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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

FIN3IPM

I NVESTMENT AND

P ORTFOLIO M ANAGEMENT

Semester 1/2016

2-2

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

2-2

LECTURE OUTLINE

1. Subject Communication

2. Subject Outline

3. Subject Assessments and Text Book

4. Asset Classes

5. Return

6. Risk

2-3

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

2-3

SUBJECT COMMUNICATION

1. Subject Lecturer and Tutor

Mail: [email protected]

Office: HU3-130

Mobile: 0449188686

2. LMS

News Forum

Student Forum

Lecture Notes

Tutorial Questions

Tutorial Answers

Online Quizzes

Group Assignment – You need to form a group of 3-4!!!

Exam Information

Other Information

2-4

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

2-4

WHAT DOES THIS SUBJECT COVER

In this subject, we will cover investment theory

Body of knowledge used to support the decision-making process of

choosing investments for various purposes

This includes

Portfolio Theory

Capital Asset Pricing Model

Efficient-Market Hypothesis

Many other concepts

The subject will give you the intellectual tools necessary

to better understand the dynamics of a complex

investment environment

2-5

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

2-5

WHAT DOES THIS SUBJECT COVER

Week

Week starting Date Topic

Activity Assessment

Resources

SILOs GCs

代写 McGraw-Hill FIN3IPM INVESTMENT PORTFOLIO MANAGEMENT

29 February 2016

Asset Classes and Risk and

Return

Lecture 1

Bodie Chapter 2 & 5

1 A-F

7 March 2016 Portfolio Theory
代写 McGraw-Hill FIN3IPM INVESTMENT PORTFOLIO MANAGEMENT

Lecture 2

Tutorial 1

Bodie Chapter 6

1 A-F

14 March 2016 Asset Pricing Theories

Lecture 3

Tutorial 2

Bodie Chapter 7

2 A-F

21 March 2016 Market Efficiency

Lecture 4

Tutorial 3

Bodie Chapter 8

5 A-F

28 March 2016 Mid Semester Break

4 April 2016 Equity Valuation

Lecture 5

Tutorial 4

Bodie Chapter 11

4 A-F

11 April 2016

Macroeconomic and

Industry Analysis

Lecture6

Tutorial 5

Bodie Chapter 12

5 A-F

18 April 2016

Financial Statement

Analysis

Lecture 7

Tutorial 6

Bodie Chapter 13

1, 2, 4, 5 A-F

25 April 2016 Bond Valuation

Lecture 8

Tutorial 7

Bodie Chapter 9

3 A-F

2 May 2016 Managing Bond Portfolios

Lecture 9

Tutorial 8

Bodie Chapter 10

3 A-F

9 May 2016

Managed Funds and Hedge

Funds

Lecture 10

Tutorial 9

Bodie Chapters 16 & 17

6 A-F

16 May 2016

Portfolio Performance and

Evaluation

Lecture 11

Tutorial 10

Bodie Chapter 18

6 A-F

23 May 2016 Exam Revision

Lecture 12

Tutorial 11

1-6 A-F

30 May–2 June 2016 STUDY VACATION

3 June–20 June 2016

CENTRAL EXAMINATION PERIOD

2-6

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

ASSESSMENT & PRESCRIBED

TEXTBOOK

Assessment Task % of Final Grade When

Weekly Online Quizzes 20% Every week, from Week 2,

due Sunday 11pm

Group Assignment 20% Due Week 11

Final Exam (3 hours) 60% During Central Exam Period

2-6

Prescribed textbook:

Principles of Investments

Bodie, Z., Drew, M., Basu, A., Kane, A., and

Marcus, A (2013)

McGraw Hill

2-7

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

IS THIS STUFF PRACTICAL

Investment theory is widely used in industry across

many fields including (but not limited to):

– Fund Management

– Investment Banking

– Personal Finance & Financial Planning

– Insurance

The knowledge taught in this subject is essential for

any good job in the finance industry!

