Ch5 Portfolio Theory -Risk and Return
Liang (Kevin) Guo
Learning Objectives
Be able to calculate ex post and ex ante risk and return statistical measures, such as holding period return, average returns, expected returns, and standard deviation.
Understand the difference between time-weighted and dollar-weighted returns, geometric and arithmetic averages.
Be able to construct portfolios of different risk levels, given information about risk free rates and returns on risky assets.
Be able to explain the CML theory.
Table of Contents
5.1 Rates of Return
5.2 Risk and Risk Premiums
5.3 Inflation and Real Rates of Return
5.4 Asset Allocation Across Risky and Risk Free Portfolios
5.5 Passive Strategies and The Capital Market Line (CML)
5.1 Rates of Return
Considering one-single period investment: regardless of the length of the period.
Holding period return (HPR): measuring Ex-Post (Past) Returns over one-single period.
HPR = [PS - PB + CF] / PB
where
PS = Sale price (or P1)
PB = Buy price ($ you put up) (or P0)
CF = Cash flow during holding period ( Such as dividend, interest)
Example: You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. What is your HPR?
Annualizing HPRs
Annualize a holding period return: translate it into percentage per year.
(1) Without compounding (Simple or APR):
HPRann = HPR/n
(2) With compounding: EAR
HPRann = [(1+HPR)1/n ]-1
where n = number of years held
Annualizing HPRs for holding periods of greater than one year
Example: Suppose you buy one share of a stock today for $45 and you hold it for two years and sell it for $52. You also received $8 in dividends at the end of the two years. What is the annual rate of return with and without compounding?
HPR =
(1) Annualized w/out compounding
(2) The annualized HPR assuming annual compounding is (n =2 ):
(
Annualizing HPRs for holding periods of less than one year
Example: Suppose you buy one share of a stock today for $45 and you hold it for 3 months and sell it for $52. You also received $8 in dividends at the end of the two years. What is the annual rate of return with and without compounding?
HPR =
(1) Annualized w/out compounding
(2) The annualized HPR assuming annual compounding is (n =0.25 ):
Investment Returns over multiple periods
The holding period return (HPR) is a simple measure of investment return over a single period.
But how to measure the performance of a mutual fund over the last ten-year period?
Several measures to find the average investment return for a time series of returns .
(a) Arithmetic average return (simple Time-weighted average)
(b) Geometric average return (Geometric time-weighted average)
(c) Dollar-weighted return
(a) Arithmetic Average Return (AAR)
(a) Arithmetic average (simple Time-weighted average)
Arithmetic means are the sum of ...
This document discusses key concepts in portfolio theory, including how to calculate investment returns over single and multiple periods. It defines holding period return (HPR) to measure single period returns and arithmetic average, geometric average, and dollar-weighted return to measure returns over many periods. It also explains how to calculate the expected return, variance, and standard deviation of investments to quantify the expected reward and risk.
This document provides an overview of key concepts in investment analysis and portfolio management. It discusses what constitutes an investment, factors that influence required rates of return such as time value of money, inflation, and risk. It also covers measures of historical and expected rates of return, risk of expected returns using variance and standard deviation, and the three determinants of required rates of return - the real risk-free rate, expected inflation, and risk premium.
1) The chapter discusses sources of investment returns including income returns from cash flows and returns from changes in the value of investments.
2) It describes how to measure returns such as dollar returns, holding period returns, and annualized returns which allow comparisons over different time periods.
3) Risk is defined as the uncertainty of investment returns and can be measured by the variability of returns using metrics like variance and standard deviation. The higher the risk, the higher the expected return required by investors.
This document discusses various methods for calculating rates of return on investments including holding period return (HPR), arithmetic average return, geometric average return, dollar-weighted average return, and annualized returns. It provides examples of calculating these different rates of return for stocks, mutual funds, and other investments. The document also covers risk measures like standard deviation, variance, value at risk (VaR), scenario analysis, and how diversifying a portfolio across multiple assets with differing correlations can reduce overall portfolio risk for a given expected return.
