ch02 risk and returnPPT课件
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– Inflation
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP
Arbitrage Pricing Theory (APT)
• Why do some authors contend that the APT model is untestable?
• What are the concerns related to the multiple factors of the APT model?
Chapter 9 - Multifactor Models of Risk and Return
Lecture Presentation Software
to accompany
Investment Analysis and Portfolio Management
Seventh Edition by
Frank K. Reilly & Keith C. Brown
Chapter 9
Chapter 9 – Multifactor Models of Risk and Return
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP
Arbitrage Pricing Theory (APT)
• Why do some authors contend that the APT model is untestable?
• What are the concerns related to the multiple factors of the APT model?
Chapter 9 - Multifactor Models of Risk and Return
Lecture Presentation Software
to accompany
Investment Analysis and Portfolio Management
Seventh Edition by
Frank K. Reilly & Keith C. Brown
Chapter 9
Chapter 9 – Multifactor Models of Risk and Return
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
--and return(公司金融英文版) ppt课件
8-8 Markowitz Portfolio Theory
% probability
Standard Deviation VS. Expected Return
Investment D
20
18
16
14
12
10
8
6
4
2
0
-50
0
50
% return
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
8-4 Markowitz Portfolio Theory
Proportion of Days
Price changes vs. Normal distribution
Expected Return (%)
McGraw Hill/Irwin
Standard Deviation
Microsoft - Daily % change 1990-2001
0.14 0.12
0.1 0.08 0.06 0.04 0.02
0
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
McGraw Hill/Irwin
Daily % Change
Copyright © 2003 by The McGraw-Hill Companies, Inc. AHale Waihona Puke l rights reserved
3_Risk and Return 风险与收益
Margin%
equity in account value of stock - loan value of stock value of stock
Risk and Return
-11-
Example 4.2
X Corp 50% 30% 1000 $70 Initial Margin Maintenance Margin Shares Purchased New Position Stock: $60,000 Loan: ($35,000) Equity: $25,000 Margin = 41.67%
Initial Position price falls to $60 Stock : $70,000 Loan: ($35,000) Equity: $35,000 Margin% = 50%
Risk and Return
-12-
Margin Calls
How far can the stock price fall before a margin call?
requirement is met not the maintenance margin
30% both Canada and US US regulator requires 25% but brokers usually require 30% Margin calls: requests to add equity to maintain 30% margin
Geometric mean reflects compound, cumulative returns over more than one period Arithmetic mean return capture typical return in a single period
CF2 Ch 05 Risk and Return 公司财务与金融 课件
Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.
Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.
21
Alternative Method: Find portfolio return in each economic state
22
Use portfolio outcomes to estimate risk and expected return
r^p = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6%.
By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.
32
Can an investor holding one stock earn a return commensurate with its risk?
The reason is due to negative correlation (r) between Alta and Repo.
24
Bonus Slide: of Two-Stock Portfolio
Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.
21
Alternative Method: Find portfolio return in each economic state
22
Use portfolio outcomes to estimate risk and expected return
r^p = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6%.
By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.
32
Can an investor holding one stock earn a return commensurate with its risk?
The reason is due to negative correlation (r) between Alta and Repo.
24
Bonus Slide: of Two-Stock Portfolio
《风险与回报》课件
投资中的风险与回报
1
投资的类型
包括股票、债券、房地产、大宗商品等不同类型的投资。
2
投资的风险与回报
不同类型的投资对应着不同的风险和回报水平。
3
如何降低投资风险
通过分散投资、定期评估投资组合和研究投资标的来降低投资风险。
风险与回报的案例分析
ห้องสมุดไป่ตู้
不同投资案例的风险与回报
通过具体的投资案例，探讨不同投资的风险水平和预期 回报。
风险计量
通过风险测度方法对风险进行定量或定性评估，如价值-at-risk(VaR)。
风险管理
风险规避
通过避免潜在风险源或采取行动 以消除或减少风险。
风险转移
将风险转嫁给其他主体，如购买 保险或与合作伙伴建立风险共担 关系。
风险接受
在面临不可避免的风险时，采取 积极措施并承担风险。
什么是回报
1 回报的定义
2 不同类型的回报
回报是投资所带来的收益或利润，可以是金钱、 资本增值、股息等形式。
包括利息收入、股票收益、房地产租金等不同类 型的回报。
风险与回报的关系
风险与回报的权衡
通常，较高的回报伴随着较高的风险，投资者需要权衡风险与回报的关系。
如何平衡风险与回报
通过多元化投资、制定风险管理策略和根据个人风险承受能力来平衡风险与回报。
风险管理对投资的影响
分析风险管理对投资决策和投资组合构建的重要性和影 响。
结论
1 风险和回报的关系是
必须平衡的
2 风险管理是投资成功
的关键
3 投资者需理性看待风
险和回报
投资者需要在追求高回报的 同时，合理控制风险。
有效的风险管理策略和工具 有助于提高投资的成功率。
第二章风险和回报 chapter2 risk and returnPPT课件
2020/7/21
Ch2 Risk and Return
2-1111
Risk measure 1:standard deviation
Stan dd eavria dtion
Varia n 2ce
n
(ki
kˆ)2Pi
i1
2020/7/21
Ch2 Risk and Return
2-1212
Example:some investment alternatives’ returns
Amount invested
For example: if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is:
($1,100 - $1,000) / $1,000 = 10%.
