代写 McGraw-Hill FIN3IPM INVESTMENT PORTFOLIO MANAGEMENT
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代写 McGraw-Hill FIN3IPM INVESTMENT PORTFOLIO MANAGEMENT
Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
FIN3IPM
I NVESTMENT AND
P ORTFOLIO M ANAGEMENT
Semester 1/2016
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Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
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
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
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SUBJECT COMMUNICATION
1. Subject Lecturer and Tutor
Mail: Nhung.Le@latrobe.edu.au
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
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
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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
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
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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
2
7 March 2016 Portfolio Theory
代写 McGraw-Hill FIN3IPM INVESTMENT PORTFOLIO MANAGEMENT
Lecture 2
Tutorial 1
2
Bodie Chapter 6
1 A-F
3
14 March 2016 Asset Pricing Theories
Lecture 3
Tutorial 2
2
Bodie Chapter 7
2 A-F
4
21 March 2016 Market Efficiency
Lecture 4
Tutorial 3
2
Bodie Chapter 8
5 A-F
28 March 2016 Mid Semester Break
5
4 April 2016 Equity Valuation
Lecture 5
Tutorial 4
2
Bodie Chapter 11
4 A-F
6
11 April 2016
Macroeconomic and
Industry Analysis
Lecture6
Tutorial 5
2
Bodie Chapter 12
5 A-F
7
18 April 2016
Financial Statement
Analysis
Lecture 7
Tutorial 6
2
Bodie Chapter 13
1, 2, 4, 5 A-F
8
25 April 2016 Bond Valuation
Lecture 8
Tutorial 7
2
Bodie Chapter 9
3 A-F
9
2 May 2016 Managing Bond Portfolios
Lecture 9
Tutorial 8
2
Bodie Chapter 10
3 A-F
10
9 May 2016
Managed Funds and Hedge
Funds
Lecture 10
Tutorial 9
2
Bodie Chapters 16 & 17
6 A-F
11
16 May 2016
Portfolio Performance and
Evaluation
Lecture 11
Tutorial 10
2
Bodie Chapter 18
6 A-F
12
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
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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
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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!
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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
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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
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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
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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
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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
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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?
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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
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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.
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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 =
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HPR x n
[(1+HPR) n ] –1
[(1+HPR) 1/n ] –1
n=no.
years
n=no.
compounding
periods
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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?
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n = 12/3 = 4 so HPR ann = HPR*n = 0.05*4 = 20%
HPR ann = (1.05 4 ) - 1 = 21.55%
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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)
n
1 T
T
avg
n
HPR
HPR
continued
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
Arithmetic Average
AAR =
n
1 T
T
avg
n
HPR
HPR
7
.1762) .3446 .0311 .2098 .2335 .4463 (-.2156
HPR avg
17.51%
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%
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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
n
1 T
T avg
n
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%
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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.
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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
J
1 I
I avg
HPR HPR
TV
V I
continued
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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:
J
1 I
I avg
HPR HPR
TV
V I
) (500/1000) (–.05 ) (300/1000) (.04 ) (200/1000) (.02 HPR avg –0.9%
continued
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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?
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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).
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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
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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
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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)
S
s
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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'
s
2
s
2
E(r)] [r p(s) σ
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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%
s
2
s
2
E(r)] [r p(s) σ
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
Ex-ante Expected Return and
Annualising the statistics:
n
1 i
2
i
) r (r
1 n
1
σ : variance post - Ex
2
periods #
period annual
periods # r r
period annual
2
σ σ : deviation standard post - Ex
n
1 T
T
n
HPR
r
HPR average r
ns observatio # n
continued
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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 )
2
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 )
2
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.)
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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
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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 =
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%
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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.
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
Skewed Distribution—Large Negative
Returns Possible (left skewed)
r Negative Positive
Median
r
= average
Implication?
is an incomplete
risk measure
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
Skewed Distribution—Large Positive
Returns Possible (right skewed)
Negative
Positive
Median
r
= average
r
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Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
Leptokurtosis
Implication?
is an incomplete
risk measure
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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
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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
2
5 . 0
p
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
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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.
σ
r r E
A
p
f p
2
.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 =
σ
r r E
A
p
f p
2
.5 0
) (
0.22 0.5
0.05 0.14
A
2
3.719
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!