Bài giảng tài chính doanh nghiệp chương 1 rủi ro và tỷ suất lợi nhuận

tài chính doanh nghiệp

Chương 1

Rủi ro và tỷ suất lợi nhuận

Lợi nhuận :các khái niệm cơ bản

1. Lợi nhuận :các khái niệm cơ bản

2. Rủi ro: các khái niệm cơ bản

3. Rủi ro riêng lẻ

4. Rủi ro thị trường (rủi ro danh mục)

5. Rủi ro và lợi nhuận: CAPM/SML

For example, if $1,000 is invested and $1,100 is

returned after one year, the rate of return for this investment is:

What is investment risk?

Two types of investment risk

Stand-alone risk

Portfolio risk

Investment risk is related to the probability

of earning a low or negative actual return.The greater the chance of lower than

expected or negative returns, the riskier the investment

Probability distributions

A listing of all possible outcomes, and the

probability of each occurrence

Can be shown graphically

Rate of Return (%) 100

15 0

-70

Firm X

Firm Y

Selected Realized Returns,

1926 – 2004

Average StandardReturn DeviationSmall-company stocks 17.5% 33.1%

Large-company stocks 12.4 20.3

Large-company stocks 12.4 20.3

L-T corporate bonds 6.2 8.6

L-T government bonds 5.8 9.3

U.S Treasury bills 3.8 3.1

Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), p28.

Why is the T-bill return independent

of the economy? Do T-bills promise a

completely risk-free return?

T-bills will return the promised 5.5%, regardless

of the economy.

No, T-bills do not provide a completely risk-free

return, as they are still exposed to inflation

return, as they are still exposed to inflation

Although, very little unexpected inflation is likely

to occur over such a short period of time.

T-bills are also risky in terms of reinvestment rate risk.

T-bills are risk-free in the default sense of the

word.

How do the returns of HT and Coll behave in relation to the market?

HT – Moves with the economy, and has

a positive correlation This is typical.

Coll – Is countercyclical with the

Coll – Is countercyclical with the

economy, and has a negative

correlation This is unusual.

Calculating the expected return

P r r

return of

rate

expected r

(0.2) (30%)

(0.4) (15%)

(0.2) (-7%)

(0.1) (-27%)

r

P r r

HT

^

1 i

i i

^

= +

+ +

+

=

= ∑

=

Summary of expected returns

HT has the highest expected return, and appears

to be the best investment alternative, but is it

Calculating standard deviation

deviation Standard

= σ

2Variance = σ

=

Variance = σ

= σ

i 2 N

1 i

i r ) P (r

=

−

Standard deviation for each investment

(0.2) 5.5)

(5.5 (0.1)

-5.5) -

(5.5

P ) r (r

2 2

N

1 i

i 2

^ i

18.8%

20.0%

13.2%

0.0%

(0.1) 5.5)

(5.5

-(0.2) 5.5)

(5.5 (0.4)

-5.5) -

(5.5

(0.2) 5.5)

(5.5 (0.1)

-5.5) -

(5.5

Coll bills

T

2

2 2

σσ

σ

Comparing standard deviations

Comments on standard

deviation as a measure of risk

Standard deviation (σi) measures

total, or stand-alone, risk.

The larger σi is, the lower the

The larger σi is, the lower the

probability that actual returns will be closer to expected returns.

Larger σi is associated with a wider

probability distribution of returns.

Comparing risk and return

HT, despite having the highest standard deviation

of returns, has a relatively average CV

Investor attitude towards risk

Risk aversion – assumes investors dislike

risk and require higher rates of return to

encourage them to hold riskier securities

Risk premium – the difference between

the return on a risky asset and a riskless

asset, which serves as compensation for

investors to hold riskier securities

Portfolio construction:

Risk and return

Assume a two-stock portfolio is created with

$50,000 invested in both HT and Collections

A portfolio’s expected return is a weighted

average of the returns of the portfolio’s

average of the returns of the portfolio’s

component assets

Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised

Calculating portfolio expected return

: average weighted

a is r

(12.4%) 0.5

r

r w r

i

^ i p

^

= +

=

=

An alternative method for determining portfolio expected return

Calculating portfolio standard

deviation and CV

3.4%

6.7) -

(7.5 0.40

6.7) -

(3.0 0.20

6.7) -

(0.0 0.10

2 2 2

3.4%

CV

3.4%

6.7) -

(12.0 0.10

6.7) -

(9.5 0.20

6.7) -

(7.5 0.40

p

2

2 p

+

=

σ

Comments on portfolio risk

measures

σp = 3.4% is much lower than the σi of

either stock (σHT = 20.0%; σColl. = 13.2%)

σp = 3.4% is lower than the weighted

average of HT and Coll.’s σ (16.6%)

p

average of HT and Coll.’s σ (16.6%)

Therefore, the portfolio provides the

average return of component stocks, but

lower than the average risk

Why? Negative correlation between stocks

General comments about risk

σ ≈ 35% for an average stock.

Most stocks are positively (though

not perfectly) correlated with the

not perfectly) correlated with the

market (i.e., ρ between 0 and 1).

Combining stocks in a portfolio

generally lowers risk.