The Investment Setting-investment ch01.pptxFamiFamz1
The Investment Setting.Why do individuals invest ?
What is an investment ?
How do we measure the rate of return on an investment ?
How do investors measure risk related to alternative investments ?
Chapter7 an introduction to risk and returnRodel Falculan
This chapter discusses risk and return in financial markets. It defines realized and expected rates of return as well as risk. Historically, riskier investments like small stocks have achieved higher average returns than less risky investments like government bonds, but also experienced greater price fluctuations. The chapter compares arithmetic and geometric average returns and explains why the geometric average best measures the compound growth rate. The efficient market hypothesis posits that market prices instantly reflect all available information.
This document discusses key concepts related to investment risk and returns. It defines investments, returns, and different types of returns including expected, required, actual, and market rates of return. It also discusses different types of risk like standalone and portfolio risk. Models for evaluating risk and return are covered, including the Capital Asset Pricing Model (CAPM) and Security Market Line (SML). The SML plots expected returns based on levels of systematic risk and can be used to identify overvalued and undervalued investments. Changes to the SML impact expected returns and the cost of capital for companies.
This document discusses key concepts in portfolio theory, including how to calculate investment returns over single and multiple periods. It defines holding period return (HPR) to measure single period returns and arithmetic average, geometric average, and dollar-weighted return to measure returns over many periods. It also explains how to calculate the expected return, variance, and standard deviation of investments to quantify the expected reward and risk.
This document provides an overview of key concepts in investment analysis and portfolio management. It discusses what constitutes an investment, factors that influence required rates of return such as time value of money, inflation, and risk. It also covers measures of historical and expected rates of return, risk of expected returns using variance and standard deviation, and the three determinants of required rates of return - the real risk-free rate, expected inflation, and risk premium.
1) The chapter discusses sources of investment returns including income returns from cash flows and returns from changes in the value of investments.
2) It describes how to measure returns such as dollar returns, holding period returns, and annualized returns which allow comparisons over different time periods.
3) Risk is defined as the uncertainty of investment returns and can be measured by the variability of returns using metrics like variance and standard deviation. The higher the risk, the higher the expected return required by investors.
This document discusses various methods for calculating rates of return on investments including holding period return (HPR), arithmetic average return, geometric average return, dollar-weighted average return, and annualized returns. It provides examples of calculating these different rates of return for stocks, mutual funds, and other investments. The document also covers risk measures like standard deviation, variance, value at risk (VaR), scenario analysis, and how diversifying a portfolio across multiple assets with differing correlations can reduce overall portfolio risk for a given expected return.
The Investment Setting-investment ch01.pptxFamiFamz1
The Investment Setting.Why do individuals invest ?
What is an investment ?
How do we measure the rate of return on an investment ?
How do investors measure risk related to alternative investments ?
Chapter7 an introduction to risk and returnRodel Falculan
This chapter discusses risk and return in financial markets. It defines realized and expected rates of return as well as risk. Historically, riskier investments like small stocks have achieved higher average returns than less risky investments like government bonds, but also experienced greater price fluctuations. The chapter compares arithmetic and geometric average returns and explains why the geometric average best measures the compound growth rate. The efficient market hypothesis posits that market prices instantly reflect all available information.
This document discusses key concepts related to investment risk and returns. It defines investments, returns, and different types of returns including expected, required, actual, and market rates of return. It also discusses different types of risk like standalone and portfolio risk. Models for evaluating risk and return are covered, including the Capital Asset Pricing Model (CAPM) and Security Market Line (SML). The SML plots expected returns based on levels of systematic risk and can be used to identify overvalued and undervalued investments. Changes to the SML impact expected returns and the cost of capital for companies.
chapter 5 notes on the significance of the logistal measuresluche7
- A nominal interest rate is the growth rate of money while a real interest rate is the growth rate of purchasing power after accounting for inflation.
