READING 44. PORTFOLIO RISK AND RETURN: PART II
non systematic risk calculation
(portfolio StD x portfolio StD) - [(portfolio beta x portfolio beta) X (market StD x market StD)] P(std) x P(std) - [PBeta x PBeta x M(std) x M(std)]
Sharpe Ratio (performance eval..)
(portfolio return - risk free rate)/portfolio risk the higher the better, more compensation for bearing risk above risk free rate limitation - measures total risk when only systematic risk is priced limitation - the ratio is not informative itself, it must be compared to another ratio limitation - numerators must be +ve
explain nonsystematic risk;
...firm specific, diversifiable. only affects the firm involved e.g. takeover threat, lower profitability, competition launching the next iphone, failure of a drug trial, major oil discoveries, or an airliner crash
interpret beta;
...this is a measure of the sensitivity of a security's return to the return of the market portfolio. How sensitive are the returns to general economic conditions High ______ portfolio indicate poor/low diversification. a positive _____ indicates that the return of an asset moves in the same direction of the market, whereas a negative ______ indicates that the return of an asset moves in the opposite direction of the market
list the CAPM assumptions;
1. Investors are risk-averse, utility-maximizing, rational individuals 2. Markets are frictionless, including no transaction costs and no taxes 3. Investors plan for the same single holding period 4. Investors have homogeneous expectations or beliefs 5. All investments are infinitely divisible 6. Investors are price takers - none can influence prices, only trades do The main objective of these assumptions is to create a marginal investor who rationally chooses a mean-variance-efficient portfolio in a predictable fashion.
calculate beta;
1. if the StD of the Market is 25%, and an IPO has a Beta of 0.7, and StD of 40%. The IPO's Beta is (0.7 x 0.4)/0.25 = 1.12 2. market portfolio increases by 47% = economy (strong) declines by 25% = economy (weak) own portfolio increases by 40% = economy (strong) declines by 20% = economy (weak) variability market => 47%- (-25%) = 72% portfolio => 40%- (-20%) = 60% 60%/72% = 0.833% 1% change in market = 0.833% change in portfolio
Return-generating models, the intercept term of the market model is the asset's estimated:
Alpha
A portfolio on the capital market line with returns greater than the returns on the market portfolio represents a(n)
Borrowing Portfolio
Return-generating models are used to directly estimate the
Expected Return of a Security
With respect to the capital market line, a portfolio on the CML with returns less than the returns on the market portfolio represents a(n):
Lending Portfolio
Optimal Risky Portfolio
Market Portfolio
market risk premium
Market Portfolio Return - Risk Free rate SP500 - Treasury Bills
Relative to portfolios on the CML, any portfolio that plots above the CML is considered:
Not Achievable
return-generating models, the slope term of the market model is an estimate of the asset's
Systematic Risk
Optimal Investor Portfolio
Tangent to the investor's indifference curve
expected return of an asset
The expected return of an asset depends on its beta risk and can be computed using the CAPM, which is given by E(Ri) = Rf + βi[E(Rm) - Rf].
explain the security market line (SML);
The graphical depiction of the CAPM it intersects the y-axis at the risk-free rate of return, and the slope of this line is the market risk premium. market line applies to any security, efficient or not
why the CAPM assumptions
The main objective of these assumptions is to create a marginal investor who rationally chooses a mean-variance-efficient portfolio in a predictable fashion.
explain the capital asset pricing model (CAPM)
The model provides a linear expected return-beta relationship that precisely determines the expected return given the beta of an asset. expected returns of assets vary only by their systematic risk as measured by beta how much compensation should investors expect for bearing a X amount of risk (cost of capital) E(r1) = Risk Free rate + (Beta x Market Risk Premium)
explain the market model;
The most common implementation of the single-index model is the ________
security characteristic line (SCL)
a plot of the excess return of the security on the excess return of the market, Jensen's alpha is the intercept and the beta is the slope
multi factor models
account for the difficulty in identifying the most relevant variable to consider when estimating returns - allows for more than one. all models contain return on the market portfolio as a key factor
security selection
after plotting the SML (CAPM - graphed), the return of securities can be plotted on the same graph. on the SML - properly valued above the SML - undervalued (+ve alpha) below the SML - overvalued (-ve alpha)
explain the capital market line (CML);
all possible combinations of the risk-free asset and an investor's optimal risky portfolio (where the line is tangent to the indifference curve) line depicting the total risk and expected return of portfolio combinations of a risk-free asset and the market portfolio does not apply to all securities or assets but only to portfolios on the efficient frontier The T-bills have a return of 5 percent. The S&P 500 has a standard deviation of 20 percent and an expected return of 15 percent. Line starts at 5% (y axis) 100% Tbills investment -> no StD with Tbills 0% (x axis) 25% Market, 75% Tbills -> E(rP) = (0.25 x 0.15) + (0.75 x 0.05), StD(P) = 0.25 x 0.20 (StD)....adjust the weightings and the StD for the Market Portfolio's %
fundamental factor model
analyze and use relationships between security returns and the company's underlying fundamentals, such as, for example, earnings, earnings growth, cash flow generation, investment in research
diversification with an equally weighted portfolio
as the number of stock increases, the volatility decreases, but only up to a certain point where the volatility converges to the average covariance of the stocks held. example historical volatility of large cap stocks is 40%, correlation between large caps is 28%. the lowest risk through diversification = sqr root of (0.28 x 0.4 x 0.4) = 21.17%
portfolio construction
assuming short selling is not allowed... 1. select securities with positive alpha, using S&P500 as the market portfolio 2. allocate more weight to securities with higher alpha 3. weight should be made proportional to the information ratio
implications of combining a risk-free asset with a portfolio of risky assets;
can result in a better risk-return trade-off than an investment in only one type of asset because the risk-free asset has zero correlation with the risky asset.
applications of the CAPM;
estimate the cost of capital or the expected rate of return performance evaluation
macro economic factor model
factors that are correlated with security returns. These factors may include economic growth, the interest rate, the inflation rate, productivity, employment, and consumer confidence
efficient frontier
gives optimal combinations of expected return and total risk
statistical factor model
historical and cross-sectional return data are analyzed to identify factors that explain variance or covariance in observed returns
Treynor Ratio (performance eval...)
it address the other ratio's limitation by switching the portfolio risk with the Beta risk limitation - the ratio is not informative itself, it must be compared to another ratio limitation - numerators must be +ve
applications of the SML
it can be used to identify the expected return of a portfolio, given its beta and the risk free rate
explain the capital allocation line (CAL);
line depicting the total risk and expected return of portfolio combinations of a risk-free asset and any risky asset a line originating at the expected return-standard deviation coordinates of the risk-free asset and lying tangent to the efficient frontier. slope of this line is known as the Sharpe ratio - the greater the slope, the better the asset
explain systematic risk;
non-diversifiable, this affects the entire market and does not impact any one company in particular. Measuring it involves using an efficient portfolio called the market portfolio - changes in prices reflect market-wide shocks...
limitations of CAPM
only systematic risk is priced only one period/objective is used true market portfolio is impossible to observe (it include non investable assets) proxies like the S&P500 are used, but if other proxies are used, return estimates will vary empirical support of its predictions are weak homogeneity is unrealistic (as optimal risky portfolios will vary)
three and four factor models
relative size and relative book to market value and beta of the asset and + relative past stock returns better predictor of US returns than CAPM
information ratio
security's alpha/nonsystematic risk measure of the abnormal return per unit of risk added by the security to a well diversified portfolio. the higher the _____ the more valuable the security
M - Squared (performance eval...)
similar to Sharpe - based on total risk. mimick the market portfolio's risk profile (systematic and unsystematic) then compare the returns of the market portfolio with yours. =Portfolio return - RFR(market StD/portfolio StD) - [Market return - RFR. if the portfolio's returns matches the market's, the _____is zero, if it outperforms the market, then it is +ve (in % terms - more useful)
Jensen's Alpha (performance eval...)
similar to Treynor - based on systematic estimate the portfolio's systematic risk by regressing daily returns with the market's daily return the coeff of the market return is an estimate of the portfolio's beta calculate risk adjusted return, using found beta and CAPM. compare the actual returns with the risk adjusted, and the difference is _____
single index model
simplest form of a return-generating model is a single-factor linear model, in which only one factor is considered.
explain why an investor should not expect to receive additional return for bearing nonsystematic risk;
the risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk. risk premium is Zero for diversifiable risk and it is in the interest of risk-averse investors to hold only well-diversified portfolios.
explain return generating models;
these can provide an estimate of the expected return of a security given certain parameters. If systematic risk is the only relevant parameter for return, then the return-generating model will estimate the expected return for any asset given the level of systematic risk.