yarmouk university chapter 05 - information...

Faculty of Economics and Business Administration

Department of Finance and Banking Sciences

B. F. 210

Principles of Financial Management (1)

Yarmouk University Chapter 05

Second Semester 2102/2013

Done by: Osama Alkhoun

Mobile 01: 0796484613

Mobile 02: 0785764063

Website: infoTechYU.weebly.com Osama Alkhoun

70

Chapter 05:

Risk and Return


71

Risk and Return

We must take the risk and return in consideration to make the best

financial decisions regarding a single security or portfolio

o Portfolio: This is a collection or group of assets.

Risk is the chance of financial loss or more formally the variability

of returns associated with a given asset.

Return is total gain or loss experienced on an investment over a

given period of time.

Its commonly measured by:

1t

1tttt

P

PPCr

:rt required return.

:C t cash flows from investment

:Pt price at period t (ending price [selling price])

:P 1-t price before period t (beginning [purchasing] price)

Example:

An investment was purchased before 2 years for a price at 20000 $ and

now its market price is 21500 $. It generated during the 2 years 800 $.

Find its return?

1t

1tttt

P

PPCr

20000

2000021500008rt

%5.11rt

20000:P

21500:P

800:C

1-t

t

t


72

Another investment is purchased for 20000 $ and now its trading for

30000 $. Find its returns?

1t

1tttt

P

PPCr

20000

20000-30000rt

%50rt

Risk References

1. Risk Indifferent: no Change in return would be required for an

increase in risk.

2. Risk Averse: an increased return would be required for an increase

of risk.

3. Risk Seeking: a decreased return would be accepted for an increase

in risk.

Probability: the chance that a given outcome will occur.

Probability Distribution: a model that relates probabilities the

associated outcomes. [total of all probabilities in the probability

distribution is 1 or 100%].

Normal Probability Distribution Bill Shaped

20000:P

30000:P

:C

1-t

t

t zero


73

Risk and Return Measurement:

Expanded Return: the most likely return on a given asset.

n

1i

ri iP*rr , when:

:r

Expected return.

:ir Return for outcome.

:ir

p Probability occurrence for an outcome.

:n Number of outcomes.


74

Example:

Given the following of two projects with their expected outcomes and

their probabilities. Find their Returns?

Project A Project B

ir ir

p ir ir

p

110 % 20% 20% 20%

22% 50% 16% 50%

-60% 30% 10% 30%

Total: 100% Total: 100%

n

1i

ri iP*rr

n

1i

ri iP*rr A

A

r =110% * 20% + 22% *50% + -60% *30%

= 15%

n

1i

ri iP*rrB

B

r = 20% * 20% + 16% *50% + 10% *30%

= 15%

To measure the risk we use the standard deviation.


75

Standard deviation ( ): the most common indicator of an assets risk

which measures the dispersion around the expected value.

ir

n

i

i prr *

2

1

Find the standard deviation for the previous questions:

ir

n

i

iA prr *

2

1

%30*%15%60%50*%15%22%20*%15%110222

A

%3.59A

ir

n

i

iB prr *

2

1

%30*%15%10%50*%15%16%20*%15%20222

B

%35.2B

The higher the standard deviation, the higher the risk.

The higher the risk the higher the required return.

If we have historical returns for an investment we can measure the

expected return by:

n

1i

i

n

rr


76

Example:

Given the following historical returns for an investment in ABC

Company. Find its expected return.

Year ir

2009 30%

2010 -10%

2011 50%

2012 5%

n

1i

i

n

rr

4

%5%50%10%30r

%75.18r

And we can measure the risk for such investments by:

n

i

i

n

rr

1

2

1

Example:

Find the risk for the previous questions:

n

i

i

n

rr

1

2

1

14

%75.18%5%75.18%50%75.18%10%75.18%302222

%58.26


77

Coefficient of Variation (CV): measures the risk per unit of return

rreturn

riskCV

The CV is more useful when we consider investments with

different returns and risks.

