# Asset Pricing Models Flashcards

Why is the Markowitz (mean variance) model impractical (4)

- Large amoutn of data required (returns, variances, covariances)
- The need to forecast the large number of inputs
- The inability of individual analysts to have the expertise to forecast all the required covariances (given their focus on a specialised industry or stocks)
- Errors in estimation of correlation coefficients can lead to nonsensical results

Optimisation procedure, single index model (10)

- compute initial position in active portfolio
- Scale initial positions to force portfgvolio weights to sum to one by dividing by their sum
- Compute the alpha of the active portfolio
- Compute the beta of the active portfolio
- Compute the initial position in the active portfolio
- Compute the beta of the active portfolio
- Adjust the initial position in the active portfolio
- Note; th e optimal portfolio now has weights
- Calcualte the risk premium of the optimal riskiy portfolio from the risk premium of the index portfolio and the alpha of the active portfolio
- Compute the variance of the optimal risky portfolio from the variance of the index portfolio and the residual variance of the active portfolio

CAPM setting (6)

- Investors are price takers - with a wealth that is small relative to the total wealth of all invetsors
- Investors plan for a single period investment horizon
- The investment universe is limited to publicly traed financial assets and a risk free asset (such that borrowers and lenders do so at the risk free rate)
- Investors do not incur taxes or transaction costs when trading
- Investors are mean-variance optimisers
- Investors hold homogeneous expectations about returns and covariances

Market equilibrium - attributes (2)

- All investors will hold portfolios containing all traded assets in the same weights as the market portfolio (M)
- The market portfolio is the tangency portfolio (M). Its capital allocation line is the best available and is called the Capital Market Line (CML)

Mutual Fund theorem

If the market portfolio is the ultimate risky portfolio, then investors can avoid fundamental security analysis and sim[ply hold a combination of the marklet portfolio and the risk free asset.

Capital Market Line is constructed:

CML is cnostructed as the Capital Allocation Line constructed from money markets and the market portfolio.

Variance of a portfolio =

Weighted sum of the elements of the covariance matrix

Measure the contribution of a single stock to overall portfolio risk

calculate the single stock’s covariance with the market portfolio.

Difference between security market line (SML) and capital market line (CML)

CML: graphs risk premiums of efficient portfolios (ie comp[rised of mkt portfolio and risk free asset) as a function of STANDARD DEVIATION.

SML: charts INDIVIDUAL ASSET risk premiums as a function of asset risk; the relevant risk measure for individual assets is the contribution of the asset to portfolio varianec - ie the BETA of the asset

SML is valid for the entire portfolio and for individual assets

Applications for CAPM (4)

- Provides a benchmark for investment performance. Recognise beta of portfolio , then investment returns are appropriately adjusted for market risk
- Consensus estimates to support stock selection. recognise a stocks exposure to market risk, then determine a fair rate of return
- Provides inputs for calculating the required rate of return on a capital budgeting project or equity valuation.
- Guide to pricing instruments in (and services of) non traded entities

Regression equation of single index model, what is the intercept

Intercept of the single index regression model is (alpha), which is the security’s expected excess turn when the market excess return is zero

Single index regression model, what is the slope coefficient

The slope coefficient is beta, ie the security’s sensitivity to the index. The amount by which the security return tends to increase or decrease for every 1% increase or decease in the return on the index.

Single index model, what is e

E is the zero mean, firm specific surprise in security returning time t, also called the residual.

Total risk =

Total risk = systematic risk + firm specific risk

COVARIANCE =

COVARIANCE = product of betas x market index risk

Correlation =

Correlations = product of correlations with the market index

Limitations of CAPM

Assumes unlimited capacity to borrow and lend, but when there are restrictions there is no unique point tendency betw CML and efficient frontier.

There is no truly risk free asset

Zero beta model and CAPM

- Developed by Black (1972)
- Zero beta model assumes beta of zero, relies on unrestricted shrt selling
- Short sell because there is another portfolio on the inefficient portion of the efficent frontier, their returns are uncorreltated so the companion portfolio’s beta must be zero
- CAPM assumes unrestricted borrowing and lending at the risk free rate, with restrictions there is no unique point of tengency between the efficient frontier and the capital market line

Multifactor SML

Attempt to recognize various sources of risk

Arbitrage pricing theory: assumptions

- Security returns can be described by a factor model
- There a sufficient securities to diversify away idiosyncratic risk
- Well functioning securities markets do not allow for the persistence of arbitrage opportunities

Arbitrage

Riskless profits

Law of one price

If two assets are equivalent in all economically relevant respects, then they should have the same market price