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Risk an Rates of Return

expected benefits or returns

to be received from an investment come in the form of the cash flows that the investment generates

expected cash flow (X)

X= sum[(Xi)*P(Xi)]
Xi=cash flow in the ith state of the economy
P(Xi)=the probability of the ith cash flow


defined as the possible variation in cash flow about an expected cash flow.

Risk may be measured by

the standard deviation about the expected cash flow

Total variability of risk and diversification can be divided into

the variability of returns unique to the security (diversifiable or unsystematic risk) and the risk related to market movements (nondiversifiable or systematic risk)

By diversifying, what kind of risk can the investor eliminate?

"unique" security risk. Systematic risk cannot be diversified away.

What does the characteristic line tell us?

the average movement in a firm's stock price in response to a movement in the general market, such as the S&P 500 index.


the slope of the characteristic line which is a measure of a stock's systematic or market risk.

If a security's beta equals one, a 10 percent increase in market returns will produce on average...

a 10 percent increase in security returns.

a security having a higher beta is...

more volatile and thus more risky than a security havng a lower beta value.

A portfolio's betais equal to

the average of the betas of the stocks in the portfolio

the required rate of return is...

the minimum rate necessary to compensate an investor for accepting the risk he or she associates with the purchase and ownership of an asset

What two factors determine the required rate of return for the investor?

(1) the risk-free rate of interest which recognizes the time value of money. (2) the risk premium which considers the riskiness (variability of returns) of the asset and the investor's attitude toward risk.


Capital asset pricing model.
The required rate of return for a given security can be expressed as--
req'd rate=risk-free rate + beta x (mkt return-risk-free rate)

Security market line

graphically illustrates the CAPM and designates the risk-return trade off existing in the market, where risk is defined in terms of beta according to the CAPM equation.

Criticism of CAPM

it relies totally on a security's sensitivity to the market for measuring risk. It is difficult to test empirically.

Historically, investors have received greater returns for greater risk-taking with the exception of

U.S. government bonds

The only portfolio with returns consistently exceeding the inflation rate is...

common stocks

Security returns vary from expected returns due to...

unanticipated changes in important economic forces, such as: industrial production, inflation, and interest rate structures.

Arbitrage Pricing Model (APM) may be expressed as follows...

where E(Ri)=the expected return for asset i, Rf=the risk-free rate, Sij=the sensitivity of stock returns to unexpected changes in economic force j, RPi=the market risk premium associated with an unexpected change in the jth economic force, N=the number of relevant economic forces.

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