The document discusses capital asset pricing theory and portfolio theory. It introduces key concepts such as the efficient frontier, which shows the set of portfolios with the highest expected return for a given level of risk. It also discusses the Capital Asset Pricing Model (CAPM), which proposes that the expected return of an asset is determined by its sensitivity to non-diversifiable risk (beta). The CAPM suggests relationships like the security market line and capital market line. However, the CAPM faces empirical criticisms and its assumptions do not always hold in the real world. Alternative models like the Arbitrage Pricing Theory were developed that allow for multiple factors to influence returns.
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Question 1Risk & Return and the CAPM. Based on the following.docxIRESH3
Question 1
Risk & Return and the CAPM.
Based on the following information, calculate the required return based on the CAPM:
Risk Free Rate = 3.5%
Market Return =10%
Beta = 1.08
Question 2
Risk and Return, Coefficient of Variation
Based on the following information, calculate the coefficient of variation and select the best investment based on the risk/reward relationship.
Std Dev.Exp. Return
Company A 7.4 13.2
Company B 11.6 18.9
Question 3
Risk and Return, Coefficient of Variation
Based on the following information, calculate the coefficient of variation and select the best investment based on the risk/reward relationship.
Std Dev.Exp. Return
Company A 10.4 15.2
· Company B 14.6 22.9
Question 4
Measures of Risk.
Address each source of risk that is measured and relate it to two models addressed in this unit.
· Your response should be at least 250 words in length.
BBA 3301, Financial Management 1
UNIT VI STUDY GUIDE
Risk and Return
Learning Objectives
Upon completion of this unit, students should be able to:
1. Explain the risk-reward relationship.
2. Calculate holding period returns.
3. Calculate required returns using the Capital Asset Pricing Model
(CAPM).
4. Calculate the coefficient of variation for varying investments.
5. Decompose sources of risk.
6. Contrast measures of risk.
7. Describe portfolio theory and diversification.
Written Lecture
Whenever a business or individual makes an investment decision, risk must be
considered. This unit focuses entirely on the risk-return relationship, providing
tools for measurement, analysis and decision making.
To begin, the term risk must be defined. From a practical or applied perspective,
risk is the probability of losing some or all of the money invested. In finance, risk
is often associated with volatility of variance in returns (around some average
return). Generally, it is assumed that investments that offer higher returns
involve greater risk. For purposes of this unit, risk is measured through two
primary measures:
Standard Deviation, and
The Beta Coefficient
The rate of return allows an investment's return to be compared with other
investments. For one-year investments, the return on a debt investment is:
k = interest paid / loan amount
The return on a stock investment is calculated by the following equation
k = [D1 + (P1 – P0)] / P0
Where:
D1 = Dividends for the “next” year (on a share of stock)
P1= Price of a share of stock, one period into the future
P0= Price of a share of stock today
The expected return on stock is the return investors feel is most likely to occur
based on current information. Return is influenced by the combination of stock
price (capita ...
what do you want to do is you can do, if only you are willing to do....right? business it not only for our own selves, but also for everybody good also.
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This is Shahan from Bangladesh. As a designer, I have extensive graphic design experience. I can assist you with creating an eye-catching, professional, and modern presentation.
There are no limits to my services. Having 100% client satisfaction is my main goal.
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Question 1Risk & Return and the CAPM. Based on the following.docxIRESH3
Question 1
Risk & Return and the CAPM.
Based on the following information, calculate the required return based on the CAPM:
Risk Free Rate = 3.5%
Market Return =10%
Beta = 1.08
Question 2
Risk and Return, Coefficient of Variation
Based on the following information, calculate the coefficient of variation and select the best investment based on the risk/reward relationship.
Std Dev.Exp. Return
Company A 7.4 13.2
Company B 11.6 18.9
Question 3
Risk and Return, Coefficient of Variation
Based on the following information, calculate the coefficient of variation and select the best investment based on the risk/reward relationship.
Std Dev.Exp. Return
Company A 10.4 15.2
· Company B 14.6 22.9
Question 4
Measures of Risk.
Address each source of risk that is measured and relate it to two models addressed in this unit.
· Your response should be at least 250 words in length.
BBA 3301, Financial Management 1
UNIT VI STUDY GUIDE
Risk and Return
Learning Objectives
Upon completion of this unit, students should be able to:
1. Explain the risk-reward relationship.
2. Calculate holding period returns.
3. Calculate required returns using the Capital Asset Pricing Model
(CAPM).
4. Calculate the coefficient of variation for varying investments.
5. Decompose sources of risk.
6. Contrast measures of risk.
7. Describe portfolio theory and diversification.
Written Lecture
Whenever a business or individual makes an investment decision, risk must be
considered. This unit focuses entirely on the risk-return relationship, providing
tools for measurement, analysis and decision making.
To begin, the term risk must be defined. From a practical or applied perspective,
risk is the probability of losing some or all of the money invested. In finance, risk
is often associated with volatility of variance in returns (around some average
return). Generally, it is assumed that investments that offer higher returns
involve greater risk. For purposes of this unit, risk is measured through two
primary measures:
Standard Deviation, and
The Beta Coefficient
The rate of return allows an investment's return to be compared with other
investments. For one-year investments, the return on a debt investment is:
k = interest paid / loan amount
The return on a stock investment is calculated by the following equation
k = [D1 + (P1 – P0)] / P0
Where:
D1 = Dividends for the “next” year (on a share of stock)
P1= Price of a share of stock, one period into the future
P0= Price of a share of stock today
The expected return on stock is the return investors feel is most likely to occur
based on current information. Return is influenced by the combination of stock
price (capita ...
what do you want to do is you can do, if only you are willing to do....right? business it not only for our own selves, but also for everybody good also.
Similar to Portfolio Valuation - CAPM-APT.ppt (20)
As Europe's leading economic powerhouse and the fourth-largest hashtag#economy globally, Germany stands at the forefront of innovation and industrial might. Renowned for its precision engineering and high-tech sectors, Germany's economic structure is heavily supported by a robust service industry, accounting for approximately 68% of its GDP. This economic clout and strategic geopolitical stance position Germany as a focal point in the global cyber threat landscape.
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This report aims to equip stakeholders across public and private sectors with the knowledge to enhance their defensive strategies, reduce exposure to cyber risks, and reinforce Germany's resilience against cyber threats.
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
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Multiply with different modes (map)
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Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
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Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
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2. 1) The investor will always try to assess what
price is optimal to buy
We can go by the prevailing market price
Assess the price payable with the help of historical
data
Price refers to cost/expected rate of returns
2) Whether the performance is efficient or not
3. Portfolio Theory
Portfolio is a mix of more than one security
Invest in individual security : Risk Max
Invest in portfolio : Risk is diversified
Pure Portfolio: Investments are held only in
single security or single class of securities
Mixed Portfolio: Investment in more than one
class or one category
4. Passive portfolio – Investments are held till the
end of the investment horizon (Period fixed for
investments)
Active Investment Portfolio – Investments are
revised periodically (as predetermined by the
investors)
Aggressive portfolio – the portfolio which is
revised frequently (daily, weekly etc.)
5. Expected Return and Risk
Empirical Criticisms of Beta
Capital Asset Pricing Model
Arbitrage Pricing Theory
6. Portfolio Theory
Investment Portfolio: collection of securities
that together provide an investor with an
attractive trade-off between risk and return
Portfolio Theory: concept of making security
choices based on portfolio expected returns
and risks
7. Check for the optimal investments available
Securities which provide you with risk surplus
Any returns more than risk free rate of returns
Determine the portfolios which are having perfect trade off between
risk and returns
Any investment portfolio giving returns
A) Equal to Rf = Moderate priced security
B) More than Rf = Over priced security
C) Less than RF = Under priced Security
8. PORTFOLIO THEORY
Basic Assumptions
Expected Return: anticipated profit over some relevant
holding period
Risk: return dispersion, usually measured by standard
deviation of returns
Probability Distribution: apportionment of likely
occurrences
Utility: positive benefit
Disutility: psychic loss
Risk Averse: desire to avoid risk
9. PORTFOLIO THEORY
Three Fundamental Assertions
Investors seek to maximize utility.
Investors are risk averse: Utility rises with
expected return and falls with an increase in
volatility.
The optimal portfolio has the highest expected
return for a given level of risk, or the lowest
level of risk for a given expected return.
Corner Portfolio – Minimum Risk and Maximum
Return portfolio
10. Portfolio Expected Rate
of Return and Risk
Expected rate of return:
Standard deviation (risk):
E R WE R
p i i
i
N
1
N
i
N
j
j
i
j
i
i
N
i
p R
R
COV
W
W
R
VAR
R
SD W 1 1
1
2
1
12. Portfolio risk increases with the
volatility of individual holdings
and the extent to which holding
have high covariance.
13. Optimal Portfolio Choice
Zero-Risk Portfolio: constant return portfolio
Efficient Portfolio: portfolio with maximum expected
return for a given level of risk, or minimum risk for a
given expected return
Efficient Frontier: collection of all efficient portfolios
Optimal Portfolio: collection of securities that provides
an investor with the highest level of expected utility
Market Portfolio: all tradable assets
14. Capital Asset Pricing Model
(CAPM)
Method for predicting
how investment returns
are determined in an
efficient capital market
15. KEY TERMS
Capital Asset Pricing Model
capital market line (CML)
security market line (SML)
systematic risk
unsystematic risk
diversifiable risk
nondiversifiable risk
security characteristic line
(SCL)
positive abnormal returns
negative abnormal return
market index bias
model specification bias
time interval bias
nonstationary beta problem
arbitrage pricing theory (APT)
arbitrage
16. CAPITAL ASSET PRICING MODEL
Basic Assumptions
Investors hold efficient portfolios; higher expected returns
involve higher risk.
Unlimited borrowing and lending are available at the risk-
free rate.
Investors have homogeneous expectations.
There is a one-period time horizon.
Investments are infinitely divisible.
No taxes or transaction costs exist.
Inflation is fully anticipated.
Capital markets are in equilibrium.
17. CAPM & Market
Efficiency
CAPM can test Efficient Market Hypothesis.
Market is efficient if only risk-free assets give risk-
free rates of return (e.g., Treasury bills).
Deviations may indicate opportunities.
Modeling predictions can suggest improvements to
market functioning.
18. Lending & Borrowing Under
the CPM
Assumption of unlimited lending and borrowing at
risk-free rate.
Lending if portion of portfolio held in risk-free
assets.
Borrowing (leverage) if more than 100% of
portfolio is invested in risky assets.
Superior returns made possible with lending and
borrowing; creates spectrum of risk preference for
different investors.
19. CAPITAL ASSET PRICING MODEL
Three Linear Relationships
Capital Market Line: linear risk-return trade-off for
all investment portfolios
Security Market Line: linear risk-return trade-off
for individual stocks
Security Characteristic Line: linear relation
between the return on individual securities and the
overall market at every point in time
20. CAPITAL ASSET PRICING MODEL
Three Linear Relationships
Capital Market Line: linear risk-return trade-off for
all investment portfolios
Standard Deviation (total portfolio risk)
E(R)
M
Rf
s = market s
21. EXPECTED RETURN & RISK
The Capital Market Line (CML)
Linear risk-return trade-off for all investment portfolios given by
F
M
R
R
F
R
R
F
M
F
P
R
R
E
R
R
R
E
R
R
E
M
P
P
M
s
s
s
s
23. Security Market Line (SML)
Security Market Line: linear risk-return trade-off for
individual stocks
Systematic Risk: return volatility tied to overall
market; also called nondiversifiable risk
Unsystematic Risk: return volatility tied specifically to
an individual company; also called diversifiable risk
Beta: sensitivity of a security’s returns to the
systematic market risk factor
25. CAPITAL ASSET PRICING MODEL
Three Linear Relationships
Security Market Line: linear risk-return trade-off
for all individual stocks
Systematic Risk
E(R)
M
Rf
= 1
27. The Security
Characteristic Line
Linear relation between the return on individual securities and
the overall market at every point in time, given by:
Positive Abnormal Returns: above-average returns that can’t
be explained as compensation for added risk
Negative Abnormal Returns: below-average returns that
cannot be explained by below-market risk
R R
it i i Mt i
28. Empirical Implications of
CAPM
Optimal portfolio choice depends on market risk-return trade-
offs and individual investors’ differences in risk preferences.
Relation between expected return and risk is linear for all
portfolios and individual assets.
Expected rate of return is risk-free rate plus relative risk (ßp)
times market risk premium.
High beta portfolios earn high risk premiums.
Low beta portfolios earn low risk premiums.
Stock price measures relevant risk for all securities.
29. EMPIRICAL CRITICISMS OF BETA
MODEL SPECIFICATION PROBLEMS
CAPM provides only incomplete description of return
volatility—volatility in individual issues can only be described
as a function of overall market volatility.
Overall market volatility very difficult to measure
Market Index Bias: distortion to beta estimates due to fact that
indexes are imperfect proxies for overall market
No single index includes all capital assets, including stocks,
bonds, real estate, collectibles, etc.
Model Specification Bias: distortion to beta estimates because
SCL fails to include other important systematic influences on
stock market volatility
30. EMPIRICAL CRITICISMS OF BETA
Data Interval & Nonstationary Beta Problems
Data Interval Problem: beta
estimation problem derived
from the fact that beta
estimates depend on data
interval studied
Nonstationary Beta Problem:
difficulty tied to the fact that
betas are inherently unstable
31. Testable Limitations Of
CAPM
ß, the slope of the regression of a security’s return on
the market return, is the only risk factor needed to
explain expected return.
ß captures a positive expected return premium for risk.
Other risk factors emerge:
firm size
low P/E, price/cash flow, P/B, and sales growth
33. Arbitrage Pricing Theory
(APT)
Multifactor asset-pricing model that allows
market ßs to represent only one of the firm’s
many risk factors.
Arbitrage: simultaneous buying and selling of
the same asset at different markets/maturities
APT suggests that asset returns might be
affected by N risk factors.
34. APT vs. CPM
Volatile returns attributable to six-factor APT
models are very unstable—explain very little of
variation in average returns.
Though both CAPM and APT theory and
evidence confirm relationship between risk and
return, neither approach gives precise estimates.
Neither provides foolproof test of EMF.
35. KEY TERMS
Capital Asset Pricing
investment portfolio
portfolio theory
expected return
risk
probability distribution
utility
disutility
risk averse
zero-risk portfolio
efficient portfolio
efficient frontier
optimal portfolio
market portfolio
capital asset pricing
model
