LM 2: Portfolio Risk & Return: Part II Flashcards
Describe macroeconomic factor models, fundamental factor models, and statistical factor models.
macroeconomic models: relationship between security returns and economic factors
fundamental models: relationship of company-specific variables
statistical models: historical data
What are the 2 beta formulas?
Bi = Cov (Ri, Rm) / Om^2
Beta = Covariance between market and investment / SD of market^2
Bi = Pi,m * Oi/ om
Beta = correlation coefficient between asset return & market return * asset return sd / market return sd
What is the portfolio standard deviation formula for a two-asset portfolio?
sd = square root
(w1^2* sd1^2 + w2^2* sd2^2) +
(2* w1* w2* correlation* sd1* sd2)
What does beta measure?
measures the sensitivity of an asset’s return to the market return.
What is covariance formula between two assets?
covariance = correlation * sd 1 * sd2
What is CAPM formula?
E (Ri) = Rf + Bi [E(Rm) - Rf)]
E (Ri) = expected return
Rf = risk free rate
Bi = beta, stock sensitivity to equity market
E(Rm) - Rf = market risk premium
E(Rm) = expected return of market
What are 2 total risk performance ratios?
- sharpe ratio
- m-squared
What are 2 systematic risk ratios?
- treynor ratio
- jensens alpha
What is the sharpe ratio , formula, and 2 limitations?
SR = Rp - Rf / SD of P
limitations:
1. uses total risk rather than systematic risk
2. meaningless by its self
sharpe ratio measure of risk-adjusted returns. how much excess return you receive for the extra volatility you endure for holding a riskier asset.
What is M2 ratio formula, and use?
total risk adjusted return
M2 = (Rp - Rf) * (Om / Op) + Rf- Rm
Rp= return portfolio
Rf = risk free
Om = SD of market
Op = SD of portfolio
M2 = sharpe ratio * SD of market + risk free rate
What is the treynor ratio formula, and the difference between the sharpe ratio?
TR = Rp - Rf / Bp
different than sharpe because it uses beta risk (systematic risk)
What is Jensen’s Alpha ratio formula, and use?
only based on systematic risk
investment strategy’s ability to beat the market, or its “edge.”
return over CAPM (expected return of an asset or investment)
Ap = Rp - [Rf + Bp * (Rm - Rf)]
What is market risk?
market risk is beta.
What is the security market line a graphical representation of?
graphical representation of CAPM
beta risk on x-axis
expected return on y-axis
What is the market model formula and what is it used for and what part of the equation is the intercept, and the slope coefficient?
singe factor model, single factor being the market. Used to predict company specific returns in the future
Ri = ai + (Bi*Rm) + ei
ai = intercept (alpha)
bi = slope coefficient (beta)
Capital market theory assumes homogeneity of expectations (the same) in terms of prices, cash flows, and discount rates; what does this mean in terms of a portfolio?
every investor will arrive at the same optimal risky portfolio
What ratio makes up the capital allocation line, and what is the formula for the ratio?
sharpe ratio = (expected portfolio return - risk free rate) / portfolio standard deviation
sharpe ratio = (E (Rp) - Rf)/ portfolio standard deviation
What is the market?
market is a portfolio that includes all risky assets
What is the expected return for the CML formula?
E (Rp) = Rf + ( e (Rm) - Rf / Standard deviation of market portfolio) * standard deviation of portfolio
What is the sharpe ratio for any return above the market portfolio?
slope = E(Rm) - Rb / Om
(expected return of market portfolio - rate of borrowing) / standard deviation of market portfolio
Whats the difference between systematic risk vs nonsystematic risk
Systematic risk is also called non-diversifiable risk or market risk. It includes risks like interest rates and economic cycles that cannot be avoided.
Nonsystematic risk is also called company-specific, industry-specific, or diversifiable risk.
What is total variance equation?
total variance = systematic variance + nonsystematic variance
What is a return generating model?
model that estimates the expected return based on certain parameters
What is a multi-factor model and what are 3 factors that can be used?
model that uses more than 1 factor to estimate the expected return, it factors things like interest rates and inflation on a regression line
- macroeconomic factors
- fundamental factors
- statistical factors
What 3 factors do fama french multi-factor models use?
- Beta
- SMB (Small minus Big): long portfolio with small cap stocks, short portfolio with large cap stocks.
- HML (High minus Low): long portfolio with high book to market, short on portfolio with low book to market
What is a single index model and formula?
generates returns using an assets sensitivity to a market index as the only factor
What is single index model formula?
Expected excess return of a security = Beta * [expected excess return of market]
What is beta formula for single index model?
SD investment / SD market
What is decomposition of total risk for a single index model formula?
total variance = systematic variance + nonsystematic variance
Oi^2 = Bi^2*Om^2 + Oe^2
systematic variance = beta * sd of market
Oe = nonsystematic variance
What are 6 assumptions of the CAPM?
- Investors are risk-averse, utility maximizing, & rational individuals
- markets are frictionless - no taxes or transaction costs
- investors plan for same holding period
- investors have homogeneous expectations
- investments are infinitely divisible (invest any amount into a particular asset)
- investors are price takers (no investor large enough to influence prices)
What are the axis plotted on security market line?
expected return on left, and beta(systematic risk) on right
What is the formula for slope of the SML?
slope = E (Rm) -Rf
What is portfolio beta on SML?
Bp = ws*Bs
ws = weight of securities
bs = beta of securities
What premium is the slope of the SML?
market risk premium
What are 2 theoretical limitations of the CAPM?
- single factor model that only includes beta risk (systematic risk)
- single period model does not consider multi-period implications of decisions
What are 5 practical limitations of the CAPM?
- market portfolio includes all assets, some of which are not investable
- proxies for market portfolio can generate different return estimates
- beta risk estimates require long history
- CAPM poor indicator of returns
- homogeneity of investor expectation is assumed to generate a single optimal risky portfolio
What are the 4 common performance appraisal ratios?
- sharpe ratio
- treynor ratio
- M2
- Jensens’s alpha
What does a positive alpha and a negative alpha for jensens alpha mean?
positive alpha = portfolio outperformed market
negative alpha = portfolio has underperformed the market
What is the security characteristic line?
straight line formed using regression analysis that summarizes a particular security’s systematic risk and rate of return.
This line shows the security’s performance versus the market’s performance.
What is the security characteristic line formula?
Ri - Rf = Ai + Bi * (Rm - Rf)
How many individual securities does it take to effectively eliminate non-systematic risk?
30 securities
What is information ratio and formula?
information ratio = A1 / Oei
information ratio = alpha / nonsystematic risk
the consistency of the fund manager in generating superior risk adjusted performance
What is a key principal of capital market theory?
in order to generate higher returns, investors must be willing to tolerate greater risk.
Will investors with a higher level or risk aversion build portfolios with greater risk or less risk?
Investors with a higher level of risk aversion will build portfolios with greater allocations to less risky assets
What is covariance?
measures the relationship of investments how closely they are connected or move in the same direction of each other.
What is capital market line?
a graphical representation of all the portfolios that optimally combine risk and return.
capital allocation line with the risky portfolio being the market portfolio that intercepts both the efficient frontier and CML
Whats the different between CAL or CML and SML?
CAL or CML only apply to efficient portfolios
SML applies to any security, efficient or not.
What kind of risk does CAPM take into consideration?and what does the CAPM tell us?
systematic risk (market risk)
financial model that calculates the expected rate of return for an asset or investment.
