Risk and CAPM

Assumptions of capital market theorem

(1) markowitz investors (2) unlimited risk-free lending and borrowing (3) homogenous expectations (4) one-period horizon (5) divisible asset (6) frictionless markets (7) no inflation and constant interest (8) equilibrium

APT assumptions

(1) returns are derived from a multifactorial model (2) unsystematic risk can be completely diversified away (3) no arbitrage opportunities exsist

implications of CAPM assumptions

1. all investors identify the same risk tangency's portfolio and combine that with the risk-free asset to create their portfolio. 2. because all investors hold the same risky portfolio, the weight of each asset must be proportional to the weight of the market. 3. the security market line (SML) is the graph of the CAPM and describes the relationship b/w the expected return and systematic risk. 4. systematic risk is the only risk priced by the market

capital asset pricing model assumption

1. investors evaluate portfolios by looking at the expected returns and SD of the portfolios over one-period horizon. 2. investors are never satiated 3. investors are risk-averse 4. individual assets are infinitely divisible 5. there is a risk-free rate that an investor can borrow and lend at 6. taxes and transaction costs are irrelevant 7. all investors have the same one-period time horizon 8. the risk-free rate is the same for all investors 9. information is freely and instantly available to all investors. 10. investors have the same homogenous expectations.

computing the average historical return

1. the arithmetic mean (AM) averages the HPY's over the number of periods the data set allows. 2. the geometric mean (GM) is the Nth root of the product of the HPRs for an N period. GM= [(HPRgm)^(1/N)] -1

random diversification

a diversification that implicitly assumes that investors do not acknowledge the standard deviations, correlations, and expected returns of the stocks in the portfolio.

efficient diversification

a diversification that uses estimates of standard deviations, correlation, and expected returns in order to diversify.

minimum variance fronteir

a graph of the expected return/variance combinations for all minimum variance portfolios

sharpe ratio

a measure that standardizes investment returns for risk (by using volatility)

the effiecent frontier

a plot of the expected returns and risk combinations of all efficent portfolios, which lie on the upper half of the minimum variance fornteir.

minimum variance portfolio

a portfolio that has the smallest variance among all portfolios with identical expected return

ineffecient portfolio

a portfolio where there is a possibility to have a higher or lower amount of either expected return or variance and maintain the other component constant.

efficent set

a set of portfolios that meet the conditions for the efficient set theorem.

modern portfolio theory

a solution put forward by Harry M. Markowitz in 1952 when he published a landmark paper that solved the portfolio selection problem\.

portfolio

a term used to describe any group of investments, which can be in the same or different asset class.

probabilistic expected rate of return

a weighted average of all the possible returns-weighted by the probability that each rate will occur.

assumptions of mean-variance analysis

all investors are risk-averse to some degree and require more compensation to handle more risk. the expected returns, variances, and covariances are known for all assets. individuals create optimal assets relying soely on expected returns, variances, and covariances. there are no transaction costs or taxes.

aribitrage pricing theory

an alternative to CAPM in determining the expected return of individual stocks and portfolios.

assumptions in portfolio selection problem

an assumption made in markowitz approach that investors always prefer more wealth to less levels of terminal wealth and that risk-averse investors will always choose the portfolio with the smaller SD.

efficient set theorem

an investor will choose from an infinite number of ways to hold a portfolio of securities an optimal portfolio that will offer maximum expected returns from varying levels or risk, and offer minimum risk for varying levels of expected returns.

chinese interpretation of risk

chinese defined risk as the combination of risk and opportunity.

positive economics

concerned with DESCRIBING economic phenomena, its very descriptive.

normative economics

concerned with explaining the way something SHOULD be, its very perspective

investor attributes

determinant of required rate of return that is comprised of investor's assessment of riskiness of the asset's cash flows and willingness to bear risk.

asset characterisitcs

determinant of required rate of return that is comprised of the amount, timing, and riskiness of expected cash flows.

systematic risk

estimated by the asset's beta, which is a standardized measure of an asset's systematic risk.

diversification

in finance the act of investing in more than one security in order to reduce risk, the more positively correlated the stocks are the less the diversification effect.

determinants of an investor's required rate of return

investor's required rate of return= asset characteristics + investor attributes

security market line

marked by the risk free rate which represents the y intercept of the graph and the slope of the line is the market risk premium, the expected return of the market minus the risk-free rate.

covariance of a two-asset portfolio

measures the strength of the relationship between the returns earned on assets 1 and 2. the formula is given by the summation of the differences between the return of asset 1 times the expected return of 1 times the return of asset 2 and the expected return of asset 2.

capital asset pricing model

one of the most celebrated model in all of finance, it describes the way that

portfolio diversification

refers to the strategy of reducing risk by combining many different types of assets into a portfolio. the strategy is affected by: (1) correlation b/w assets: lower correlation means greater benefit (2) # of assets included: more assets lead to greater benefit

mean-variance analysis

refers to the use of expected returns, variances, and covariances of individual investments to analyze the risk-return tradeoff of combinations of these assets.

market risk

systematic risk is nondiversifiable; cannot be diversified away. EXAMPLES: the unexpected changes in interest rates, unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.

correlation of a two-asset portfolio

the correlation is equal to the covariance divided by variance of asset 1 and 2. the covariance is divided by the variances because the covariance is bounded from negative to positive infinity.

investment

the current commitment of dollars for a period of time in order to derive future payments that will compensate the investor for: the time the funds are committed, the expected rate of inflation, the uncertainty of future payment.

portfolio selection problem

the dilemma of selecting which of the many possible combination of securities that can comprise a portfolio should be chosen.

volatility (vol)

the finance term for the standard deviation of a stock;s return. the greater the SD, the greater the uncertainty, and the greater the risk.

HPR formula

the formula can also be described as ending value/ beginning formula. Annual HPR= HPR^(1/N) Holding Period Yield (HPY)= HPR-1

global minimum variance portfolio

the portfolio with the smallest variance among all possible portfolios

risk

the probability that an actual return will differ from our expected return, uncertainty in the distribution of outcomes.

beta

the ratio of a stocks standard deviation to the standard deviation of the market multiplied by the correlation to the market.

Historical return

the return of an investment over the time period the investment is held.

ROI- return on investment

the return on an investment, not necessarily an investment.

expected return

the return that an investor expects to earn on an asset, given its price, growth potential, etc.

required return

the return that an investor requires on an asset given its risk and market interest rate.

expected return of a three-asset portfolio

the same formula that is used for the expected return of the two-asset portfolio is used for the three-asset portfolio.

SD of stock

the square root of the summation of the difference of the return of a stock minus the expected return squared times the probability of that return

holding period return (HPR)

the total return on investment during a period of time. also defined as the amount of initial dollar of investment would become if the investment was held and all dividends and interest are reinvested.

variance of a three-asset portfolio

the variance and the SD is the same as the two-asset portfolio is the same but there is an addition of two more covariance terms.

expected return of a two-asset portfolio

the weight of the two assets w1 and w2 should add up to 100%.

expected return of a portfolio

the weighted average of the expected returns on the individual assets that are included in the portfolio.

perfect markets

there are no frictions that impede investments, the assumption allows for investors to focus less on how one should invest and more to what the price of the security would be if everyone invested as such.

company-unique risk

unsystematic risk is diversifiable, which cannot be reduced through diversification. EXAMPLES: a company's labor force goes on strike, company personal dies in a plane crash, or a huge tank leaks and floods a company's production area.