2-7

2-8

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

SOME GOOD QUOTES

“Genius is 1% talent and 99% percent hard work”

Albert Einstein

“Learning is not child’s play; we cannot learn without

pain”

Aristotle

“Having knowledge but lacking the power to express it

clearly, is no better than never having any ideas at all”

Pericles

2-8

2-9

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

ASSET CLASSES

• Money markets – short term debt securities

– Treasury notes

– Bank-accepted bills

– Certificates of deposits

• Bond markets – long term debt securities

– Government bonds

– Corporate bonds

– Asset backed securities

• Equities – ownership stake in cash flows

– Ordinary shares

– Preference shares

• Derivatives - value derived from another security

– Options

– Forwards

– Futures

2-9

2-10

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Money Markets

• Treasury Notes

– Issued by the commonwealth government

– Maturity of between 5 and 26 weeks

– Highly liquid

– No default risk

– Traded at a discount

• Certificates of Deposits

– Issued by banks

– Maturity of 185 days or less

– Less liquid compared to TN, but still very liquid (especially CDs with less

than 3 months to maturity)

– Traded at a discount

• Bank-accepted Bills

– Issued by non-financial firm and guaranteed by a bank

– Maturities typically between 30 days and 180 days

– Traded at discount

2-10

2-11

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Bond Markets

• Government Bonds

– Issued by the commonwealth government

– Maturities in excess of one year, commonly in excess of 10 even 20 years

– Pay period coupons (effectively interest rate, calculated as a percentage of

the principal amount)

– Tradable on secondary market

– No default risk

• Corporate Bond

– Issued by a corporation

– All other characteristics the same as for government bonds

– Credit risk exists

• Asset Backed Security

– A security backed by a pool of assets (such as mortgage loans)

– The “pool backer” passes through monthly mortgage repayments made by

homeowners to the investors

– Has all the characteristics of a bond - initial investment, which

subsequently entitles you to periodic payments

2-11

2-12

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Equity Markets

• Ordinary Shares

– Residual claim on corporate cash flows

– As owners, have voting rights at annual meetings

– In the event of bankruptcy, what will shareholders receive?

– What is the maximum loss on a share purchased?

• Preference Shares

– Hybrid between debt and equity

– Entitled to fixed dividend (more akin to interest payment than dividend)

– Priority over ordinary shares (in case of bankruptcy) but junior to all debt

holders

2-12

2-13

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Derivative Markets

• Options

– Can be either call or put options

– Call options give the holder the right but not the obligation to buy the

underlying asset for a pre-determined price

– Put options give the holder the right but not the obligation to sell the

underlying asset for the pre-determined price

– The “pre-determined price” is known as a strike price or an exercise price

– The option will also have a maturity day

– Example:

– How much would 50 28 June 2012 call options with a strike price of 50

cost?

– What does the price of CBA need to be for you to profit from your call

option?

2-13

2-14

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Derivative Markets

• Futures

– An obligation to buy/sell the underlying asset at a pre-determined

price

– The “pre-determined” price is known as the futures price

– Maturity day is the day on which the transaction will occur

– Buying a futures contract obliges you to buy the underlying asset

– Selling a futures contract obliges you to sell the underlying asset

Which contract gives you greater flexibility?

 Options contract

 Futures contract

Which contract is more likely to cost more?

 Options contract

 Futures contract

2-14

2-15

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Rates of Return

One period investment: regardless of the length of the

period.

Holding period return (HPR):

HPR = [P S – P B + CF] / P B where

P S = Sale price (or P 1 )

P B = Buy price ($ you put up) (or P 0 )

CF = Cash flow during holding period

– HPR is expressed as a percentage of the initial

buy price.

2-15

2-16

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Rates of Return

Unadjusted HPR is not very useful as it simply tells us

the return we made over the holding period.

– Since most investments are held over a different period, it is

hard for us to compare the relative performance of different

investments.

