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expected return= risk free+factor sens x price of risksolve this to get price of risk
1)All investors are risk averse; they prefer less risk to more for the
same level of expected return2)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.
(LLUTT): L (liquidity) - L (legal) - U (unique circumstance) - T (tax) - T (time)
cov with mkt/mkt variance
result in combination of active port indentified by the model and market (passive) port
when all investors share same expectation, CAL becomes CML
expected return on how to allocate risky/risky free assets
numerator:exposure factor( exposure factor1 x cov1+exposure factor2 x
cov2)denominator:active risk squarefor a single factor: active factor
risk/ active rik square
misleading. perfect timing port will perform at least as well of t bills
(active sensitivity of factor - benchmark) ^2 x factor variance
sample std deviation x (Return of port - return of benchmark)
No arbitrage, can diversified all un-systematic risk, many assets available, factor model describe return
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
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