- The Fisher hypothesis states that the nominal interest rate equals the real interest rate plus expected inflation.
- The breakeven inflation rate derived from Treasury securities implies the inflation expectations of market participants over the next 10 years.
- Sources of investment risk include macroeconomic fluctuations, changing industry fortunes, and firm-specific developments.
The document discusses the trade-off between risk and return in investments. It provides three key points:
1. Expected return represents the marginal benefit of investing while risk is the marginal cost. There is always a trade-off between higher expected return and higher expected risk.
2. The discounted cash flow (DCF) method uses three steps to value risky assets: determining expected cash flows, choosing a discount rate reflecting the asset's risk, and calculating present value.
3. Risk and return are positively correlated both across asset classes and for individual securities - investors require a higher expected return to accept more risk. However, diversification can reduce unsystematic risk for a portfolio.
The document discusses risk and return in investments. It defines key concepts like holding period return (HPR), expected return, standard deviation, variance, and coefficient of variation. It provides examples of calculating HPR for stocks based on purchase price, selling price, and dividends. Expected return is the average HPR and can be calculated in different ways. Risk is the variability in returns and can be measured using standard deviation, variance, beta, etc. The document also discusses portfolio returns and how to calculate expected portfolio return based on individual asset expected returns and weights.
Portfolio Mgt Ch 01 The Investment SettingSalik Sazzad
This document discusses key concepts related to investment analysis and portfolio management. It defines key terms like real rate of return, inflation premium, and risk premium. It also covers topics like measuring historical rates of return using holding period return and equivalent annual return. The document discusses measuring risk using standard deviation and beta. It explains that the required rate of return on an investment is determined by the real risk-free rate, expected inflation, and the risk premium required for the investment's inherent risk.
This document discusses various methods of measuring risk, including variance, standard deviation, skewness, kurtosis, and the components of risk such as project-specific risk, competitive risk, industry risk, market risk, and international risk. It then discusses the capital asset pricing model (CAPM) and how it uses beta to measure non-diversifiable risk and translate that into an expected return. The document provides an example of estimating beta for Disney stock.
by G-10
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
Rasik Rownak Hossain
Shakib Fardous
Md. Rakibul Islam
Effat Ara Saima
Rafia Sultana
Tanvir Ahmed
Md.Shahidul Islam
SK Shourov Ahemmed
Tamjedul Alam Evan
Romana Haque Saima
Sarkar Muhammad Shohag
Khademul Islam
Jannatul Ferdous
Sheikh Hamim Hasan
Toufique Ul Haque Tuhin
Kerobin Hasda
The document discusses various concepts related to portfolio management and investments. It defines portfolio management as building and overseeing investments to meet long-term financial goals and risk tolerance. It also defines investment, investor, holding period return (HPR), holding period yield (HPY), arithmetic mean (AM) and geometric mean (GM) for calculating historical returns. It provides examples to calculate expected returns and discusses different types of risk like business, financial, liquidity and inflation risk.
This document provides an overview of key concepts from Chapter 1 of the textbook "Analysis of Investment and Management of Portfolio" including:
- Why individuals invest, including balancing present vs. future consumption
- Defining investment and the components of return including time value, inflation, and risk premium
- Calculating historical rates of return through holding period return, yield, arithmetic vs. geometric mean
- Measuring portfolio returns by taking a weighted average of individual investment returns
The summary covers the essential topics and calculations discussed in the chapter introduction on measuring and evaluating investment returns.
This document discusses key concepts in capital market theory and risk/return analysis, including:
1) Defining average and expected rates of return, and how to measure risk for individual assets using standard deviation and variance.
2) Calculating historical average returns for securities and determining the relationship between higher risk and higher expected returns.
3) Explaining how expected risk is calculated using variance, and how risk-averse, risk-neutral, and risk-seeking investors approach investments differently depending on risk and return levels.