– To overcome this we generally express returns over a

common time period – most commonly an annual period

How to annualize:

– If holding period greater than 1 year:

 Without compounding: HPR ann = HPR/n

 With compounding: HPR ann =

– If holding period is less than 1 year:

 Without compounding: HPR ann =

 With compounding: HPR ann =

2-16

HPR x n

[(1+HPR) n ] –1

[(1+HPR) 1/n ] –1

n=no.

years

n=no.

compounding

periods

2-17

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Rates of Return

An example when the HP is < 1 year: Suppose you

have a 5% HPR on a 3-month investment. What is the

annual rate of return with and without compounding?

• Without compounding:

• With:

Q: Why is the compound return greater than the simple

return?

2-17

n = 12/3 = 4 so HPR ann = HPR*n = 0.05*4 = 20%

HPR ann = (1.05 4 ) - 1 = 21.55%

2-18

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Arithmetic Average

Finding the average HPR for a time series of returns:

• Without compounding:

• n = number of time periods

• This method assumes that returns will not compound

(ie. each periods return is independent of other

periods returns)





1 T

avg

HPR

continued

2-19

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Arithmetic Average

AAR =





1 T

avg

HPR

.1762) .3446 .0311 .2098 .2335 .4463 (-.2156

HPR avg 

     



17.51%

An example: You have the following rate s of return on a stock:

2000 –21.56%

2001 44.63%

2002 23.35%

2003 20.98%

2004 3.11%

2005 34.46%

2006 17.62%

2-20

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Geometric Average

With compounding (geometric average or GAR: geometric average

return):

GAR = 15.61%

1 ) HPR (1 HPR

/ 1

1 T

T avg















 





1 1.1762) 1.3446 1.0311 1.2098 1.2335 1.4463 (0.7844 HPR

1/7

avg

         15.61%

An example: You have the following rate of return on a stock:

2000 –21.56%

2001 44.63%

2002 23.35%

2003 20.98%

2004 3.11%

2005 34.46%

2006 17.62%

2-21

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Measuring Ex-post (past) Returns

Q: When should you use the GAR and when should you use the

AAR?

A: When you are evaluating PAST RESULTS (ex-post):

• Use the AAR (average without compounding) if you ARE

NOT reinvesting any cash flows received before the end of

the period.

• Use the GAR (average with compounding) if you ARE

reinvesting any cash flows received before the end of the

period.

2-22

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Measuring Ex-post (past)

Returns

Finding the average HPR for a portfolio of assets for a

given time period:

•Where:

VI = amount invested in asset I,

J = total # of securities, and

TV = total amount invested;

•Thus VI/TV = percentage of total investment invested

in asset I

















 

1 I

I avg

HPR HPR

V I

continued

2-23

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Measuring Ex-post (past) Returns

• For example: Suppose you have $1000 invested in a stock

portfolio in September. You have $200 invested in Share A,

$300 in Share B and $500 in Share C. The HPR for the month

of September for Share A was 2%, for Share B 4% and for

Share C –5%.

• The average HPR for the month of September for this portfolio

is:

















 

1 I

I avg

HPR HPR

V I

) (500/1000) (–.05 ) (300/1000) (.04 ) (200/1000) (.02 HPR avg        –0.9%

continued

2-24

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Dollar-weighted Return

• Measuring returns when there are investment changes

(buying or selling) or other cash flows within the

period.

• An example: Today you buy one share of stock

costing $50. The stock pays a $2 dividend one year

from now.

– Also one year from now you purchase a second

share of stock for $53.

– Two years from now you collect a $2 per share

dividend and sell both shares of stock for $54 a

share.

Q: What was your average (annual) return?

2-25

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Dollar-weighted Return

Dollar-weighted return procedure (DWR):

•Find the internal rate of return for the cash

flows (i.e. find the discount rate that makes the

NPV of the net cash flows equal zero).

2-26

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Dollar-weighted return

• This measure of return considers changes in both

investment and security performance.

• Initial investment is an _______

• Ending value is considered as an ______

• Additional investment is an _______

• Security sales are an ______

outflow

inflow

outflow

inflow

2-27

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Dollar-weighted Return

• Dollar-weighted return procedure (DWR):

• Find the internal rate of return for the cash

flows (i.e. find the discount rate that makes

the NPV of the net cash flows equal zero.)

NPV = $0 = –$50/(1 + IRR)^0 – $51/(1 + IRR)^1 + $112/(1 + IRR)^2

• Solve for IRR:

IRR = 7.117% average annual dollar weighted return

The DWR gives you an average return based on the share's

performance and the dollar amount invested (number of shares

bought and sold) each period.

continued

Total cash flows each year

Year

0 1 2

-$50 $ 2 $ 4

-$53 $108

Net -$50 -$51 $112

2-28

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Measuring ex-ante Returns

(Scenario or Subjective Returns)

Subjective or scenario approach

• Subjective expected returns

E(r) = expected return

p(s) = probability of a state

r(s) = return if a state occurs

1 to s states

E(r) = p(s) r(s)

2-29

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Measuring ex-ante Returns

(Scenario or Subjective Returns)

Subjective or scenario approach

• Variance vs Standard Variation

 = [2] 1/2

E(r) = expected return

p(s) = probability of a state

rs = return in state 's'



  

E(r)] [r p(s) σ

2-30

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Numerical Example: Subjective or

Scenario Distributions

State Prob. of state Return

1 .2 –.05

2 .5 .05

3 .3 .15

E(r) = (.2)(–0.05) + (.5)(0.05) + (.3)(0.15) = 6%

 2 = [(.2)(–0.05 – 0.06) 2 + (.5)(0.05 – 0.06) 2 + (.3)(0.15 – 0.06) 2 ]

 2 = 0.0049% 2

 = [ 0.0049] 1/2 = .07 or 7%



  

E(r)] [r p(s) σ

2-31

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Ex-ante Expected Return and  

Annualising the statistics:









1 i

) r (r

1 n

σ : variance post - Ex

periods #

period annual

   

periods # r r

period annual

 

σ σ : deviation standard post - Ex 





1 T

HPR

HPR average r 

ns observatio # n 

continued

2-32

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Average 0.011624

Variance 0.003725

St. dev 0.061031 n 60

n-1 59

31 0.027334 0.000246811 3/1/2005

32 -0.088065 0.009937839 4/1/2005

33 0.037904 0.000690654 5/2/2005

34 -0.089915 0.010310121 6/1/2005

35 0.0179 3.93874E-05 7/1/2005

36 -0.017814 0.000866572 8/1/2005

37 -0.043956 0.003089121 9/1/2005

38 0.010042 2.50266E-06 10/3/2005

39 0.022495 0.00011818 11/1/2005

40 -0.029474 0.001689005 12/1/2005

41 0.05303 0.001714497 1/3/2006

42 0.09589 0.007100858 2/1/2006

43 -0.003618 0.000232311 3/1/2006

44 0.002526 8.27674E-05 4/3/2006

45 0.083361 0.005146208 5/1/2006

46 -0.016818 0.000808939 6/1/2006

47 -0.010537 0.000491104 7/3/2006

48 -0.001361 0.000168618 8/1/2006

49 0.04081 0.000851813 9/1/2006

50 0.01764 3.61885E-05 10/2/2006

51 0.047939 0.001318787 11/1/2006

52 0.044354 0.001071242 12/1/2006

53 0.02559 0.000195054 1/3/2007

54 -0.026861 0.001481106 2/1/2007

55 0.005228 4.09065E-05 3/1/2007

56 0.015723 1.68055E-05 4/2/2007

57 0.01298 1.83836E-06 5/1/2007

58 -0.038079 0.002470321 6/1/2007

59 -0.034545 0.002131602 7/2/2007

60 0.017857 0.000038854 8/1/2007

Monthly Source Yahoo finance

HPRs

Obs DIS (r - r avg )

1 -0.035417 0.002212808 9/3/2002

2 0.093199 0.006654508 10/1/2002

3 0.15756 0.021297275 11/1/2002

4 -0.200637 0.045054632 12/2/2002

5 0.068249 0.00320644 1/2/2003

6 -0.026188 0.001429702 2/3/2003

7 -0.00183 0.000181016 3/3/2003

8 0.087924 0.005821766 4/1/2003

9 0.050211 0.001489002 5/1/2003

10 0.004734 4.74648E-05 6/2/2003

11 0.099052 0.00764371 7/1/2003

12 -0.068896 0.006483384 8/1/2003

13 -0.016478 0.000789704 9/2/2003

14 0.109174 0.009516098 10/1/2003

15 0.019343 5.95893E-05 11/3/2003

16 0.019409 6.06076E-05 12/1/2003

17 0.02829 0.000277753 1/2/2004

18 0.095035 0.00695741 2/2/2004

19 -0.061342 0.005324028 3/1/2004

20 -0.085344 0.00940277 4/1/2004

21 0.018851 5.22376E-05 5/3/2004

22 0.079128 0.004556811 6/1/2004

23 -0.103832 0.013330149 7/1/2004

24 -0.028414 0.001603051 8/2/2004

25 0.004562 4.98687E-05 9/1/2004

26 0.105671 0.008844901 10/1/2004

27 0.061998 0.002537528 11/1/2004

28 0.041453 0.000889761 12/1/2004

29 0.028856 0.000296963 1/3/2005

30 -0.024453 0.001301505 2/1/2005

Monthly Source Yahoo finance

HPRs

Obs DIS (r - r avg )

1 -0.035417 0.002212808 9/3/2002

2 0.093199 0.006654508 10/1/2002

3 0.15756 0.021297275 11/1/2002

4 -0.200637 0.045054632 12/2/2002

5 0.068249 0.00320644 1/2/2003

6 -0.026188 0.001429702 2/3/2003

7 -0.00183 0.000181016 3/3/2003

8 0.087924 0.005821766 4/1/2003

9 0.050211 0.001489002 5/1/2003

10 0.004734 4.74648E-05 6/2/2003

11 0.099052 0.00764371 7/1/2003

12 -0.068896 0.006483384 8/1/2003

13 -0.016478 0.000789704 9/2/2003

14 0.109174 0.009516098 10/1/2003

15 0.019343 5.95893E-05 11/3/2003

16 0.019409 6.06076E-05 12/1/2003

17 0.02829 0.000277753 1/2/2004

18 0.095035 0.00695741 2/2/2004

19 -0.061342 0.005324028 3/1/2004

20 -0.085344 0.00940277 4/1/2004

21 0.018851 5.22376E-05 5/3/2004

22 0.079128 0.004556811 6/1/2004

23 -0.103832 0.013330149 7/1/2004

24 -0.028414 0.001603051 8/2/2004

25 0.004562 4.98687E-05 9/1/2004

26 0.105671 0.008844901 10/1/2004

27 0.061998 0.002537528 11/1/2004

28 0.041453 0.000889761 12/1/2004

29 0.028856 0.000296963 1/3/2005

30 -0.024453 0.001301505 2/1/2005

Ex-post Expected Return &   (cont.)

2-33

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Using Ex-post Returns to

Estimate Expected HPR

Estimating expected HPR (E[r]) from ex-post data

• Use the arithmetic average of past returns as a

forecast of expected future returns as we did, and

perhaps apply some (usually ad-hoc) adjustment

to past returns.

Problems?

- Which historical time period?

- Have to adjust for current economic situation

- Unstable averages

- Stable risk

2-34

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Real vs. Nominal Rates

Fisher effect: approximation

real rate  nominal rate – inflation rate

r real  r nom – i

Example r nom = 9%, i = 6%

r real  3%

Fisher effect: exact

r real = or

r real =

The exact real rate is less than the approximate real rate.

[(1 + r nom ) / (1 + i)] – 1

r real = real interest rate

r nom = nominal interest rate

i = expected inflation rate

(r nom – i) / (1 + i)

(9% – 6%) / (1.06) = 2.83%

2-35

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Normal Distribution

E[r] = 10%

 = 20%

Average = Median

Risk is the

possibility

of getting

returns

different

from

expected.

 measures deviations

above the mean as well as

below the mean.

