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.

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

CML Equation

Market Model: Expected return, variance and Cov

Checking if adding new asset to portfolio is optimal

Tangency portfolio std deviation

Appraisal ratio

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

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. rÃªmmber 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

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

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

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