Fin 400 Ch 3

Assumptions of CAPM

1) single holding period 2) identical expectations 3) can borrow or lend unlimited amounts at risk free rate 4) assets are perfectly divisible 5) no taxes and no transaction costs 6) buying and selling won't influence stock prices 7) quantities of all assets are given and fixed

Security Market Line (SML)

Also part of the CAPM, gives risk/return relationship for individual stocks measure of risk is the beta

CML on expected rate of return

Any efficient portfolio is equal to the risk free rate plus a risk premium

Arbitrage Pricing Theory vs CAPM

CAPM is a single factor model APT risk and return is more complex and may be due to multiple factors such as GDP growth, expected inflation, tax rate changes, and dividend yield

Problems with CAPM

Its virtually impossible to prove investors behave like the CAPM theory

Efficient Portfolios

Offers most return for given amount of risk or least risk for a given amount of return

Volatility def.

amount of uncertainty or risk about the size of changes in a security's value

CAPM*

an equilibrium model that specifies the relationship between risk and required rate of return for assets held in well diversified portfolios only 1 factor affects risk:

CAPM/SML

based on expectations, betas are calculated using historical data, but it still provides a good framework for thinking about risk and return

Beta

beta = 1.0 average risk beta less than 1, less risky than average beta more than 1, more riskier than average most stocks have betas in range of .5 to 1.5

SML Indicates

betas of portfolios of 10 or more randomly selected stocks are reasonably stable

Higher volatility =

can change dramatically over a short time period in either direction

Capital Market Line (CML)

linear combinations of the risk free asset and Portfolio M Portfolio below the CML are inferior: CML defines the new efficient set, all investors will choose a portfolio on the CML Gives risk/return relationship for efficient portfolios

CML Formula

r(portfolio) = rf + [(rm - rf)/sdm] *sdp

Expected return of portfolio with several stocks Formula

r(portfolio) = w(stock a) * r(stock a) + (1 - wstock a) * r(stock b)

Required return for Stock under APT

r(stock) = rf + (rstock -rf)*b(stock1 to factor) +(rstock2 -rf)*b(stock2 to factor) +..... Sum (r(stock) - rf)*b(stock and factor)

SML Formula

r(stock) = rf + RP(market) * B(stock)

How betas are calculated

regression line of past returns on stock vs returns on the market at least 3 years of monthly returns/ 1 year of weekly returns; most analysts use 5 years of monthly returns

Lower volatility =

security's value doesn't fluctuate as dramatically but changes at a steady pace over a period of time

Status of APT

slow acceptance because model doesn't specify what factors influence stock returns