Example:

Find the CV for two projects

Project A:

%3.59 ,

and %15

r

Project B:

%35.2 ,

and %15

r

rreturn

riskCV

%15

%3.59ACV %93.3ACV

rreturn

riskCV

%15

35.2BCV %16.0ACV

Then we choose the Project B.


78

Example:

Given the following two projects with their

r and σ

Project σ ir

A 9% 12%

B 10% 20%

rreturn

riskCV

%12

%9ACV %75.0ACV

rreturn

riskCV

%20

%10BCV %50.0BCV

Which project is better?

Sol: the CV lower is better, and then the project B is better.

Risk of Portfolio

Efficient Portfolio: a portfolio that maximizes return for a given

level of risk. Or minimizes the risk for a given level of return.

Portfolio Return: is weighted average of returns on the individual

assets from which it’s formed.

n

i

iip rwr1

*

iw : Proportion of the asset from the total portfolio

ir : Return on an asset


79

Example:

Find the expected return from this portfolio with total 100000 $.

Stocks Return

ABBK 15 %

JOCM -3 %

TAMR 10 %

APOT 5 %

Sol:

n

i

iip rwr1

*

100000

25000*%5

100000

25000*%10

100000

25000*%3

100000

25000*%15pr

%25*%5%25*%10%25*%3%25*%15

pr

%25.1%50.2%75.0%75.3

pr

%75.6

pr

ABBK

25000

JOCM

25000

TAMR

25000

APOT

25000


80

Example:

An investor invests his money in a portfolio which consists of the

following investments:

Find the expected return from this portfolio.

Stocks Money

Invested Return

ABC 30000 $ 10%

XYZ 25000 $ -5%

EFG 15000 $ 25 %

KLM 20000 $ 16 %

Sol:

n

i

iip rwr1

*

90000

20000*%16

90000

15000*%25

90000

25000*%5

90000

30000*%10pr

0356.004167.001389.0033.0

pr

09638.0

pr 9.638%


81

Example:

Given the following information about a portfolio. Find its expected

return.

Company ir iw

A 5% 30%

B 10% 50%

C -3% 20%

Total 100%

n

i

iip rwr1

*

%20*%3%50*%10%30*%5

pr

006.005.0015.0

pr

059.0

pr 5.9%


82

Correlation ( ):

A statistical measure of relationship between any two variables.

The degree of correlation is measured by the correlation coefficient

which ranges from [+1 perfectly positively correlated] to

[-1 perfectly negatively correlated].

The perfectly positively correlated move exactly together

[direction, amount]

The perfectly negatively correlated move exactly in the opposite

directions [direction]

When the correlation is positive the variables move in the same

direction, while when it’s negative the variables move in the

opposite direction.

Some assets are uncorrelated: two variables that have no

interaction and correlation coefficient is zero.

-1 0 1

Negative Positive

Opposite

Direction

Uncorrelated

Area

Same

Direction


83

Diversification:

The correlation is an important topic in developing an efficient

portfolio.

To reduce overall risk its best to diversify by combining or adding

to portfolio assets that have a negative the overall variability of

returns (risk)

Combining uncorrelated assets can reduce risk but not so

effectively as combining negatively correlated assets, in the same

time it’s more effectively than combining positively correlated

assets.

The less the correlation the better the diversification that can

reduce risk.

The higher the risk the higher the expected return.

The less correlation the best diversification which reduce the risk

and provide sufficient returns.


84

Types of Risks:

The total risk consists of two kinds of risks as follows:

o Total Risk = Non Diversifiable Risk + Diversifiable Risk.

Non Diversifiable Risk: the relevant portion of an assets risk

attributable to market factors that effects all firms can’t be

eliminated by diversifiable.

o Called: Systematic, Market Risk.

Diversifiable risk: the portion of an assets risk that is attributable

to firm- specific, random causes can be eliminated by

diversification.

o Called: Unsystematic, Firm Risk.


85

Capital Asset Pricing Model (CAPM)

The basic theory that links risk and return for all assets

Total Risk = Non Diversifiable Risk + Diversifiable Risk

Zero

By constructing a portfolio we increase the securities we hold so

this will decrease the diversifiable risk of the portfolio and by that

we can eliminate all diversifiable risk so the only relevant risk is

non diversifiable risk.

Beta Coefficient

A relative measure of non diversifiable risk, it’s an index of the degree of

moment of an assets return to change in the market return which is the

return on the market portfolio of all traded securities in the market.

The steeper the slope of beta curve the more risky it is.

Risk ( )

Diversifiable

Non Diversifiable

# Of Security in portfolio

Risk Asset

Return Market

beta


86

The beta ( ) for the market is considered to be equal to [1], when beta

( ) for a security is [0.5] it moves only half as the market (in the same

direction). When beta ( ) = 2 twice as the market beta ( ) = -2

twice as the market in the opposite direction.

Portfolio betas

The weighted betas of the individual assets included in a portfolio

i

n

iip w

1

Measure for non diversifiable

wi: weighted of each security in a proportion to the portfolio

i: Beta for an asset of a portfolio.

Note: beta ( ) Risk

An investor wants to assess the risk of two portfolios to choose the best one.

Project A Project B

wi

i wi

i

0.1 1.65 0.1 0.8

0.3 1.0 0.1 1.0

0.2 1.3 0.2 0.65

0.2 1.1 0.5 0.75

0.2 1.25 0.1 1.5

i

n

iiA w

1

= (0.1*1.65) + (0.3*1.0) + (0.2*1.3) + (0.2*1.1) + (0.2*1.25)

= 1.195 = 1.2

i

n

iiB w

1

= (0.1*0.8) + (0.1*1.0) + (0.2*0.65) + (0.5*0.75) + (0.1*1.5)

= 0.91

Then the project B is better. When beta is large then, the higher the risk.


87

The Capital Asset Pricing Model (CAPM) can be divided into two parts:

1. The Risk Free return (RF): required return on risk free assets

usually treasury bills.

2. The Risk Premium: a premium required for taking an investment

that have a risks.

Market risk premium: return required for taking an average amount of

risk from the market portfolio.

Risk Premium Market = Return for the market – Risk Free

RPM = RM – RF

Risk Premium for a security = [RPM]

= [RM - RF]

Required Return = RF + RP

= RF + [RPM]

= RF + [RM - RF]

RF %

Return %

Risk premium

Risk Free

Required Free Return

Risk (Beta)

Risk Free Return

Risk Premium for Security

Risk Premium Market


88

Example:

Suppose that RF = 5%, and RM = 11%

Find the required return for a security where the beta = 1.5

Required Return = RF + [RM - RF]

= 5% + 1.5 [11% - 5%]

= 5% + 1.5 [6%]

= 5% + 9%

= 14%

The higher the Beta ( ) [risk] the higher the required return

The lower the Beta ( ) [risk] the lower the required return

Example:

ABC Corporation a software developer wishes to determine the required

Return on an investment which has a Beta ( ) of 1.5 the risk free return

7% and the market return is 11% given these information help him to

determine the required return.

Beta =1.5

RF = 7%

RM = 11%


= 7% + 1.5 [11% - 7%]

= 7% + 1.5 [4%]

= 7% + 6%

= 13%


89

Page 273 Problem 25:

a. Find the required return for an asset with beta 0.9 when the risk

free rate 8% and market return 12%.

Beta =0.9

RF=8%

RM=12%

RR = ?


= 8% + 0.9 [12% - 8%]

= 8% + 0.9 [4%]

= 8% + 3.6%

= 11.6%

b. Find the risk free for an asset with a required return 15% and beta

1.25 when the market returns 14%.

Beta =1.25

RM=14%

RR = 15%

RF =?


15% = RF + 1.25 [14% – RF]

15% = RF + 0.75 – 1.25RF

1.25RF = RF + 0.75 – 15%

0.25RF = 2.5%

RF = 10%


90

c. Find the market return for an asset with required return 16% and

beta of 1.1 when the risk free rate 9%.

RR=16%

Beta = 1.1

RF=9%

RM=?


16% = 9% + 1.1 [RM – 9%]

16% = 9% + 1.1 RM – 9.9%

16% - 9% + 9.9% = 1.1 RM

16.9% = 1.1 RM

RM = 15.36%

d. Find the beta for an asset with required return 15% and of 1.1 when

the risk free rate and market return are 10% and 12.5%.

Beta = ?

RM=12.5%

RR=15%

RF=10%


15% = 10% + [12.5% – 10%]

15% = 10% + [2.5%]

15% - 10% = [2.5%]

5% = [2.5%]

= 2


91

The Security Market Line (SML)

The deception of the CAPM:

A graph that reflects the required return in the market place for each of

non diversifiable risk (beta).

Factors affecting the SML:

1. Inflationary expectations:

Changes in inflation can affect the risk free return because

RF = R*+IP,

R*: real state of interest

IP: Infection Premium.

The Inflationary expectations affects the inflation premium and this will

change (affect) the RF, this also will affect (changes) required return

[RR = RF + (RM - RF)] and the change will be translated in a shift in the

SML.

Return

Risk (beta)

RF

SML


92

Parallel shift (upward or downward) to the SML.

Assume that the required return for an asset is 13% and the risk free

return in 7% includes 2% real rate and 5% inflation premium. =1.5

and the market return = 11%.

If the inflation premium increased to be 8%, find the required return

New:

RF = R* + IP

= 2% + 8%

= 10%

RM = RF + [PRM]

= 10% + [11% - 7%]

= 10% + 4%

= 14%


= 10% + 1.5 [14% - 10%]

= 10% + 1.5 [4%]

= 10% + 6%

= 16%

Return

Risk (beta)

RF1

SML2

RF3

RF2

SML1

SML3

Increase in

inflation

Decrease in

inflation

Deflation

Original


93

2. changes in Risk aversion:

The slope of the SML reflects the general risk preferences of investor

in the market place.

Most investors are risk averse they require increased returns for

increased risk.

The steeper the slope of SML the greater the degree of risk

aversion.

Any changes in the risk of an investment that results from

factors such as economic conditions, market crashes, etc… this

will cause the risk

Premium to increase and this will affect the required return and

increase it and this can be translated in a relation in the SML.

14%

13%

16%

11%

10%

Return

Risk (beta)

SML2

7%

SML1

Deflation

1 1.5

Return

Risk

RF

SML2

SML1

SML3

Increase in

risk aversion

Decrease in

risk aversion


94

Example:

Assume that an investment with a beta of 1.5 the risk free is 7% and the

return in the market is 11%. Assume that, the return in the market

increase because of economics factors to be 14% find:

1. The old RR.

2. The new RR.

Old:


= 7% + 1.5 [11% - 7%]

= 7% + 1.5 [4%]

= 7% + 6%

= 13%

New:


= 7% + 1.5 [14% - 7%]

= 7% + 1.5 [7%]

= 7% + 10.5%

= 17.5%


95

4 – Question P5-27

Security market line (SML) assumes that the risk free rate is currently 9%

and that market return is currently 13%.

a. Draw the SML on a set of non diversifiable risk (x-axis) required

return (y-axis) axes.

b. Calculate and label the market risk premium on the axes in part a.

RM = RF + [PRM]

13% = 9%+ [PRM]

13% - 9% = [PRM]

PRM = 4%

c. Given the previous data, calculate the required return on assets A

having a beta of 0.8 and asset B having a beta of 1.3.

Required Return (A) = RF + [RM - RF]

= 9% + 0.8 [13% - 9%]

= 9% + 0.8 [4%]

= 9% + 3.2%

= 12.2%

Required Return (B) = RF + [RM - RF]

= 9% + 1.3 [13% - 9%]

= 9% + 1.3 [4%]

= 9% + 5.2%

= 14.2%

Non diversifiable risk

Required return


96

d. Draw in the betas and required returns from part c for assets A and

B on the axes in part a. label the risk premium associated with each

of these assets, and discuss them.

