finance final 2

Payback= ____decision model to ___.

Easy, administer

Payback

Assumes that there is an

outflow of cash at the beginning of the

project and a series of cash inflows during future periods.

Payback

How soon will I recover my

initial investment?

Beta = the

measure of risk.

Sigma = the

measure of volatility

Risk

A measure of the uncertainty within a

group of potential outcomes.

Risk

It’s an event in which there is a

chance of some loss or gain.

Risk

If there is no uncertainty,

there is no risk, and we can say that the event is risk-free.

We associate risk with ____.

uncertainty

Why measure and analyze the risk of an investment?

We want to make an

informed decision.

Can we measure risk?

Yes.

Compared to our own __performance ( σ Sigma)

historic

Compared to a ____ performance (β Beta

benchmark (others)

Calculating the Variance and Std Deviation of Returns

This works with

$$ and % (returns).

Calculating the Variance and Std Deviation of Returns

in spreadsheet form:

=VAR.S(choose data range)

=STDEV.S(choose data range)

Diversification Lowers, but does

not eliminate all risk

When some stocks that move down are combined with other stocks that move up at the same time,

overall risk of portfolio falls.

No matter what we do, we simply can’t eliminate

all risk because risk falls into two buckets:

No matter what we do, we simply can’t eliminate all risk because risk falls into two buckets:

systemic (systematic) & firm-specific (non-systematic).

We can minimize nonsystematic risk through diversification but can never get rid of

Systematic risk unless we only by the risk free asset.

As we add more assets to a portfolio, we’re able to

eliminate more firm-specific risk.

if we add enough stocks to the portfolio, we

eventually end up

with only systematic risk

Higher expected returns are typically accompanied by

wider range of possible outcomes, thus more risk.

Diversification spreads wealth over a _____. This is to reduce some, but not all, ___.

variety of investment opportunities, risk

That’s because there are two components of risk:

• Nonsystematic risk that we can

eliminate through diversification.

That’s because there are two components of risk:

Systematic risk that we

cannot eliminate through diversification.

Market-wide risk that impact all stocks

Standard deviation (Sigma) is a measure of a stock’s

volatility,including both systematic and nonsystematic risk.

Standard deviation (Sigma) does a good job of measuring ________– or the _______

stand-alone risk, variability of a stock’s returns relative to its own average return.

stock’s returns relative to its own average return.

But it tells us nothing of the stock’s performance compared to a

benchmark of other stocks.

β is the relative tendency of a

security’s returns to respond to overall market fluctuations.

Beta measures the_________. It is a relative measure vs the ___

sensitivity of a stock vs the market (benchmark), entire market.

Beta captures the

variability of a particular stock’s returns relative to the variability of the market’s returns

The “market” is a portfolio of all

risky assets – which is impossible to work with.

As a proxy or substitute, we typically use the ___ as the Market.

S&P 500

The Market Beta (β) =

always 1.0

Risk is defined as "the possibility of ____“ and Volatility is defined as “a tendency to____

loss or injury, change quickly and unpredictably.

Risk refers to the possibility of loss, which is

outcome focused.

Volatility on the other hand, refers to a ____ change, which isn’t centered on the ___.

quick, unpredictable_, outcome

The most frequently used measure of volatility is called

standard deviation.

Standard deviation takes the

variation from the average and standardizes it into units that are comparable

Volatility acts as noise, while Beta (risk) is

worth paying attention to.

different Sigma, but same Beta

The Beta riskiness of an entire portfolio is observed by calculating the

weighted average of Betas in the portfolio.

So, taking on more risk can cause more reward in an “__” market, or more risk can mean less reward

in a “___” market.

up_, down

For investors to accept more risk when owning an asset,

they require a

higher return.

Just investing in the market carries risk – greater than the

risk-free rate.

If there is no prospect of a higher return, then smart investors will just

invest in Treasuries.

EXPECTED RETURN

default risk, maturity risk, risk-free rate, Smart investors want

compensation for these risks. Market trading sets YTMs to cover these risks.

This illustrates risk for bonds. We noted two kinds of risk

that must be accounted for after the risk-free rate.

Stock investors face risk when they choose the

_______. And any individual company has ____ relative to the market

overall market instead of risk-free Treasuries, some risk

COMPANY RISK RELATIVE TO MARKET

This is how variable a stock’s returns are relative to the market. Even in a portfolio.

OVERALL MARKET RISK

The market is a very large portfolio.

Risk and Return – Stocks

Smart investors buying risky assets want:

1) At least the risk-free rate.

(2) Compensation for taking on market risk generally.

(3) Compensation related to risk of any particular asset/stock

– relative to the market

PREMIUM FOR COMPANY RISK RELATIVE TO

MARKET

for stocks = beta (β)

PREMIUM FOR MARKET RISK – FOR INVESTING

IN THE MARKET GENERALLY

market risk premium = (rm - rf)

RISK-FREE RATE

risk-free rate (rf)

Capital Asset Pricing Model

r = rf + β(rM - rf)

It is also useful to measure project specific risk - the riskier the project, the

higher the required return.