2. the probability of earning a low or negative actual return.
2020/7/21
Ch2 Risk and Return
2-9 9
Investment return possibility distribution.
Probability density
Firm X
Firm Y
-70
0
15
Rate of 100 Return (%)
2020/7/21
Expected Rate of Return
Ch2 Risk and Return
2-5 5
Return distribution (dispersed)
Economy Prob.
RiskandReturn
_
r
2
24
Standard Deviation Formulas
• When eliminating the bias, Variance and Standard Deviation become:
^
1 n 1
n j 1
r s
_
r
2
25
The Reward-to-Volatility (Sharpe) Ratio
19
Variance and Standard Deviation
Variance (VAR):
2 p(s)r(s) E(r)2
s
Standard Deviation (STD):
STD 2
20
Scenario VAR and STD
• Example VAR calculation:
σ2 = .25(.31 - 0.0976)2+.45(.14 - .0976)2 + .25(-0.0675 - 0.0976)2 + .05(-.52 - .0976)2 = .038
• Example STD calculation:
.038
.1949
21
Time Series Analysis of Past Rates of Return
• Nominal rate = real rate + inflation forecast
R r E(i)
6
Taxes and the Real Rate of Interest
• Tax liabilities are based on nominal income – Given a tax rate (t) and nominal interest rate (R), the Real after-tax rate is:
RiskandReturn投资分析与投资组合管理.ppt
= reaction in asset i’s returns to movements in a common bik factor
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
Arbitrage Pricing Theory (APT)
Rt Et bi1i bi2i ... bik k i
For i = 1 to N where:
Ri = return on asset i during a specified time period
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
Lecture Presentation Software
to accompany
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
Arbitrage Pricing Theory (APT)
Rt Et bi1i bi2i ... bik k i
For i = 1 to N where:
Ri = return on asset i during a specified time period
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
Lecture Presentation Software
to accompany
RiskandReturn(投资分析与投资组合管理)
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
Arbitrage Pricing Theory (APT)
Bik determine how each asset reacts to this common factor
Each asset may be affected by growth in GNP, but the effects will differ
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
Arbitrage Pricing Theory (APT)
Bik determine how each asset reacts to this common factor
Each asset may be affected by growth in GNP, but the effects will differ
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
Chapter_RiskandReturn(公司理财原理,Brealey_My(PPT)
Principles of Corporate Finance
Seventh Edition
Richard A. Brealey Stewart C. Myers
Chapter 8
Risk and Return
Slides by
Matthew Will
McGraw Hill/Irwin
第一页，共三十C五o页p。yright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
8- 2
Topics Covered
Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives
McGraw Hill/Irwin
Copyrig第h二t 页©，2共0三0十3五b页y。The McGraw-Hill Companies, Inc. All rights reserved
McGraw Hill/Irwin
Copyrig第h三t 页©，2共0三0十3五b页y。The McGraw-Hill Companies, Inc. All rights reserved
8-4 Markowitz Portfolio Theory
Price changes vs. Normal distribution
frontier.
