Investment Management

Simplifies the problem of estimating covariances and correlations by decomposing the risk into systematic and firm specific.

We impose restrictions on the uncertainty of the of the asset returns structure.

They are able to decompose the returns into systematic and firm specific components. The model allows to have a better discription of the security returns by allowing for the possibility that stocks have different sensitivity to the various risk factors.

CAPM assumes only one source of systematic risk while APT assumes several sources of risk.

Security returns can be described by a factor model; Thera are sufficient securities to diversify away firm specific risk; Well functioning capital markets do not allow for the persistence of arbitrage opportunities.

If an investor can construct a zero investment portfolio with a sure profit.

If two assets are equivalent in all aspects, they should have the same market price. If not, there is an arbitrage opportunity.

Arbitrage opportunities will quickly disappear because when Arbitrageuers observe a violation of the law of one price, they engage in arbitrage activity.

All securities have finite expected values and variance; Some can form well diversified portfolios; There are no taxes, no transaction costs.

APT gives also a Benchmark but underlies the importance of a reward for the systematic risk only; Assumption of a rational equilibrium in capital markets that preclude arbitrage; Any portfolio can serve as a benchmark portfolio; Equal beta portfolios must have equal expected returns in market equilibrium; APT can be extended to multifactor model.

Doesn't give a guide on where we should look for the factors; only factors that substantially explain returns; no expanation on magnitude and sign of the factors.

IP = montly growth rate; EI = change in expected infaltion; UI = unanticipated inflation; CG = excess returns of long-term corporate bonds over long-term government bonds; GB = excess return of long-term government bonds over T-Bills

Because the APT can overcome some of the limitations of the CAPM.

Using a proxy for the market portfolio has two difficulties: the proxy might be mean-variance efficient even when the true market portfolio is not; the procy itself might be inefficient but this alone implies nothing about the efficiency of the true market protfolio.

By using different proxies, the return differs.

Statistical problem caue d by measurement errors in beta for the first pass regression; the slope will be too flat and the intercept too high.

Average excess returns are linear and increase with beta, the measure of systematic risk; average excess returns are not affected by the nonsystematic risk.

CAPM and Multifactor APT are elegant theories of how exposure to systematic risk factors should affect expected return; they fail in identifying what these systematic risk factors must be.

They noticed, that value stocks outperformed growth stocks.

It uses market index, firm size and book-to-market ratio. SMB = return small firms minus big firms; HML = return high b2m ratio to small b2m ratio.

Information is immediately and correctly impounded in prices; If this does not happen then the information could be used to trade until the price fully reflects the information.

A market where security prices fully and correctly reflect all available information.

Technical analysis is useless because the information should already be included in the price.

Should provide no significant returns because it relies on publicly available information.

EMH advocates passive investing; Build a well diversified portfolio because prices are fair.

EMH ignores the risk return tradeoff; Modern definition of EMH: profits are seen as economic rent control for risk premium.

Trading in an efficient market may lead to profits as a reward for taking the risk of holding risky assets.; Normal returns are admissable abnormal returns are not. Admissable = acceptable

Weak-form: the information set includes only the past history of prices; Semistrong: Includes all information known to all market participants Strong: Includes all information known to any market participants.

Geometric average is the time weighted average return.

It is the internal rate of return when we consider investment over a period during which cash was added to or withdrawn from the portfolio.

Because returns have to be adjusted for risk, some managers concentrate on agressive stocks and therefore outperform more conservative managers.

Incremental return and volatility of the portfolio relative to the risk-free alternative investment as a measure of the reward-to-variability ratio.

Average excess return perunit of systematic risk similar to the Sharpe ratio, but replaces volatility with the beta of the portfolio in the denominator.

Jensen's alpha measures the average return on the portfolio over and above that predicted by the CAPM.