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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-1 Chapter 5.

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Presentation on theme: "Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-1 Chapter 5."— Presentation transcript:

1 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-1 Chapter 5

2 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-2 Chapter Summary  Objective: To introduce key concepts and issues that are central to informed decision making Determinants of interest rates The historical record Risk and risk aversion Portfolio risk

3 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-3 Factors Influencing Rates  Supply Households  Demand Businesses  Government’s Net Supply and/or Demand Central Bank Actions

4 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-4 Q0Q0 Q1Q1 r0r0 r1r1 Funds Interest Rates Supply Demand Level of Interest Rates

5 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-5 Fisher effect: Approximation R = r + i or r = R - i Example: r = 3%, i = 6% R = 9% = 3%+6% or r = 3% = 9%-6% Fisher effect: Exact Real vs. Nominal Rates or Numerically:

6 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-6 HPR = Holding Period Return P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one Rates of Return: Single Period

7 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-7 Ending Price = 48 Beginning Price = 40 Dividend = 2 Rates of Return: Single Period Example

8 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-8 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Characteristics of Probability Distributions

9 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-9 Symmetric distribution r s.d. Normal Distribution

10 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-10 Subjective returns ‘s’= number of scenarios considered p i = probability that scenario ‘i’ will occur r i = return if scenario ‘i’ occurs Measuring Mean: Scenario or Subjective Returns

11 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-11 E(r) = (.1)(-.05)+(.2)(.05)...+(.1)(.35) E(r) =.15 = 15% Numerical example: Scenario Distributions ScenarioProbabilityReturn 10.1-5% 20.25% 30.415% 40.225% 50.135%

12 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-12 Using Our Example:  2 =[(.1)(-.05-.15) 2 +(.2)(.05-.15) 2 +…] =.01199  = [.01199] 1/2 =.1095 = 10.95% Subjective or Scenario Distributions Measuring Variance or Dispersion of Returns Standard deviation = [variance] 1/2 = 

13 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-13 Summary Reminder  Objective: To introduce key concepts and issues that are central to informed decision making Determinants of interest rates The historical record Risk and risk aversion Portfolio risk

14 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-14 Annual HPRs Canada, 1957-2001 SeriesMean (%) St. Deviation (%) Stocks10.8016.24 LT Bonds8.9710.60 T-bills7.183.70 Inflation4.443.33

15 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-15 Annual HP Risk Premiums and Real Returns, Canada SeriesRisk Premium (%) Real Return (%) Stocks3.626.36 LT Bonds1.804.53 T-bills-2.74 Inflation--

16 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-16 Annual HPRs US, 1926-1999 SeriesG Mean (%) A Mean (%) Std Dev (%) Sm Stocks12.618.839.6 Lg Stocks11.113.120.2 LT Bonds (Gov)5.15.48.1 T-bills3.8 3.3 Inflation3.13.24.5

17 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-17 Annual HP Risk Premiums and Real Returns, US SeriesRisk Premium (%) Real Return (%) Sm Stocks15.015.6 Lg Stocks9.39.9 LT Bonds (Gov)1.62.2 T-bills-0.6 Inflation--

18 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-18 Summary Reminder  Objective: To introduce key concepts and issues that are central to informed decision making Determinants of interest rates The historical record Risk and risk aversion Portfolio risk

19 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-19 W = 100 W 1 = 150; Profit = 50 p =.6 W 2 = 80; Profit = -20 1-p =.4 E(W) = pW 1 + (1-p)W 2 = 122  2 = p[W 1 - E(W)] 2 + (1-p) [W 2 - E(W)] 2  2 = 1,176 and  = 34.29% Risk - Uncertain Outcomes

20 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-20 W 1 = 150 Profit = 50 p =.6 W 2 = 80 Profit = -20 1-p =.4 100 Risky Investment Risk Free T-bills Profit = 5 Risk Premium = 22-5 = 17 Risky Investments with Risk-Free Investment

21 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-21  Investor’s view of risk Risk Averse Risk Neutral Risk Seeking  Utility  Utility Function U = E ( r ) –.005 A  2  A measures the degree of risk aversion Risk Aversion & Utility

22 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-22 Risk Aversion and Value: The Sample Investment U = E ( r ) -.005 A  2 =22% -.005 A (34%) 2 Risk AversionAUtility High5-6.90 3 4.66 Low 116.22 T-bill = 5%

23 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-23 Dominance Principle 1 2 3 4 Expected Return Variance or Standard Deviation 2 dominates 1; has a higher return 2 dominates 3; has a lower risk 4 dominates 3; has a higher return

24 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-24 Utility and Indifference Curves  Represent an investor’s willingness to trade-off return and risk Example (for an investor with A=4): Exp Return (%) St Deviation (%) 1020.0 1525.5 2030.0 2533.9 U=E(r)-.005A  2 2 2 2 2

25 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-25 Indifference Curves Expected Return Standard Deviation Increasing Utility

26 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-26 Summary Reminder  Objective: To introduce key concepts and issues that are central to informed decision making Determinants of interest rates The historical record Risk and risk aversion Portfolio risk

27 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-27 Portfolio Mathematics: Assets’ Expected Return Rule 1 : The return for an asset is the probability weighted average return in all scenarios.

28 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-28 Portfolio Mathematics: Assets’ Variance of Return Rule 2: The variance of an asset’s return is the expected value of the squared deviations from the expected return.

29 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-29 Portfolio Mathematics: Return on a Portfolio Rule 3: The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio, with the portfolio proportions as weights. r p = w 1 r 1 + w 2 r 2

30 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-30 Portfolio Mathematics: Risk with Risk-Free Asset Rule 4: When a risky asset is combined with a risk-free asset, the portfolio standard deviation equals the risky asset’s standard deviation multiplied by the portfolio proportion invested in the risky asset.

31 Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 5-31 Rule 5: When two risky assets with variances  1 2 and  2 2 respectively, are combined into a portfolio with portfolio weights w 1 and w 2, respectively, the portfolio variance is given by: Portfolio Mathematics: Risk with two Risky Assets

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