Returns distribution for two perfectly negatively correlated stocks (ρ = -1.0)

Returns distribution for two perfectly positively correlated stocks (ρ = 1.0)

-10

0 15

-10

Creating a portfolio:

Beginning with one stock and adding

randomly selected stocks to portfolio

σp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio

Expected return of the portfolio would

Expected return of the portfolio would

remain relatively constant

Eventually the diversification benefits of

adding more stocks dissipates (after about

10 stocks), and for large stock portfolios, σ

Illustrating diversification effects of

0

Stand-Alone Risk, σσσσp

Breaking down sources of riskStand-alone risk = Market risk + Diversifiable risk

Market risk – portion of a security’s stand-alone

Market risk – portion of a security’s stand-alone risk that cannot be eliminated through

diversification Measured by beta

Diversifiable risk – portion of a security’s

stand-alone risk that can be eliminated through

Failure to diversify

If an investor chooses to hold a one-stock

portfolio (doesn’t diversify), would the investor

be compensated for the extra risk they bear?

NO!

Stand-alone risk is not important to a

Stand-alone risk is not important to a

well-diversified investor

Rational, risk-averse investors are concerned with σp, which is based upon market risk

There can be only one price (the market

return) for a given security

No compensation should be earned for

Capital Asset Pricing Model

Measures a stock’s market risk, and

shows a stock’s volatility relative to the market.

market.

Indicates how risky a stock is if the

stock is held in a well-diversified

portfolio.

Can the beta of a security be

negative?

Yes, if the correlation between Stock

i and the market is negative (i.e.,

ρi,m < 0).

If the correlation is negative, the

If the correlation is negative, the

regression line would slope

downward, and the beta would be

negative.

However, a negative beta is highly

unlikely.

Calculating betas

Well-diversified investors are primarily

concerned with how a stock is expected to

move relative to the market in the future

Without a crystal ball to predict the future,

Without a crystal ball to predict the future,

analysts are forced to rely on historical data

A typical approach to estimate beta is to run

a regression of the security’s past returns

against the past returns of the market

The slope of the regression line is defined as

Tính beta như thế nào ?

Chạy hàm hồi quy regression với các

biến số là suất sinh lời cổ phiếu trên

trục Y và suất sinh lời thị trường trên

trục X.

trục X.

Độ nghiêng (hệ số góc) của đường hồi quy đo lường sự biến động tương quan của cổ phiếu hay là hệ số beta (b)

VD: dùng số liệu suất sinh lời quá

khứ của cổ phiếu KWE để tính beta

Lưu ý:

suất sinh lời trung bình của cổ phiếu

bao gồm: thu nhập từ cổ tức và chênh lệch giá cổ phiếu theo thời gian

lệch giá cổ phiếu theo thời gian

Suất sinh lời thị trường là chênh lệch giá trị thị trường của các cổ phiếu theo thời gian

Beta for KWE

Tính beta như thế nào ?

Đường hồi quy và beta, tính bằng

EXCELL với hàm “regression” và b = 0.83.

Thường sử dụng suất sinh lời trung

Thường sử dụng suất sinh lời trung

bình hằng tháng của 4 hay 5 năm để tạo đường hồi quy Đôi khi có thể

dùng số liệu trung bình 52 tuần của 1 năm.

Illustrating the calculation of beta

.

r i

_

20 15

Beta coefficients for

HT, Coll, and T-Bills

Comparing expected returns

and beta coefficients

Security Expected Return Beta

The Security Market Line (SML):

Calculating required rates of return

SML: ri = rRF + (rM – rRF) bi

r = r + (RP ) b

ri = rRF + (RPM) biAssume the yield curve is flat and that

rRF = 5.5% and RPM = 5.0%.

What is the market risk premium?

Additional return over the risk-free rate

needed to compensate investors for

assuming an average amount of risk

Its size depends on the perceived risk of

Its size depends on the perceived risk of

the stock market and investors’ degree of

risk aversion

Varies from year to year, but most

estimates suggest that it ranges between

Calculating required rates of return

Expected vs Required returns

r) r

( d Undervalue

12.1%

12.4%

HT

r

r

( ued Fairly val

5.5

5.5

bills

-T

r) r

( Overvalued

9.9

9.8

USR

r) r

( ued Fairly val

10.5

10.5

Market

^

^

^

=

<

=

An example:

Equally-weighted two-stock portfolio

Create a portfolio with 50% invested in

HT and 50% invested in Collections.

The beta of a portfolio is the weighted average of each of the stock’s betas.

The beta of a portfolio is the weighted average of each of the stock’s betas.

bP = wHT bHT + wColl bColl

bP = 0.5 (1.32) + 0.5 (-0.87)

Calculating portfolio required returns

The required return of a portfolio is the weighted average of each of the stock’s required returns

rP = wHT rHT + wColl rColl

r = 0.5 (12.10%) + 0.5 (1.15%)

rP = 0.5 (12.10%) + 0.5 (1.15%)

rP = 6.63%

Or, using the portfolio’s beta, CAPM can be used

to solve for expected return

rP = rRF + (RPM) bP

rP = 5.5% + (5.0%) (0.225)

Factors that change the SML

What if investors raise inflation expectations

by 3%, what would happen to the SML?

Factors that change the SML

What if investors’ risk aversion increased, causing the market risk premium to increase

by 3%, what would happen to the SML?

Verifying the CAPM empirically

The CAPM has not been verified

completely.

Statistical tests have problems that

Statistical tests have problems that

make verification almost impossible.

Some argue that there are additional risk factors, other than the market risk premium, that must be considered.

More thoughts on the CAPM

Investors seem to be concerned with both

market risk and total risk Therefore, the

SML may not produce a correct estimate of ri

r = r + (r – r ) b + ???

ri = rRF + (rM – rRF) bi + ???

CAPM/SML concepts are based upon

expectations, but betas are calculated using historical data A company’s historical data may not reflect investors’ expectations about future riskiness