CFA Level 2 – Portfolio Management

Mean – variance analysis assumption
1)All investors are risk averse; they prefer less risk to more for the same level of expected return
2)Expected returns for all assets are known.
3)The variances and covariances of all asset returns are known.
4)Investors need only know the expected returns, variances, and covariances of returns to determine optimal portfolios. They can ignore skewness, kurtosis, and other attributes of a distribution.
5)There are no transaction costs or taxes.
Relationship b/w variance and number of assets in portfolio
Relationship b/w variance and number of assets in portfolio
CML Equation
CML Equation
Market Model: Expected return, variance and Cov
Market Model: Expected return, variance and Cov
Checking if adding new asset to portfolio is optimal
Checking if adding new asset to portfolio is optimal
Tangency portfolio std deviation
Tangency portfolio std deviation
Appraisal ratio
Appraisal ratio
Market Model Assumption
Market Model Assumption
APT Assumption
No arbitrage, can diversified all un-systematic risk, many assets available, factor model describe return
Investment Constraints
(LLUTT): L (liquidity) – L (legal) – U (unique circumstance) – T (tax) – T (time)
Correlation b/w 2 assets given its betas and std dev of market
Correlation b/w 2 assets given its betas and std dev of market
arbitrage portfolio given expected returns of individual portfolio and their factor sensitivity
arbitrage portfolio must have zero sensitivity to the factor. so we need to find the weight of each individualmportfolio with the long portfolio weight sum to 1 and the short portfoliomweight sum to -1. the arbitrage profit is weight x expexted return of all portfolio. rêmmber that weight x sensitivity of long port = sensitivity of short port
factor risk/price of risk
expected return= risk free+factor sens x price of risk
solve this to get price of risk
liquidity requirements incl what
does not incl wht is planned
estimate beta of a stock from its cov with market and mkt variance
cov with mkt/mkt variance
std deviation in perfect timing port
misleading. perfect timing port will perform at least as well of t bills
TB model result in what kind of port
result in combination of active port indentified by the model and market (passive) port
what is CAL
expected return on how to allocate risky/risky free assets
what is CML
when all investors share same expectation, CAL becomes CML
tracking risk
sample std deviation x (Return of port – return of benchmark)
information ratio
(avg port return – avg benchmark return) / tracking risk
active risk square
variance x (port return – benchmark return)
active risk square =active factor risk + active specific risk
FMCAR
numerator:exposure factor( exposure factor1 x cov1+exposure factor2 x cov2)
denominator:active risk square
for a single factor: active factor risk/ active rik square
active factor risk
(active sensitivity of factor – benchmark) ^2 x factor variance