c7: risk, return + capm

• investment returns Measure the financial results of an investment with the scale and timing effect. these can be historical or anticipated
• the Scale (size) problem with dollar returns states that A meaningful judgment can be made only with returns compared to the scale of investment. to fix, we calculate returns in percentage terms
• the Timing problem with dollar investment returns is that The sooner dollar returns occur, the better. to fix, we calculate returns in percents
• An asset’s stand-alone risk pertains to the probability of earning a return on one asset less than that expected. The greater the chance of a return being below expected, the greater the risk
• The coefficient of variation (CV) measures the risk per unit of return
• A risk-averse investor will invest in risky assets/portfolios only if they are provided with compensation for their risk via a risk premium
• risk premium is the excess return on the risky asset. it's the difference between expected return on risky assets and the return on risk-free assets.
• Investors often hold portfolios, not a single asset, so an asset going up or down is important, but what matters most is the return on the portfolio and its risk. so we analyze the risk/return of an asset in terms of how it'll affect the overall risk/return of the portfolio it's held in
• The expected return on a portfolio is the weighted average of the expected returns on the individual assets forming the basket. the weights are the fraction of the total portfolio invested in each asset
• the Correlation Coefficient, (ρ) Measures the tendency of 2 variables to move together. it Estimates the correlation from a sample of historical data often called R (capital)
• a set of portfolios maximizes the expected return at each level of portfolio risk. Equally, a set of portfolios minimizes risk for each expected return
• Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another. However, a minimum level of risk cannot be diversified away, and that is the systematic portion.
• The risk (variance) of an individual asset’s return can be broken down into Market risk & Diversifiable risk
• Market risk of an individual asset’s return consists of economy-wide random events that affect almost all assets
• Diversifiable risk of an individual asset’s return results from random events that affect a single security or small groups of securities
• diversification eliminates about half of a stock’s stand-alone (unsystematic) risk so the stock’s relevant risk is its contribution to a well-diversified portfolio’s risk, (ie. its systematic or market risk)
• The Capital Asset Pricing Model (CAPM) specifies the relationship between risk and required return on assets when they are held in well-diversified portfolios
• capm assumption #1: All investors focus on a single holding period and seek to maximize the expected utility of their terminal wealth by choosing among alternative portfolios based on the expected return and standard deviation
• capm assumption #2: All investors can borrow or lend an unlimited amount at a given risk-free rate (rfr) with no restrictions on short sales
• capm assumption #3: Investors have homogeneous expectations
• capm assumption #4: All assets are perfectly divisible and liquid.
• capm assumption #5: There are no transaction costs
• capm assumption #6: There are no taxes.
• capm assumption #7: All investors are price takers
• capm assumption #8: The quantities of all assets are given and fixed.
• the relevant risk for a stock is the amount of risk the stock contributes to a well-diversified portfolio. Beta (b) measures this relevant risk (ie. the responsiveness of an asset to movements in the market portfolio)
• A stock with a high standard deviation tends to have a high beta because it contributes a relatively large amount of risk to a well-diversified portfolio
• A stock with a high correlation with the market will also have a large beta
• The tendency of a stock to move up/down with the market is reflected in its beta coefficient. the regression line slope is equal to beta. this shows the stock's movement in response to the general market
• Average-risk stock (b = 1) Returns tend to move up and down, on average, with the market, as measured by some index
• Risky stock (b > 1) Returns are more volatile than the market
• Safe stock (b < 1) Returns are less volatile than the market
• Betas are usually positive, so Choose a lower-beta stock in a well-diversified portfolio
• The beta of a portfolio Portfolio betas can be explained in the same way as individual stock betas; it's the weighted average of its individual securities’ betas. Adding a low-beta stock reduces the risk of the portfolio.
• Market risk and diversifiable risk are 2 components of a stock’s risk
• since diversifiable risk can be eliminated by diversification, market risk is the only risk relevant to a rational, diversified investor
• Investors must be compensated for bearing the market risk
• we measure The market risk of a stock is by its beta coefficient, which is an index of the stock’s relative volatility. If b = 1, then the stock is about as risky as the market, but if The b > 1, the stock is more risky
• The beta of a portfolio is a weighted average of the individual securities’ betas
• Beta is the most relevant measure of any stock’s risk.