The Arbitrage Pricing Theory (APT) provides an alternative to the Capital Asset Pricing Model (CAPM) for estimating expected returns. The APT assumes returns are generated by multiple systematic risk factors rather than a single market factor. It allows for assets to be mispriced and does not require assumptions of a market portfolio or homogeneous expectations. Under the APT, the expected return of an asset is equal to the risk-free rate plus the product of each risk factor's premium and the asset's sensitivity to that factor.
This document discusses risk and return, including key concepts such as:
- Risk is defined as the potential variability in investment returns, while return refers to the total gain or loss on an investment.
- There is typically a relationship between higher risk and higher potential returns.
- Standard deviation and beta are common measures used to quantify investment risk. Beta specifically measures the volatility of a security compared to the overall market.
- Portfolio risk can be reduced through diversification among assets with low or negative correlations. However, some systematic market risk cannot be diversified away.
- The Capital Asset Pricing Model (CAPM) describes the expected return of an asset based on its beta and the expected market return.
The document discusses various concepts related to security risk and return, including:
1. Calculating returns from security investments
2. Understanding historical return and risk
3. Efficient market hypothesis and its implications
4. Calculating expected returns and the impact of diversification on risk
It also covers risk-return tradeoff, systematic risk, security market line, and using the Capital Asset Pricing Model.
This document discusses key concepts related to risk and return including:
1. Definitions of actual, expected, and required returns. Expected return should equal required return for fair pricing.
2. Sources of total risk including systematic and unsystematic risk. Unsystematic risk is diversifiable while systematic risk requires compensation.
3. Measures of return such as holding period return and arithmetic/geometric means. Measures of risk include variance, standard deviation, and downside risk.
4. The relationship between risk and return showing that higher risk investments require higher expected returns. Investor indifference curves illustrate risk preferences.
5. Models relating return and risk including the CAPM and multifactor models. Security pricing relates
This is the fifth presentation for the University of New England Graduate School of Business course GSB711 Managerial Finance, offered by Dr Subba Reddy Yarram. This presentation examines risk, return and the Capital Asset Pricing Model (CAPM).
This document discusses risk and return, defining risk as the potential divergence between actual and expected outcomes. It outlines measures of return such as dollar return, percentage return, and holding period return. Risk is measured using standard deviation, which indicates how spread out returns are from the mean. Higher standard deviation means higher risk. Charts of market indexes like the Dow Jones Industrial Average show the volatility of returns over time.
This document discusses risk and return, defining risk as the potential divergence between actual and expected outcomes. It presents data on market indexes like the Dow Jones Industrial Average, NASDAQ, and S&P/TSX over time, showing fluctuations. It then covers calculating returns, including dollar returns, percentage returns, and holding period returns. Risk is measured using standard deviation, which captures how spread out returns are from the mean. The relationship between risk and return is important for investors, corporations, and financial intermediaries.
This document discusses risk and return, defining risk as the potential divergence between actual and expected outcomes. It outlines measures of return such as dollar return, percentage return, and holding period return. Risk is measured using standard deviation, which indicates how spread out returns are from the mean. Higher standard deviation means higher risk. Charts of market indexes like the Dow Jones Industrial Average show the volatility of returns over time.
1. Nicks Enchiladas Incorporated has preferred stock outstand.docxjackiewalcutt
1. The document provides examples and explanations of stock valuation models, including the discounted dividend model and the constant growth model.
2. The constant growth model assumes dividends and stock prices will grow at a constant rate indefinitely. It provides a simplified equation to value a stock based on the next expected dividend, required rate of return, and long-term growth rate.
3. An example applies the constant growth model to value a stock with a $1.15 dividend growing at 8% annually and a required return of 13.4%, calculating the stock price as $23.
The document discusses different methods for calculating rates of return on investments. It provides details on simple rates of return, adjusted rates of return, and holding period returns. Historical data on rates of return for various asset classes like stocks, bonds, and bills from 1926-1999 is presented, showing average annual returns and standard deviations. The risk-return relationship and concept of risk premiums are also covered.
