Finance Exam 2 (Ackermann)

RISK AND RETURN

RISK AND RETURN

Investors demand _______ for time and risk:

Compensation

Probabilities are between ___ and ___:

0 and 1

Probabilities must sum to....

1

A table of probabilities and outcomes is known as what?

A probability distribution

Distributions can be what two things?

1. discrete

2. continuous (like a normal distribution)

What is the formula for the mean or expected value of a discrete random variable X?

E(X) = prob1X1 + prob2X2 ....

1 = one possible outcome

prob = probability of that outcome

X = the return if outcome happens

The amount of dispersion in a graph of the probability distribution function is measured by what?

Variance and standard deviation

The ____ of a stock is the amount of dispersion in a graph:

Risk

- the more dispersion, the more risk

T or F: the standard deviation of individual stocks in a PORTFOLIO is a relevant measure of risk

False, the standard deviation is only a measure of risk for stocks that are not part of a portfolio

Portfolio theory

Encourages diversification of assets

Covariance and correlation measure what?

How two stocks move together

How a stock moves with the market

Covariance

Sum of prob[X - E(Rx)][Y - E(Ry)]

A negative covariance indicates what?

Stocks tend to move in opposite directions

The covariance gives a sense of what?

The magnitude and the direction of how two stocks move together

Correlation coefficients show what?

How tightly two stocks "track" each other (independent from magnitude)

The correlation coefficient falls between what two numbers ALWAYS?

-1.0 and 1.0

CorrXY = ?

CorrXY = (CovXY / sdXsdY)

sdX = ?

standard deviation of X

If CorrXY is zero, then the movements of stocks....

are unrelated to each other

Positive values of CorrXY mean what?

Stocks move in same direction

To earn rewards, you must do what?

Take risks; "be in it to win it"

Most investors like what?

Stocks with lots of return and low risk

What is one way you can lower the risk of a portfolio?

Through diversification

- By owning many stocks, if one stock does poorly, it is likely that another stock in the portfolio might do well and offset the loss

What are the most important things to know about a stock portfolio?

Return and risk!

Expected portfolio return equation:

E(Rp) = sum of W x E(R)

W = weight

E(R) = expected return

Portfolio risk is not what?

It is NOT a weighted average of the individual standard deviations of the stocks

Knowing how stocks move together is important for what?

Determining the risk of a portfolio

As covariance becomes more ______, the portfolio is made less risky:

Negative

Standard deviation equation:

the square root of the variance

Variance equation:

Wx^2sdx^2 + Wy^2sdy^2 + 2WxWyCovxy

The risk of a portfolio is less than what?

Than the risk of either stock by itself

The lower the correlation between the stocks, the lower the what?

The lower the standard deviation of the portfolio of both stocks (and lower standard deviation means lower risk)

The investor's goal is what?

To maximize return and minimize risk

- the investor can choose the weights of the different stocks in the portfolio to attain different risk-return combinations

Efficient Portfolio Frontier

What are the two types of risk?

1. Non-systematic risk

2. Systematic risk

Non-systematic risk

Risk that can be diversified away by holding a portfolio of stocks as opposed to a single stock

What are some other names for non-systematic risk?

Diversifiable risk, unique risk, company specific risk

What are some sources of non-systematic risk?

strikes, lawsuits, industrial accidents

- these are risks that may affect a single company but will not affect all firms in the economy at the same time

Why do investors not require compensation in the form of higher returns for non-systematic risk?

Because non-systematic risk can be diversified away/reduced by diversification

Systematic risk

Risk that cannot be diversified away

- most firms in the market are affected in the same way by this type of risk

What are some other names for systematic risk?

non-diversifiable risk, market risk

Why do investors require compensation for systematic risk?

Because they cannot get rid of systematic risk just by diversifying their portfolio

- the higher the level of systematic risk present, the higher the required rate of return

Rate of return

The rate that shareholders demand for an investment

Total Risk = ?

Total Risk = Systematic Risk + Non-systematic Risk

What is the standard deviation when an asset is riskless?

Standard deviation is zero

Weights always add up to ______:

1.0

When we combine a riskfree asset with a risky asset, the risk-return tradeoff is what?

A straight-line

Expected Return - Standard Deviation Graph

Any portfolio is what?

