chapter 8 and 10 powerpoints Flashcards
two drawbacks of the Markowitz Procedure
Requires a huge number of estimates to fill the covariance matrix
Provides no guideline to the forecasting of the security risk premium to construct the efficient frontier of risky asset
advantages of index models
simplify the estimation of the covariance matrix
Enhance the analysis of security risk premiums
Decompose risk into relevant sources of security risk called factors (like systematic risk) versus firm diversifiable risk
Are as accurate as the Markowitz algorithm
Simplify estimates to those common forces that affect most firms
arbitrage opportunity
Whenever a wide set of securities is mispriced and investors can exploit this opportunity
when has arbitrage happened
Whenever a wide set of securities is mispriced and investors earned a risk-free economic profit
arbitrage
involves the simultaneous purchase and sale of equivalent securities in order to profit from discrepancies in their price relationship
The basic principle of capital market theory
In equilibrium securities are properly priced
why does the capital market theory not support arbitrage
If securities are mispriced then strong pressure on security prices will restore the equilibrium (proper equilibrium prices)
As a result, in equilibrium, capital markets satisfy the no arbitrage condition
Arbitrage Pricing Theory or APT
when we want to capture countless economy wide affecting risk factors in a model that explains securitiesβ returns
we obtain a multifactor version of the security market line in which each factor is a separate source of risk with its own risk premium
A single factor APT assumes
securities are affected by a single common risk factor
what do index models assume
one risk factor, the market factor, affects all security prices
how can we price the holding period return on a security using the single factor APT method?
the single factor model
ri = ERi + π½π Β· mi + ei
ri: represents the holding period return that can be earned on the security
ERi: the expected return on the security as of the beginning of the holding period
mi: the unanticipated return achieved on the security caused by unanticipated movements (shocks) in the risk factor
ei: the unanticipated return achieved on the security caused by unanticipated movements (shocks) in the firm itself
the single factor model: the mi and ei assumptions
The expected value of both mi and ei is zero because we cannot expect unanticipated events
The correlation between mi and ei is assumed to be zero: shocks to the risk factor are uncorrelated with firm specific shocks
If our risk factor is a good proxy for the whole economy (or capital market) then our risk factor is called the market factor
in the single factor model, what is the risk when investing in security i
Shocks in the market (mi)
Shocks in the firm itself (ei)
Ο^2 for i in the single factor model
Ο^2 (for i) = π½^2π Β· Ο^2m + Ο^2ei
the covariance between two securities using the single factor model
cov (ri, rj) = π½^π Β· π½^j Β· Ο^2m
the conclusion for the returns of firms with similar market exposure (betas) single factor model framework
should lead to the same expected return
not same realized return
the regression equation
π π(π‘) = πΌπ + π½ππ π(π‘) + ππ(π‘)
Ri(t): is called the dependent variable
RM(t): is called the independent variable
πΌ and π are called the coefficient of the regression
ei(t): is called the residual of the regression
π π(π‘) with a hat above is the estimated dependent variable
the single index model on a portfolio
π p(π‘) = πΌp + π½pπ π(π‘) + πp(π‘)
π½p = (Eπ½t) /n
πΌp = (EπΌt) /n
πp = (Eπt) /n
π^2π = π½^2π Β· π^2π + π^2πp
π^2πp = (π^2π_) / n
As n gets large, π^2πp becomes negligible
how do obtain the estimated dependent variable (π π(π‘) with a hat above)
by evaluating our regression model for every observation of the independent variable
Security Characteristic Line
π π(π‘) = πΌπ + π½ππ π(π‘) + ππ(π‘)
how do we estimate the Security Characteristic Line
- we need to calculate the excess return of both our security βiβ and the market βMβ
- we regress (on EXCEL for this course), the excess return of our security βiβ on the excess market return βMβ
β> The intercept of this line is πΌπ
β> The slope of this line (coefficient of RM(t) ) is our π½π
- Check whether the intercept and the slope are significant
- Check the explanatory power of our SCL for this particular security
We need to check whether the intercept and the slope are statistically significant
how do we check whether the intercept and the slope are statistically significant in the
Security Characteristic Line
when we are saying that the slope and the intercept are statistically significant, it means that they are different from zero
we will rely on the t-statistics to measure the significance of our estimated alpha and beta
If the estimated t-statistics is greater than 1.96 then we can say that we are 95% confident that our estimated coefficient is different from zero
we are satisfied with a 95% confidence level
How to obtain the t-statistics for our estimated slope (beta) and intercept
(alpha):
π‘π½^ = (π½^ - 0) / Standard error π½^
The standard error measures the level of imprecision in estimating our coefficient
(alpha, or beta
the the higher the standard error relative to the estimated coefficient, the more the likelihood that our result would be less than 1.96, the less we are confident that our estimated coefficient is statistically different from zero
R-square
measures how much variation in the dependent variable (the stock in our case) is explained by independent variable (the market)
measured as the ratio of the total variation in the estimated dependent variable to the total variation in the actual observed dependent variable