The document discusses the relationship between risk and return when investing. It states that there is a trade-off between expected risk and expected return, with higher risk investments typically offering higher returns to compensate investors for taking on more risk. It also discusses how diversification across multiple assets can reduce the non-systematic/diversifiable risk in a portfolio, but not the systematic/market risk that is related to movements in the overall market. The document defines beta as a measure of a stock's systematic risk relative to the market.
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2. How many Male, Female, ND, and Other are there in each ALIGN. (Bar comparison chart)
3. How many red-haired heroes do Marvel and DC have?
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2. Human immunodeficiency virus (HIV) preferentially destroys CD4+ cells. Specifically, what effect does this have on antibody and cell-mediated immunity?
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chapter 5 notes on the significance of the logistal measuresluche7
- A nominal interest rate is the growth rate of money while a real interest rate is the growth rate of purchasing power after accounting for inflation.
- The Fisher hypothesis states that the nominal interest rate equals the real interest rate plus expected inflation.
- The breakeven inflation rate derived from Treasury securities implies the inflation expectations of market participants over the next 10 years.
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The document discusses the trade-off between risk and return in investments. It provides three key points:
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The document discusses risk and return in investments. It defines key concepts like holding period return (HPR), expected return, standard deviation, variance, and coefficient of variation. It provides examples of calculating HPR for stocks based on purchase price, selling price, and dividends. Expected return is the average HPR and can be calculated in different ways. Risk is the variability in returns and can be measured using standard deviation, variance, beta, etc. The document also discusses portfolio returns and how to calculate expected portfolio return based on individual asset expected returns and weights.
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This document discusses various methods of measuring risk, including variance, standard deviation, skewness, kurtosis, and the components of risk such as project-specific risk, competitive risk, industry risk, market risk, and international risk. It then discusses the capital asset pricing model (CAPM) and how it uses beta to measure non-diversifiable risk and translate that into an expected return. The document provides an example of estimating beta for Disney stock.
by G-10
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
Rasik Rownak Hossain
Shakib Fardous
Md. Rakibul Islam
Effat Ara Saima
Rafia Sultana
Tanvir Ahmed
Md.Shahidul Islam
SK Shourov Ahemmed
Tamjedul Alam Evan
Romana Haque Saima
Sarkar Muhammad Shohag
Khademul Islam
Jannatul Ferdous
Sheikh Hamim Hasan
Toufique Ul Haque Tuhin
Kerobin Hasda
The document discusses various concepts related to portfolio management and investments. It defines portfolio management as building and overseeing investments to meet long-term financial goals and risk tolerance. It also defines investment, investor, holding period return (HPR), holding period yield (HPY), arithmetic mean (AM) and geometric mean (GM) for calculating historical returns. It provides examples to calculate expected returns and discusses different types of risk like business, financial, liquidity and inflation risk.
This document provides an overview of key concepts from Chapter 1 of the textbook "Analysis of Investment and Management of Portfolio" including:
- Why individuals invest, including balancing present vs. future consumption
- Defining investment and the components of return including time value, inflation, and risk premium
- Calculating historical rates of return through holding period return, yield, arithmetic vs. geometric mean
- Measuring portfolio returns by taking a weighted average of individual investment returns
The summary covers the essential topics and calculations discussed in the chapter introduction on measuring and evaluating investment returns.
This document discusses key concepts in capital market theory and risk/return analysis, including:
1) Defining average and expected rates of return, and how to measure risk for individual assets using standard deviation and variance.
2) Calculating historical average returns for securities and determining the relationship between higher risk and higher expected returns.
3) Explaining how expected risk is calculated using variance, and how risk-averse, risk-neutral, and risk-seeking investors approach investments differently depending on risk and return levels.