Expected Return (%)
T
rf
McGraw Hill/Irwin
S
Standard Deviation
Copyri第gh十t一©页，2共00三3十b五y页T。he McGraw-Hill Companies, Inc. All rights reserved
Seventh Edition
Richard A. Brealey Stewart C. Myers
Chapter 8
Risk and Return
Slides by
Matthew Will
McGraw Hill/Irwin
第一页，共三十C五o页p。yright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
8- 2
Topics Covered
Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives
McGraw Hill/Irwin
Copyrig第h二t 页©，2共0三0十3五b页y。The McGraw-Hill Companies, Inc. All rights reserved
McGraw Hill/Irwin
Copyrig第h三t 页©，2共0三0十3五b页y。The McGraw-Hill Companies, Inc. All rights reserved
8-4 Markowitz Portfolio Theory
Price changes vs. Normal distribution
frontier.
Expected Return (%)
T
rf
McGraw Hill/Irwin
S
Standard Deviation
Copyri第gh十t一©页，2共00三3十b五y页T。he McGraw-Hill Companies, Inc. All rights reserved
2章Risk and Return 学习课件,财务管理英文版
Topic 4(Chapter 2)part1
Risk and Return
Basic return concepts Basic risk concepts Stand-alone risk Portfolio risk Risk and return: CAPM/SML
Rate of Return
When two investments have the same expected returns but different standard deviations, most people choose the one with the lower standard deviation and therefore,the lower risk.
p
n
(kpi
kˆp)2Pi
i1
p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 + (10.0 - 9.6)20.40 + (12.5 - 9.6)20.20 + (15.0 - 9.6)20.10)1/2 = 3.3%.
p is much lower than: either stock (20% and 13.4%).
average of HT and Coll (16.7%).
The portfolio provides average return but much lower risk. The key here is negative correlation.
Two-Stock Portfolios
Two stocks can be combined to form a riskless portfolio if r = -1.0.
Risk and Return
Basic return concepts Basic risk concepts Stand-alone risk Portfolio risk Risk and return: CAPM/SML
Rate of Return
When two investments have the same expected returns but different standard deviations, most people choose the one with the lower standard deviation and therefore,the lower risk.
p
n
(kpi
kˆp)2Pi
i1
p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 + (10.0 - 9.6)20.40 + (12.5 - 9.6)20.20 + (15.0 - 9.6)20.10)1/2 = 3.3%.
p is much lower than: either stock (20% and 13.4%).
average of HT and Coll (16.7%).
The portfolio provides average return but much lower risk. The key here is negative correlation.
Two-Stock Portfolios
Two stocks can be combined to form a riskless portfolio if r = -1.0.
RiskandReturn(投资分析与投资组合管理).pptx
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
• How is risk estimated in a multifactor setting?
Arbitrage Pricing Theory (APT)
• CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
• How is risk estimated in a multifactor setting?
Arbitrage Pricing Theory (APT)
• CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark
风险与收益实用培训教程(ppt 20页)
第五章 风险与收益
• 第一节 风险与收益概述 一、风险(Risk) 二、收益(Return) 第二节单一投资项目风险与收益度量 一、概率分布 二、期望收益率 三、方差与标准差 四、标准离差率 五、风险收益 ※第三节 投资组合的风险度量 一、投资组合收益率 二、投资组合风险
1
第一节 风险与收益概述
一、风险的概念(Risk)
Rr bQ
• 风险报酬斜率即b系数取决于全体投资者对待风
险的态度，即风险偏好。可分为三类： • 风险厌恶型： • 投资者期望报酬率 投资项目的期望报酬率 • 风险中立型： • 投资者期望报酬率 投资项目的期望报酬率 • 风险喜好型： • 投资者期望报酬率 投资项目的期望报酬率
17
• 任何投资者宁愿要肯定 的某一报酬率，而不愿意要 不肯定的同一报酬率。（风 险反感）
n
2)所有可能结果的概率之和等于1，即： Pi 1 i1
3）必然事件的概率等于1，不可能事件的概率 等于0。
10
3、概率分布 • 把所有可能的结果都列示出来，且每种结