Returns > E[r] may not be

considered as risk, but with

symmetric distribution, it is

ok to use  to measure

risk.

2-36

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Skewed Distribution—Large Negative

Returns Possible (left skewed)

r Negative Positive

Median

= average

Implication?

 is an incomplete

risk measure

2-37

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Skewed Distribution—Large Positive

Returns Possible (right skewed)

Negative

Positive

Median

= average

2-38

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Leptokurtosis

Implication?

 is an incomplete

risk measure

2-39

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Value at Risk (VaR)

Value at risk attempts to answer the following question:

• How many dollars can I expect to lose on my portfolio

in a given time period at a given level of probability?

• The typical probability used is 5%.

• We need to know what HPR corresponds to a 5%

probability.

• If returns are normally distributed then we can use a

standard normal distribution table or Excel to

determine how many standard deviations below the

mean represents a 5% probability:

– From Excel: =Norminv (0.05,0,1) = –1.64485

standard deviations

continued

2-40

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Value at Risk (VaR)

From the standard deviation we can find the corresponding

level of the portfolio return:

VaR = E[r] + –1.64485

For example: a $500 000 stock portfolio has an annual

expected return of 12% and a standard deviation of 35%.

What is the portfolio VaR at a 5% probability level?

VaR = 0.12 + (– 1.64485 * 0.35)

VaR = –45.57% (rounded slightly)

VaR$ = $500 000 x –.4557 = – $227 850

What does this number mean?

continued

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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Value at Risk (VaR)

VaR versus standard deviation:

• For normally distributed returns VaR is equivalent to

standard deviation (although VaR is typically reported

in dollars rather than in % returns)

• VaR adds value as a risk measure when return

distributions are not normally distributed.

– Actual 5% probability level will differ from 1.68445

standard deviations from the mean due to kurtosis

and skewedness.

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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Risk Premium and Risk Aversion

• The risk-free rate is the rate of return that can be

earned with certainty.

• The risk premium is the difference between the

expected return of a risky asset and the risk-free rate.

Excess return or risk premium asset = E[r asset ] – rf

• Risk aversion is an investor’s reluctance to accept

risk.

• How is the aversion to accept risk overcome?

- By offering investors a higher risk premium.

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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Quantifying Risk Aversion

 

5 . 0

f p A r r E     

E(r p ) = Expected return on portfolio p

r f = the risk-free rate

0.5 = scale factor

A x  p 2 = proportional risk premium

The larger A is, the larger will be the investor's added

return required to bear risk

continued

2-44

Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Quantifying Risk Aversion (cont.)

Rearranging the equation and solving for A

Many studies have concluded that investors’

average risk aversion is between 2 and 4.

r r E

f p

.5 0

) (







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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Using A

What is the maximum A

that an investor could have

and still choose to invest in

the risky portfolio P?

Maximum A =

r r E

f p

.5 0

) (







0.22 0.5

0.05 0.14









3.719

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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

'A' and Indifference Curves

• The A term can be used to create indifference curves.

• Indifference curves describe different combinations of

return and risk that provide equal utility (U) or satisfaction.

• U = E[r] – 1/2A p 2

• Indifference curves are curvilinear because they exhibit

diminishing marginal utility of wealth.

• The greater the A the steeper the indifference curve

and, all else equal, such investors will invest less in

risky assets.

• The smaller the A the flatter the indifference curve

and, all else equal, such investors will invest more in

risky assets.

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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Indifference Curves

• Investors want

the most

return for the

least risk.

• Hence

indifference

curves higher

and to the left

are preferred.

I 2

I 1

I 3

U = E[r] - 1/2A p 2

1 2 3

I I I  

continued

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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e

Next Week…

• Next we will cover Portfolio Theory – a key concept upon

which most of the theories covered in this subject are

based.

• Tutorials start in Week 2

• Make sure you enroll into a class

• Tutorial participation is mandatory – helpful to your assessments.

• Please remember: active engagement during lectures and tutorials

guarantees higher marks!