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
    2-2
    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
    2-3
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    Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
    2-3
    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
    2-4
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    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
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    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
    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
    2-6
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
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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
    2-9
    2-10
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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
    2-10
    2-11
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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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    2-13
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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?
    2-13
    2-14
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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
    2-14
    2-15
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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.
    2-15
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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 =
    2-16
    HPR x n
    [(1+HPR) n ] –1
    [(1+HPR) 1/n ] –1
    n=no.
    years
    n=no.
    compounding
    periods
    2-17
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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?
    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
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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
    2-19
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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%
    2-20
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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.
    2-22
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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
    2-23
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
    2-24
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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
    2-27
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
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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
    2-29
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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
    2-30
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
    2-31
    Copyright © 2013 McGraw-Hill Education (Australia) Pty Ltd
    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
    2-32
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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.)
    2-33
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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
    2-34
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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%
    2-35
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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.
    2-36
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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
    2-37
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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
    2-38
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    Bodie, Drew, Basu, Kane and Marcus Principles of Investments, 1e
    Leptokurtosis
    Implication?
     is an incomplete
    risk measure
    2-39
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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
    2-40
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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
    2-41
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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.
    2-42
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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.
    2-43
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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
    2-44
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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
    ) (
    2-45
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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
    2-46
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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.
    2-47
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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
    2-48
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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!