果出现的次数有概率表示，就构成了概率 分布。
11
二、期望收益率
• 1、期望值： • 1）概念：是一个概率分布中的所有可能结果，以各自
2）可分散风险，又称非系统风险或企业特别 风险。其按形 成的原因可分为经营风险和财 务风险两大 类。
经营风险（商业风险）：是由生产经营的不确 定性引起的
财务风险（筹资风险）：是由负债筹资引起的
4
二、收益(Return)
投资活动可分为固定资产投资和金融资产（即证券） 投资。衡量一项投资赚钱能力的大小，一般有收益 额和投资报酬率，其中投资报酬率即利润率是单位 投入资本赢得的利润。
24
• 第一节 风险与收益概述 一、风险(Risk) 二、收益(Return) 第二节单一投资项目风险与收益度量 一、概率分布 二、期望收益率 三、方差与标准差 四、标准离差率 五、风险收益 ※第三节 投资组合的风险度量 一、投资组合收益率 二、投资组合风险
1
第一节 风险与收益概述
一、风险的概念(Risk)
Rr bQ
• 风险报酬斜率即b系数取决于全体投资者对待风
险的态度，即风险偏好。可分为三类： • 风险厌恶型： • 投资者期望报酬率 投资项目的期望报酬率 • 风险中立型： • 投资者期望报酬率 投资项目的期望报酬率 • 风险喜好型： • 投资者期望报酬率 投资项目的期望报酬率
17
• 任何投资者宁愿要肯定 的某一报酬率，而不愿意要 不肯定的同一报酬率。（风 险反感）
n
2)所有可能结果的概率之和等于1，即： Pi 1 i1
3）必然事件的概率等于1，不可能事件的概率 等于0。
10
3、概率分布 • 把所有可能的结果都列示出来，且每种结
果出现的次数有概率表示，就构成了概率 分布。
11
二、期望收益率
• 1、期望值： • 1）概念：是一个概率分布中的所有可能结果，以各自
2）可分散风险，又称非系统风险或企业特别 风险。其按形 成的原因可分为经营风险和财 务风险两大 类。
经营风险（商业风险）：是由生产经营的不确 定性引起的
财务风险（筹资风险）：是由负债筹资引起的
4
二、收益(Return)
投资活动可分为固定资产投资和金融资产（即证券） 投资。衡量一项投资赚钱能力的大小，一般有收益 额和投资报酬率，其中投资报酬率即利润率是单位 投入资本赢得的利润。
24
Lecture2 risk and returnPPT课件
value weighted index
Initial index value =(25*20+100*1)=600 Final index value=(30*20+90*1)=690 Percentage change/Return=690/600-1=15%
15
III Equally Weighted Index
Wilshire 5000 broadest, about 6000 stocks from NYSE, Amex and NASDAQ
Investors can base their portfolios on an index (index mutual funds, exchange traded funds (ETFs))
S&P500, FTSE 100
11
I price-weighted average
Average of stock prices in the market Or the price of a portfolio that invests one
share in each stock in the market Stocks with higher prices have greater impact DJIA, Nikkei 225;
9
Market Index
Dow Jones 30 large blue-chip corporations, computed since 1896
S&P500 broadly based index of 500 firms
NASDAQ More than 3000 firms traded on the NASDAQ market
Initial index value =(25*20+100*1)=600 Final index value=(30*20+90*1)=690 Percentage change/Return=690/600-1=15%
15
III Equally Weighted Index
Wilshire 5000 broadest, about 6000 stocks from NYSE, Amex and NASDAQ
Investors can base their portfolios on an index (index mutual funds, exchange traded funds (ETFs))
S&P500, FTSE 100
11
I price-weighted average
Average of stock prices in the market Or the price of a portfolio that invests one
share in each stock in the market Stocks with higher prices have greater impact DJIA, Nikkei 225;
9
Market Index
Dow Jones 30 large blue-chip corporations, computed since 1896
S&P500 broadly based index of 500 firms
NASDAQ More than 3000 firms traded on the NASDAQ market
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HT – Moves with the economy, and has a positive correlation. This is typical.
Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual.
20.0% 0.0% 7.0% 15.0%
35.0% -10.0% 45.0% 29.0%
50.0% -20.0% 30.0% 43.0%
5-6 6
Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return?
The greater the chance of lower than expected or negative returns, the riskier the investment.
5-3 3
Probability distributions
A listing of all possible outcomes, and the probability of each occurrence.
T-bills will return the promised 8%, regardless of the economy.
No, T-bills do not provide a risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time.
Can be shown graphically.