Notice that the stock moves in the same direction as the market. Just by more.

Calculate beta in four ways:

Regression analysis, stock returns versus market returns.

Beta is coefficient of X. (Market is S&P 500.)

(2) % chg in stock / % chg in market.

=SLOPE(stock returns, market returns)

(4) COV(stock returns, market returns) / VAR(market returns)

Calculate beta excel

=SLOPE(stock returns, market returns), COV(stock returns, market returns) / VAR(market returns)

slope function

Avg return on stock / avg return on market

rise/run

• The stock is more sensitive than stock market.

• The stock is more risky than the stock market.

For a portfolio’s beta, we can use a weighted average

of the betas of the securities in the portfolio :

wi is the percentage weight of the individual asset in the portfolio.

• βi is the beta of the individual asset.

The sum of the percentage weights equal ___

The sum the weights times the betas equal the ____

1., portfolio’s beta

The beta of a portfolio is the average of the betas of the individual

holdings, weighted by the investment in each security.

If the overall market moves + or -20%, a diversified portfolio of stocks with beta = 0.5 would have one-half the volatility (+ or- 20% × 0.5 = + or - 10%).

Beta = 1.0: Moves

just like the market. Same level of risk.

Beta > 1.0:

More variable than market. Riskier than market overall.

Beta < 1.0:

Less variable than market. Less risky than market overall.

Beta < 0: Moves

opposite the market (up when market goes down).

____ = growth rate

ROE × Plowback %

Plowback % is also sometimes called

retention ratio.

This is the full return. It’s (r) and E(r) — a____

It’s a required return to make ______

future expected return, investing take place.

Current Risk-free rate = ___

Market rate of return = ___

Historic Market risk premium = ___

Risk measure = ___

rf_, rM, (rM – rf)_, β

Risk-free rate = rf

• We use yield on _____

CURRENT 1-year Treasury Bill.

Why the most current 1YR UST?

If you don’t buy a stock, you will park your money in T-Bills until you are

ready to buy a stock—and the T-Bill you will buy is the CURRENT T-Bill.

Broad market return = rm

• We use a

long-term AVERAGE return of the stock market (S&P 500)

ong-term average Treasury bill return = rf

• We use a

long-term AVERAGE historical return on 1-year Treasury bill

Market risk premium = (rM – rf)

aka Equity Premium aka “average risk premium”

• We use

HISTORIC difference between Market and T-Bill

Market risk premium = (rM – rf)

aka Equity Premium aka “average risk premium”

• We use HISTORIC difference between Market and T-Bills.

Why historic?

It’s investor behavior, on average.

Risk measure = Beta (β)

• We use_____

• A particular stock’s beta is the ___risk relative to the market

HISTORIC relationship between the returns of an

individual equity investment and the returns of the

entire Stock Market, additional

Required Return = (r)

• It’s what investors ___by investing in a stock.

• It’s what they want to give_____. By

investing in a stock.

• This is the investor’s____

And it is the “r” we might use as a ___

want , up their capital for., opportunity cost., discount rate.

r is also called

required return

discount rate

interest rate

cost of capital (cost of

equity capital when using

CAPM)

YTM (for bonds)

hurdle rate (in capital

budgeting)

it also always an opportunity cost

A current one-year Treasury yields 4.5%, which is a little higher than the 5-year average of the one-year yield of 4.1%. A good estimate of a long-term return on S&P 500 is about 9.2%. And your company’s stock beta is 1.2.

What is an estimate of your company’s required return (r)?

CAPM = r = rf + (rm – rf)β

r = rf + β(rM - rf) where Theory of the relationship between

risk and return

= rf + β(rM - rf) States that the

expected risk premium on any security equals its Beta times the Market Risk Premium

The market was up last month by 3.0%. A specific stock was up 3.6%. What is an estimate of the stock’s beta?

Beta = % chg in stock / % chg in market

On average, when the Market changed 1%, the individual stock

(Turbo Tech) changed 0.8%.

B = 0.8

When the Market runs out 1%,

Turbo Tech rises up 0.8%.

Stock is less sensitive than Market.

Stock is less risky than Market.

r =

Risk-free rate + Beta × (Average risk premium)

Risk-Free Rate = 1.75%.

Market Risk Premium = “average risk premium” = 7.0%

What is the risk premium for a stock that has a Beta of 0.8?

Risk premium on stock = .80 × 7.0% = 5.6%

Risk-Free Rate = 1.75%.

Market Risk Premium = “average risk premium” = 7.0%

What is the risk premium for a stock that has a Beta of 0.8?

Risk premium on stock = .80 × 7.0% = 5.6%

) = 1.75% + 5.6% = 7.35%