The Arbitrage Pricing Theory (APT) provides an alternative to the Capital Asset Pricing Model (CAPM) for estimating expected returns. The APT assumes returns are generated by multiple systematic risk factors rather than a single market factor. It allows for assets to be mispriced and does not require assumptions of a market portfolio or homogeneous expectations. Under the APT, the expected return of an asset is equal to the risk-free rate plus the product of each risk factor's premium and the asset's sensitivity to that factor.
This document discusses risk and return, including key concepts such as:
- Risk is defined as the potential variability in investment returns, while return refers to the total gain or loss on an investment.
- There is typically a relationship between higher risk and higher potential returns.
- Standard deviation and beta are common measures used to quantify investment risk. Beta specifically measures the volatility of a security compared to the overall market.
- Portfolio risk can be reduced through diversification among assets with low or negative correlations. However, some systematic market risk cannot be diversified away.
- The Capital Asset Pricing Model (CAPM) describes the expected return of an asset based on its beta and the expected market return.
The document discusses various concepts related to security risk and return, including:
1. Calculating returns from security investments
2. Understanding historical return and risk
3. Efficient market hypothesis and its implications
4. Calculating expected returns and the impact of diversification on risk
It also covers risk-return tradeoff, systematic risk, security market line, and using the Capital Asset Pricing Model.
This document discusses key concepts related to risk and return including:
1. Definitions of actual, expected, and required returns. Expected return should equal required return for fair pricing.
2. Sources of total risk including systematic and unsystematic risk. Unsystematic risk is diversifiable while systematic risk requires compensation.
3. Measures of return such as holding period return and arithmetic/geometric means. Measures of risk include variance, standard deviation, and downside risk.
4. The relationship between risk and return showing that higher risk investments require higher expected returns. Investor indifference curves illustrate risk preferences.
5. Models relating return and risk including the CAPM and multifactor models. Security pricing relates
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2. The constant growth model assumes dividends and stock prices will grow at a constant rate indefinitely. It provides a simplified equation to value a stock based on the next expected dividend, required rate of return, and long-term growth rate.
3. An example applies the constant growth model to value a stock with a $1.15 dividend growing at 8% annually and a required return of 13.4%, calculating the stock price as $23.
The document discusses different methods for calculating rates of return on investments. It provides details on simple rates of return, adjusted rates of return, and holding period returns. Historical data on rates of return for various asset classes like stocks, bonds, and bills from 1926-1999 is presented, showing average annual returns and standard deviations. The risk-return relationship and concept of risk premiums are also covered.
The document discusses the relationship between risk and return when investing. It states that there is a trade-off between expected risk and expected return, with higher risk investments typically offering higher returns to compensate investors for taking on more risk. It also discusses how diversification across multiple assets can reduce the non-systematic/diversifiable risk in a portfolio, but not the systematic/market risk that is related to movements in the overall market. The document defines beta as a measure of a stock's systematic risk relative to the market.
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1. Sensation refers to an actual event; perception refers to how we .docxketurahhazelhurst
1. Sensation refers to an actual event; perception refers to how we interpret the event. What are some cultural differences that might affect responses to particular stimuli, particularly in taste and pain?
2. Most of us feel like we never get enough sleep. What are the stages of sleep and what is the importance of sleep? What are some common sleep disorders and treatments?
.
1. The Institute of Medicine (now a renamed as a part of the N.docxketurahhazelhurst
1. The Institute of Medicine (now a renamed as a part of the
National Academies of Sciences, Engineering, and Medicine
) defined patient-centered care as: "Providing care that is respectful of and responsive to individual patient preferences, needs, and values, and ensuring that patient values guide all clinical decisions.”[1] While this definition clearly emphasizes the importance of a patient’s perspective in the context of clinical care delivery, it does not allow managers to focus on the actual “person” inside the institutional role of the patient.