US Water
Martin
-70
0
15
Rate of 100 Return (%)
Expected Rate of Return
5-4 4
Selected Realized Returns, 1926 – 2001
Average Standard
Return Deviation
Small-company stocks
17.3% 33.2%
Large-company stocks
12.7
20.2
L-T corporate bonds
6.1
8.6
L-T government bonds 5.7
9.4
U.S. Treasury bills
3.9
3.2
CHAPTER 2 Risk and Rates of Return
Stand-alone risk Portfolio risk Risk & return: CAPM / SML
5-11
Investment returቤተ መጻሕፍቲ ባይዱs
The rate of return on an investment can be calculated as follows:
($1,100 - $1,000) / $1,000 = 10%.
5-2 2
What is investment risk?
Two types of investment risk
Stand-alone risk Portfolio risk
Investment risk is related to the probability of earning a low or negative actual return.
Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2002 Yearbook (Chicago: Ibbotson Associates, 2002), 28.
5-5 5
Investment alternatives
Economy Prob.
Recession 0.1
Below avg 0.2
Average 0.4
Above avg 0.2
Boom
0.1
T-Bill 8.0% 8.0% 8.0% 8.0% 8.0%
HT
Coll
USR
MP
-22.0% 28.0% 10.0% -13.0%
-2.0% 14.7% -10.0% 1.0%
5-8 8
Return: Calculating the expected return for Martin Product and US Water
^
k expected rate of return
^
n
k k i Pi
i1
^
k M artin (100%) (0.3) (15%) (0.4)
T-bills are also risky in terms of reinvestment rate risk.
T-bills are risk-free in the default sense of the word.
5-7 7
How do the returns of HT and Coll. behave in relation to the market?
(-70%) (0.3) 15%
5-9 9
Summary of expected returns for all alternatives
HT Market USR T-bill Coll.
Exp return 17.4% 15.0% 13.8% 8.0% 1.7%
HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?
Return =
______(A_m_o_u_n_t_re_c_e_iv_ed__–_A_m_o_u_n_t invested)
Amount invested
For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is:
Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual.
20.0% 0.0% 7.0% 15.0%
35.0% -10.0% 45.0% 29.0%
50.0% -20.0% 30.0% 43.0%
5-6 6
Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return?
The greater the chance of lower than expected or negative returns, the riskier the investment.
5-3 3
Probability distributions
A listing of all possible outcomes, and the probability of each occurrence.
T-bills will return the promised 8%, regardless of the economy.
No, T-bills do not provide a risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time.
Can be shown graphically.
US Water
Martin
-70
0
15
Rate of 100 Return (%)
Expected Rate of Return
5-4 4
Selected Realized Returns, 1926 – 2001
Average Standard
Return Deviation
Small-company stocks
17.3% 33.2%
Large-company stocks
12.7
20.2
L-T corporate bonds
6.1
8.6
L-T government bonds 5.7
9.4
U.S. Treasury bills
3.9
3.2
CHAPTER 2 Risk and Rates of Return
Stand-alone risk Portfolio risk Risk & return: CAPM / SML
5-11
Investment returቤተ መጻሕፍቲ ባይዱs
The rate of return on an investment can be calculated as follows:
($1,100 - $1,000) / $1,000 = 10%.
5-2 2
What is investment risk?
Two types of investment risk
Stand-alone risk Portfolio risk
Investment risk is related to the probability of earning a low or negative actual return.
Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2002 Yearbook (Chicago: Ibbotson Associates, 2002), 28.
5-5 5
Investment alternatives
Economy Prob.
Recession 0.1
Below avg 0.2
Average 0.4
Above avg 0.2
Boom
0.1
T-Bill 8.0% 8.0% 8.0% 8.0% 8.0%
HT
Coll
USR
MP
-22.0% 28.0% 10.0% -13.0%
-2.0% 14.7% -10.0% 1.0%
5-8 8
Return: Calculating the expected return for Martin Product and US Water
^
k expected rate of return
^
n
k k i Pi
i1
^
k M artin (100%) (0.3) (15%) (0.4)
T-bills are also risky in terms of reinvestment rate risk.
T-bills are risk-free in the default sense of the word.
5-7 7
How do the returns of HT and Coll. behave in relation to the market?
(-70%) (0.3) 15%
5-9 9
Summary of expected returns for all alternatives
HT Market USR T-bill Coll.
Exp return 17.4% 15.0% 13.8% 8.0% 1.7%
HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?
Return =
______(A_m_o_u_n_t_re_c_e_iv_ed__–_A_m_o_u_n_t invested)
Amount invested
For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: