Factor portfolio (definition)

Arbitrage portfolio

Tracking portfolio

A factor portfolio is a portfolio with a factor sensitivity of one to a particular factor and zero to all other factors.

An arbitrage portfolio is a portfolio with factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero.

A tracking portfolio is a portfolio with a specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index.

Macroeconomic factor models:

Macroeconomic factor models use unexpected changes (surprises) in macroeconomic variables as the factors to explain asset returns. One example of a factor in this type of model is the unexpected change in gross domestic product (GDP) growth

Fundamental factor models use: 

In fundamental factor models, the factors are characteristics of the stock or the company that have been shown to affect asset returns, such as book-to-market or price-to-earnings ratios.

A statistical factor model:

identifies the portfolios that best explain the historical cross-sectional returns or covariances among assets. The returns on these portfolios represent the factors.

If an investors’ portfolio lies on the capital market line (CML) at the point where the CML touches the efficient frontier then this implies the investor has:

100% of their funds invested in the market portfolio

Valid methods for reducing instability in the minimum variance frontier (2):

(1) Improving the statistical quality of inputs

(2) adding constraints against short sales 

Mean-variance analysis assumes that investors only need to know ______ (3 things) in order create optimal portfolios.

(1) expected returns

(2) variances

(3) covariances

The SML graphically represents the relationship between:

return and systematic risk (as measured by beta)

E(R_p) = RFR + [(E(R_M) - RFR) / S_M]*S_p

E(R_M) = expected return on market portfolio

S_M = SD of market portfolio

S_P = SD of portfolio

SLOPE of CML = [(E(R_M) - RFR) / S_M]

equals SHARPE RATIO

Variance of an equally-weighted portfolio:

(2)

Previous formula establishes:

(1) Number of stocks to acheive diversification

(2) Higher average correlation, _____ stocks it takes to acheive diversification

Var_p = (1/n)(s²₁) + [(n-1)/n]*cov

Var_p = s²₁*[(1-p)/n + p] 

n = # of assets

cov = average covariance

p=correlation

(1) relatively small number

(2) fewer

The multifactor model is:

a time-series regression that explains variation in one asset

Macrofactor models (3 things):

Fundamental factor models (2 things):

Macrofactor models include explanatory variables such as the business cycle, interest rates, and inflation

Fundamental factor models include explanatory variables such as firm size and the price-to-earnings ratio. 

The risk and return coordinate for the market portfolio is:

the tangency point for the capital market line (CML)

The CML has the ______ slope of any possible portfolio combination.

The slope of the CML is ______ and is maximized for the ________

steepest

the Sharpe ratio. Maximized for market portfolio

Tolerance for risk for endowments and foundations?

Average or above average tolerance for risk, in part due to their relatively longer investment time horizons. 

What portfolio(s) will plot on the SML?

What portfolio(s) will plot on the CML?

All portfolios will plot on the SML.

The only portfolio that will plot on the CML is the market portfolio, because it is perfectly diversified.

Investment constraints (6 things):

(1) liquidity needs

(2) time horizon

(3) tax concerns

(4) legal factors

(5) regulatory factors

(6) unique circumstances

The CAPM predicts that all investors hold the ______

The capital allocation line is then the _____ and the market price of risk is ______.

The security market line (SML) describes the relationship between ______, where risk is measured by _____.

market portfolio

capital market line (CML) and the market price of risk is the slope of the CML.

between asset risk and expected return, where risk is measured by beta

CAPM (does/not) assume that all investors hold the market portfolio.

APT (does/not).....

Because the CML is a straight line, it implies that all the portfolios on the CML are:

perfectly positively correlated

As the number of variables in a regression increases, effect on:

(1) R²

(2) Adjusted R²

(3) F-statistic

(1) always increases

(2) up/down

(3) up/down

Same as 2-asset, but after 2W1W2 terms do:

(1) cov(1,2)

or

(2) p(1,2)s1s2

Capital Allocation Line (CAL):

(1) graphically

(2) best risky portfolio

(3) formula for best risky portfolio

(4) formula for CAL

(5) formula for CML when mkt portfolio is tangency port.

(1) line from the RFR to the point of tangency of the efficient frontier

(2) pt of tangency between CAL and efficient frontier

(3) Sharpe ratio

(4) E(R_CAL) = R_f + [E(R_p)-R_f/s_p]*s_p

(5) same as CAL just do R(market) instead of R(p)

The market model (used for + formula):

Makes 3 predictions (formulas):

Regression model often used to estimate betas for common stocks

Return(i) = Alpha(i) + Beta(i)*Return(Mkt) + Error

(1) E(Return_i) = Alpha(i) + Beta(i)*E(R_mkt)

(2) Variance(i) = Beta_i²*s_m² + s²_error

(3) Cov_ij = Beta_iBeta_js²_M

Forecast Beta_i,t = Alpha₀ + Alpha₁Beta_i,t-1

Alpha₀ = 1/3      Alpha₁ = 2/3