A risky asset

- a portfolio can be thought of as a risky asset just like an individual stock

How can we obtain the best expected return for any level of risk?

By combining a riskfree asset with the market portfolio

Market portfolio

A weighted combination of all risky investments weighted by their value in the overall economy

Dow Jones

The average price of 30 selected industrial stocks, used as a measure of general market trends

T or F: the Dow Jones is not a market portfolio

True

A widow/the widower curve indicates that one should invest what?

3/4 of money in risk-free assets

A young gun curve indicates that one should invest what?

3/4 in riskier assets

The new frontier that should be invested in is called....

The market portfolio (M)

For a well-diversified portfolio, the amount that X (an additional investment) contributes to the risk of the portfolio depends on what?

Only on the covariance of X with the existing portfolio

- this means we can measure risk as the covariance of an individual stock with the investor's existing portfolio

Proxy

Agent, substitute, person authorized to act on behalf of another

In finance, we typically use what as a proxy for the investor's portfolio?

Some market index, such as the S&P 500

The market index is indicated by what letter?

M

The market index M represents what?

The average investor's portfolio

What is the relevant measure of the risk of a stock?

The covariance of its return with the market index

T or F: the variance of a stock measures its risk

FALSE, the variance of a stock does not measure its risk

The more a stock covaries _______ with the market, the riskier it is:

Positively

Beta of an asset

The measure of a stock's price sensitivity to that of the market index

Beta is commonly used to measure what?

Systematic risk

- this is closely related to the covariance of the asset with the market portfolio

CovXM =

CovXM = CorrXM sdX sdM

Covariance = correlation coefficient times standard deviation of X times standard deviation of the market

Beta equation:

Bx = (Covariance of asset / variance of market)

Variance

Standard deviation squared

The systematic risk of an asset is measured by what?

The asset's Beta

Covariance can also be called what?

Correlation coefficient

If an asset's beta is 2.0, what does this mean?

That it is twice as risky as the market

ex: if S&P falls 5%, the expected decline in the stock will be 10%

A beta of 1.0 means what?

That the stock is exactly as risky as the market index

The average stock has a beta of what?

1.0 (same as market index)

The beta of a risk-free asset is ____

Zero

How can you calculate a beta?

Run a regression

- You run a regression of the returns of the stock on the returns of the market index

Rstock =

Rstock = a + b Rmarket

- the value of b is an estimate of the beta

A regression program tells you the value of what?

b (an estimate of beta)

The slope of the line on a regression graph is what?

The beta of the stock

- it tells you how far the price of the stock is expected to move if the market moves 1%

The slope is the beta of the stock. What does it tell you?

How much the stock is expected to change when market changes

What is the beta of a portfolio?

The weighted average of the betas of the individual stocks

CAPM

Capital Asset Pricing Model

- a linear model that relates risk and return

Re = Rf + Beta(Rm-Rf).

Required Return equation

Required Return = Risk-free rate + Risk premium

For a risk-free security, what is the risk premium?

Zero

What is an example of a risk-free security?

Government bill

The risk premium for a risky stock is what?

Greater than zero

How can you determine the required return?

Using CAPM

Kx = RF + Beta[E(Rm) - RF]

Kx, or the required return for asset x, can be denoted as what?

E(Rx)

- this is the expected return of asset x

What does E(Rm) indicate?

Expected return on the market index

RF = ?

Riskfree rate

If Beta = 1.0, then what does Kx equal?

Kx = E(Rm) because if the beta is 1.0, then it is exactly as risky as the market index so the expected returns will be the same

What is the risk premium?

It is the amount of return above the risk-free rate that investors demand for holding risky stocks

B[E(Rm) - RF]

What is the market risk premium?

The market risk premium is the excess return that investors require for choosing to purchase stocks over "risk-free" securities

E(Rm) - RF

Since the beta of the market is 1.0, any stock that has this beta has the market risk premium.

The graph of Kx vs. Beta is called what?

The security market line

Security market line

This tells us how the required return of an asset varies with its beta

The portfolio risk is equal to what?

The standard deviation of the portfolio

Expected return

the return on a risky asset expected in the future

MARKET EFFICIENCY

MARKET EFFICIENCY

What does market efficiency mean?

Means you get exactly what you pay for when you buy a stock