Beta

Required Return

14.2%

12.2%

0.8 1.3


97

Page 274 – Question P5-28

Shift in the Security market line (SML) assumes that the risk free rate RF

is currently 8% and that market return RM is 12% AND asset A has a

beta (a) of 1.10.

a. Draw the SML on a set of non diversifiable risk (x-axis) required

return (y-axis) axes.

b. Use CAPM to calculate the required return RA, on asset A, and depict

asset A’s beta and required return on the SML drawn in part a.


= 8% + 1.1 [12% - 8%]

= 8% + 1.1 [4%]

= 8% + 4.4%

= 12.4%

c. Assume that as a result of recent economic events, inflationary

expectations have declined by 2%, lowering RF and RM to 6% and

10%, respectively. Draw the new SML on the axes in part a, and

calculate and show the new required return for asset A.


= 6% + 1.1 [10% - 6%]

= 6% + 1.1 [4%]

= 6% + 4.4%

= 10.4%


Required return


98

d. Assume that as a result of recent economic events, investors have

become more risk averse causing the market returns to rise by 1%,

to 13%. Ignoring the shift in part c, draw the new SML on the same

set of axes that you used before, and calculate and show new

required return for asset A.


= 6% + 1.1 [12% - 6%]

= 6% + 1.1 [6%]

= 6% + 6.6%

= 12.6%

e. From the previous changes, what conclusions can be drawn about

the impact of (1) decreased inflationary expectations and (2)

increased risk aversion on the required returns of risky assets?


99

Page 274 – Question P5-29

Integrative – risk, return, and CAPM Wolff enterprises must consider

several investment project, A through E, using the capital asset pricing

model (CAPM) and its graphical representation, the security market line

(SML). Relevant information is presented in the following table.

Item Rate of Return Beta, b

Risk Free asset 9% 0

Market portfolio 14 1.00

Project A -- 1.50

Project B -- 0.75

Project C -- 2.00

Project D -- 0

Project E -- - 0.5

a. Calculate (1) the required rate of return and (2) the risk premium

for each project, given its level of non diversifiable risk.

1. Required Return = RF + [RM - RF]

= 9% + 1.0 [14% - 9%]

= 9% + 1.0 [5%]

= 9% + 5%

= 14%

2. Risk premium for the market = RM - RF

= 14% - 9%

= 5%


100

b. Use in your finding in part a, to draw the security market line

(required return relative to non diversifiable risk).

c. Discuss the relative non diversifiable of projects A through E.

d. Assume that as a result of recent economic events, investors to

become less risk averse, causing the market returns to decline by

2%, to 12%. Calculate the new required return for asset A through

E, and draw the new security market line (SML) on the same set of

axes that you used in part B.

RM = 12% - 2% = 10%


= 9% + 1.50 [10% - 9%]

= 9% + 1.50 [1%]

= 9% + 1.5%

= 10.5%

Required Return (B) = RF + [RM - RF]

= 9% + 0.75 [10% - 9%]

= 9% + 0.75 [1%]

= 9% + 0.75%

= 9.75%


Required return


101

Required Return (C) = RF + [RM - RF]

= 9% + 2 [10% - 9%]

= 9% + 2 [1%]

= 9% + 2%

= 11%

Required Return (D) = RF + [RM - RF]

= 9% + 0 [10% - 9%]

= 9% + 0 [1%]

= 9% + 0%

= 9%

Required Return (E) = RF + [RM - RF]

= 9% + -0.5 [10% - 9%]

= 9% + -0.5 [1%]

= 9% + -0.5%

= 8.5%

e. Compare your finding in parts a and b with those in part d. what

conclusion can you draw about the impact of a decline in investor

risk aversion on the required returns of risky assets?

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