Section III.A. Flashcards
What are the Key MPT Assumptions?
Normal return distributions
Fixed asset correlations
Investors are rational
Investors are risk-averse
Risk is known and constant
All information is public
No taxes or transactions costs
Key Aspects of MPT
- Return vs. Risk
- Mean Variance Optimization (MVO)
- Efficient Frontier
- How portfolios may be constructed
from this methodology (portfolio
construction)
Return vs. Risk
*Risk measured as standard deviation
*Return (absolute vs. relative)
*Risk adjusted returns
Market Risk Premium
Mean Variance Optimization - Inputs Necessary?
Security’s expected returns
Expected risk
Expected cross-security correlations
Portfolio optimization (including MVO) involves a mathematical procedure called quadratic programming. Which two objectives are considered?
To maximize return and minimize risk
What is the Efficient Frontier?
a set of optimal portfolios with the highest expected return for a set (or defined) amount or risk as measured by standard deviation
Portfolio Construction
- Theoretically (using MPT as a foundation) it is possible to build efficient portfolios if your primary
goal is to optimize risk adjusted returns. - You may maximize returns for a given level of risk or you may minimize risk for a target amount of return.
Capital Allocation Line (CAL)
- The CAL is sometimes called the Capital Asset Line
- Defined: this line represents all possible combinations of risk free and risky assets; represents possible returns by taking on different levels of risk
- Different from the Capital Market Line (CML)
- Different from the Securities Market Line (SML)
What are the criticisms of MPT?
Challenging MPT Assumptions:
Investment returns are not normally distributed
Asset correlations are not fixed
Investors are not rational
Investors are not exclusively risk-averse
Risk is not known and constant
All information is not publicly known
Taxes and transactions costs are real
What is the Sharpe Ratio?
What is the “Kinked” CAL?
The so-called “kink” in a Capital Allocation Line indicates that:
a. leverage is being used, and
b. the rate to borrow exceeds the lending rate
What are “positive diversification effects”?
What is the Brinson Beebower & Hood study?
1986 study of 91 of the largest pension funds
Conclusion: regarding the determinants of portfolio performance:
– Asset allocation is the primary determinant of a portfolio’s return variability
–Security selection and market timing played only a minor role in portfolio performance
What is the Black-Litterman Model?
What is Efficient Market Hypothesis (EMH)?
*EMH says stock prices already reflect all available information
- A forecast about favorable future performance leads to favorable current performance, as market
participants rush to trade on new information.
–Result: Prices change until expected returns are exactly commensurate with risk.
What are the versions of EMH?
- Weak
- Semi-strong
- Strong
What is the “Weak Form” of EMH?
*claims that past price movements and volume do not impact prices
- technical analysis is not beneficial
- fundamental analysis can add value
What is the “Semi-Strong Form” of EMH?
- claims all public information is reflected in a stock’s current price
- states that neither technical nor fundamental analysis can add value
What is the “Strong Form” of EMH?
- claims all public and private
information is reflected in a stock’s current price - states that not even insider information can add value (i.e., produce outperformance)
What is Fundamental Analysis?
using economic and accounting information to predict stock prices
– Try to find firms that are better than everyone else’s estimate.
– Try to find poorly run firms that are not as bad as the market thinks.
– Semi strong form efficiency and fundamental analysis
What is CAPM?
- a theoretical model that attempts to explain the relationship between risk and expected return
- the model holds that investors should be compensated for both the time value of money and risk taken
- the CAPM formula allows one to calculate the expected return of an asset = (risk free rate) +
(market risk premium times the beta of the asset)
What is Systematic (Market Risk)?
- also called “market risk” and “non
diversifiable risk” - systematic risk is the inherent risk that comes from having exposure to the overall market
- MPT suggests that systematic risk cannot be mitigated through diversification
What is Non-Systematic (Idiosyncratic) Risk?
- also called “diversifiable” or “unsystematic risk “
- this risk refers to factors that may affect one asset or investment but not another
- MPT suggests that this risk may be mitigated through diversification
What is the Security Market Line (SML)?
- the SML is a graphical expression of the CAPM
- the slope of the SML represents the market risk premium
What does the SML look like Graphically?