In the same sense that a person who is incarcerated in a prison may receive extremely humane treatment, the “person” is still defined into the role of an “inmate,” and as such cannot, by definition, be granted the same rights and privileges as a non-institutionalized member of the civil order enjoys. In other words, I may be placed in a cell with great empathy and understanding of my preferences, needs, and values, but I am still being locked-up in jail.
No one is suggesting that being admitted into a jail cell is the same as being admitted into a hospital bed. There are many obvious differences between the two, including the basic purpose of the two institutions.
But while much is different, what is the same is how a pre-existing set of structured behaviors and processes are used to firmly, and without asking or negotiating, radically transform a “regular” person into a defined role of a “patient” that then can be diagnosed, treated, and discharged back into the world once the patient has finished their “time” in the “system.”
While patient-centered care emphasizes the value of increased sensitivity to a patient’s preferences, needs, and values, what we want to focus on is how decisions made by healthcare leaders affect the actual experience of a person receiving that care.
So with the "real person" in mind, this week's question is:
What can healthcare leaders do in improve the actual personal experience that "real people" go through as our "patients?"
(Be sure to develop your answers AFTER you review the definition and roles of "Leadership" in the readings for this week).
[1] Institute on Medicine, Crossing the Quality Chasm: A New Health System for the 21st Century, March, 2001
2. Health Information Technonogy - PPP Discussion
The board has created an innovation fund designed to foster improved quality, increased access, or reduced costs in healthcare delivery. Select a health information technology related to genomics, precision medicine, or diagnostics that you would propose to be funded for implementation. Prepare a PowerPoint presentation that describes the selected health information technology, what it does, why it would be beneficial, and what risks may be involved. Please note, this activity is weighted 5% toward the final grade. The PowerPoint should be no more than 5-6 slides with the presenter's notes. Follow the APA format.
.
1. The Documentary Hypothesis holds that the Pentateuch has a number.docxketurahhazelhurst
1. The Documentary Hypothesis holds that the Pentateuch has a number of underlying documents (alt., sources) that were ultimately gathered and sewn into the Pentateuch as we now have it. The method of separating those underlying documents is called source criticism. Please perform a source-critical analysis of Gen 1-3. In so doing, please identify the significant features that distinguish each underlying document. Note: There are many such features.
2. Why are covenants important in the Bible? What do they accomplish? Are they all the same, whether in structure or outlook? Do the different writers view them differently? What does the ancient Near Eastern background to the biblical covenant contribute to our understanding?
3. Dt 6:4 used to be translated
“Hear, O Israel: The LORD [YHWH] our God, the LORD [YHWH] is one.”
Currently, we translate
“Hear, O Israel: The LORD [YHWH] is our God, the LORD [YHWH] alone.”
In all likelihood, the second translation is grammatically preferable. What is the interpretive difference between “one” and “alone”? Is it significant? How, if at all, does this verse relate to the First Commandment? How does this verse relate to Gen 1:26, 3:22, and 11:7? How does this verse relate to the variant non-MT variant in Dt 32:8-9 (as reproduced in HarperCollins)? Why is any of this important?
Be sure to provide a careful, well-written essay which gives ample biblical examples (proof texts) to support the point(s) you wish to make.
.
1. Search the internet and learn about the cases of nurses Julie.docxketurahhazelhurst
1. Search the internet and learn about the cases of nurses Julie Thao and Kimberly Hiatt.
2. List and discuss lessons that you and all healthcare professionals can learn from these two cases.
3. Describe how the principle of beneficence and the virtue of benevolence could be applied to these cases. Do you think the hospital adminstrators handled the situations legally and ethically?
4. In addition to benevolence, which other virtues exhibited by their colleagues might have helped Thao and Hiatt?
5. Discuss personal virtues that might be helpful to second victims themselves to navigate the grieving process.
Scholarly article, APA format, and no grammar error
.
