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The efficient frontier is a subset of the minimum-variance portfolio,
representing that portion of the minimum-variance frontier beginning
with the minimum-variance portfolio and continuing above it.
The Fundamental Law states that forecasts are to be independent of each other, not dependent.
Slope CML, [E(Rm) - Rf] / std dev Market
E(R) = RF + [E(Rp) - RF] ×σ/σp
describes the combinations of expected return and standard deviation
of return available to an investor from combining her optimal portfolio
of risky assets with the risk-free asset. Thus the CAL describes the
expected results of the investor's decision on how to optimally allocate
her capital among risky and risk-free assets.
Arbitrage Pricing Theory and the Factor ModelAPT describes the
expected return on an asset (or portfolio) as a linear function of the
risk of the asset (or portfolio) with respect to a set of factors.
E(Ri) = Rf + βi[E(Rm)-Rf)]whereE(Ri) = the expected return on asset
iRF = the risk-free rate of returnE(RM) = the expected return on the
market portfolioβi = Cov(Ri, RM)/Var(RM)
The information ratio provides the mean active returns per unit of
active risk. The higher information ratio demonstrates that active
management has benefited the portfolio.
(1) active factor risk is the contribution to active risk squared
resulting from the portfolio's different-from-benchmark exposures
relative to factors specified in the risk model (or systematic risk),
and (2) active specific risk (or asset selection risk) is the
contribution to active risk squared resulting from the portfolio's
active weights on individual assets as those weights interact with
assets' residual risk (also referred to as idiosyncratic risk).
An efficient portfolio is one offering the highest expected return for
a given level of risk as measured by variance or standard deviation of
return.
The Sharpe ratio measures a portfolio's return in excess of the
risk-free return relative to the standard deviation of that return. For
any portfolio, adding an investment with a Sharpe ratio that is greater
than that of the existing portfolio will always lead to a mean-variance
improvement at the margin.
The minimum-variance frontier is the set of portfolios that have minimum variance for their level of expected return.
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