What is Arbitrage Pricing Theory (APT)?
- seeks to explain security returns beyond the usual metrics by introducing risk factors such as expected return, sector and
systematic factors - while far more expansive than CAPM given the flexibility of the model, it is limited in accuracy because it cannot measure unanticipated changes in the variables
What are Arbitrage Pricing Theory Assumptions?
- Does not require an expected market return.
- Uses the asset’s expected return and the risk premium of a number of macro economic factors.
- Arbitrageurs use APT to buy underpriced assets and short those that are overvalued.
APT and CAPM?
APT
* Equilibrium means no arbitrage opportunities.
* APT equilibrium is quickly restored even if only a few investors recognize an arbitrage opportunity.
* The expected return beta relationship can be derived without using the true
CAPM
* Model is based on an inherently unobservable “market”
* Rests on mean variance efficiency. The actions of many small investors
restore CAPM equilibrium.
* CAPM describes equilibrium for all assets.
APT Application
Challenges MPT
- Can’t predict asset returns using the
relationship between the same asset
and many common risk factors - Predicts asset returns through a linear combination of many different
independent macro economic variables
APT Model
- APT applies to well diversified portfolios and not necessarily to individual stocks.
- With APT it is possible for some individual stocks to be mispriced not lie on the SML.
- APT can be extended to multifactor models.
Fama-French Three Factor Model
- Market (aka: equity) premium
- Size and book to market ratios explain returns on securities.
- High book to market firms experience higher returns
(value - Smaller firms experience higher returns.
What is Momentum: a Fourth Factor?
- The original Fama French model augmented with a momentum factor has become a common four factor model used to evaluate abnormal performance of a stock portfolio.
- Winners minus losers (WML)
winners/losers based on past returns.
Optimal Portfolios and
Non Normal Returns
- Fat tailed distributions can result in extreme values of VaR (value at risk) and ES (expected shortfall) and encourage smaller allocations to the risky portfolio.
- If other portfolios provide sufficiently better VaR and ES values than the mean variance efficient
portfolio, we may prefer these when faced with fat tailed distributions.
The Minimum Variance Portfolio?
- The minimum variance portfolio is
the portfolio composed of the risky assets that has the smallest standard deviation, the portfolio with least risk. - When correlation is less than +1, the
portfolio standard deviation may be smaller than that of either of the individual component assets. - When correlation is -1, the standard deviation of the minimum variance portfolio is zero.
What are we looking for with Minimum Variance Portfolio?
What we’re looking for is the mix of assets that provides the smallest variance or standard deviation.
In the case of two assets that are perfectly negatively correlated (i.e., Corr Coeff = - 1), we know that the standard deviation of the minimum variance portfolio is zero.
In other words, because these two assets are perfectly negatively correlated, we can combine A & B in the right mix such that there is no variance and a fixed return (i.e., risk free return) is provided. (Page 628)
What is Semi-Variance (downside deviation)?
- a measurement of dispersion
measures data that is below the mean or target value of a data set - considered a better measurement of downside risk
- semi variance is the average of the squared deviations of all values less than the average or mean
What is Value-at-Risk (VaR)?
*
Defined:
–
VaR is a measure of risk that quantifies
potential loss (e.g., $1 million), the probability of the potential loss (e.g., 3%), and the time frame for potential loss (e.g., three months)
* Assumes market to market pricing, no trading, and normal market conditions.
* A measure of loss most frequently associated with extreme negative returns
*
VaR is the quantile of a distribution below which
lies q % of the possible values of that distribution
– The 5% VaR , commonly estimated in
practice, is the return at the 5 th percentile when returns are sorted from high to low
What is Expected Shortfall (ES)?
- Also called conditional tail expectation (CTE)
- More conservative measure of downside risk than VaR
– VaR takes the highest return from the worst cases
– ES takes an average return of the worst cases
What is Sortino Ratio?
- a risk adjusted measure of return that uses downside volatility (semi standard deviation) to measure risk
- unlike the Sharpe ratio, Sortino only uses negative returns in the calculation to measure downside risk
- considered a more effective way to than other ratios to measure high volatility portfolios
