on a security depends on the risk free rate and an risk premium. • Difference in expected return across securities arises from difference in risk premium which can be fully explained by beta. Example: CAPM and Expected Return Assume rf = 8% and rM=15%. 1) How much is the market risk premium? 2) Use CAPM to compute the expected rate of return on a stock with beta=1.25 Capital Asset Pricing Model • The CAPM world assumes that stock market is dominated by well-diversified investors, i.e. every investor holds an two-asset portfolio consisting of the market portfolio and/or the risk free asset. • Investors are concerned with only market risk in individual stocks. • An investor’s risk preference determines how he/she allocates funds between market portfolio and risk free asset. Example: Two Fund Separation Jessica and John both has $10,000 to invest in stock market and T-bills, but they have very different risk preference. Jessica believes that life is full of adventures and she is ready to take risks; while John thinks that stability builds a peaceful mind and he always tries to avoid risk. Therefore, Jessica puts 80% of her money in market portfolio but John only puts 20%. Now assume market portfolio return is 10% and T-bill rate is 4%. If CAPM is turn, please answer the following question: 1) What will be Jessica’s and John’s expected return on their investment? 2) Is Jessica’s investment strategy superior to John’s? (Hint: Sharpe ratio) 3) What happens when Jessica stead borrow $2,000 and invest the total of $12,000 in market portfolio? Security Market Line Security Market Line - Plot the expected return against beta according to CAPM. - We only need two benchmark securities (each with expected rate of return and beta) to specify the security market line. (e.g. T-bill and market portfolio) Over-pricing and Under-pricing Asset A is under-priced; asset B is over-priced. CAPM and Investment Projects • Company cost of capital and project cost of capital are different. • We can find a matched company for a project so that they have similar risk, and then use the beta for this company to estimate expected return for the project. – Pure-play method Beyond CAPM • Three factor model Expected Re turn : ri rf i (rm rf ) i rSML i rHML – Two other risk factors related to firm size and book to market ratio help explain the difference in expected return on stocks