1. Search the internet and learn about the cases of nurses Julie Tha.docxketurahhazelhurst
1. Search the internet and learn about the cases of nurses Julie Thao and Kimberly Hiatt.
2. List and discuss lessons that you and all healthcare professionals can learn from these two cases.
3. Describe how the principle of beneficence and the virtue of benevolence could be applied to these cases. Do you think the hospital adminstrators handled the situations legally and ethically?
4. In addition to benevolence, which other virtues exhibited by their colleagues might have helped Thao and Hiatt?
5. Discuss personal virtues that might be helpful to second victims themselves to navigate the grieving process.
use reference and scholarly nursing article.
.
1. Review the three articles about Inflation that are found below th.docxketurahhazelhurst
1. Review the three articles about Inflation that are found below this.
Globalization and Inflatio
n
Drivers of Inflation
Inflation
and Unemploymen
t
2. Locate two JOURNAL articles which discuss this topic further. You need to focus on the Abstract, Introduction, Results, and Conclusion. For our purposes, you are not expected to fully understand the Data and Methodology.
3. Summarize these journal articles. Please use your own words. No copy-and-paste. Cite your sources.
4.The replies are due by the deadline specified in the Course Schedule.
Please post (in APA format) your article citation.
.
1. Review the following request from a customerWe have a ne.docxketurahhazelhurst
1. Review the following request from a customer:
We have a need to replace the aging Signage Application. This application is housed in District 4 and serves the district as well as two other districts. We would like a new application that can be used statewide to track all information related to road signs.
The current system is old and doesn’t do most of what we need it to.
The current system has a whole bunch of reports, but no way for the user to update them by themselves without getting IT involved.
We also can’t create our own reports, on-demand, when we need to. Currently, data is entered into the application manually by Administrative Staff, but in the future, we would like to be able to take a picture of the road sign using a phone app, and have it automagically populate the database with geospatial location and other information. We thought about having a Smart Watch interface, but we don’t need that. Also, the current method does not have any way to manage the quality of the data that is entered, so there is a lot of garbage information there. There is no way to centrally manage security access, with the existing application. We want to get real time alerts when a sign gets knocked over in an accident and have a dashboard that shows where signs have been knocked over across the state. This is kind of important, but not super-critical. We need to store location information, types of signs, when a new sign is installed, who installed it, etc. We plan to provide the phone app to drivers in each district who will drive around, take pictures of the signs, and upload them to the database at the end of each day, or in realtime, if a data connection is available.
Back in Central Office, reviewers will review the sign information and validate it. A report will be printed every month with the results and a map. There are probably other things, but we can’t think of anything else right now.
2. List the main goal(s) of this request
3. Write all the user stories you see (include value statements and acceptance criteria, if possible)
4. Prioritize the user stories as
a. Critical
b. Important
c. Useful
d. Out of Scope
5. Are the user stories sufficiently detailed? If not, what steps would you take to split them/further define them?
6. What are the known Data Entities?
7. Is there an implied business process? Draw an activity diagram or a flow chart of it
8. Who are the actors/roles?
9. What questions would you ask of the stakeholders to get more information?
10. What technology should be used to implement the solution?
11. What would you do next as the assigned Business Analyst working on an Agile team?
.
1. Research risk assessment approaches.2. Create an outline .docxketurahhazelhurst
1. Research risk assessment approaches.
2. Create an outline for a basic qualitative risk assessment plan.
3. Write an introduction to the plan explaining its purpose and importance.
4. Define the scope and boundaries for the risk assessment.
5. Identify data center assets and activities to be assessed.
6. Identify relevant threats and vulnerabilities. Include those listed in the scenario and add to the list if needed.
7. Identify relevant types of controls to be assessed.
8. Identify the key roles and responsibilities of individuals and departments within the organization as they pertain to risk assessments.
9. Develop a proposed schedule for the risk assessment process.
10. Complete the draft risk assessment plan detailing the information above. Risk assessment plans often include tables, but you choose the best format to present the material. Format the bulk of the plan similar to a professional business report and cite any sources you used.
.
1. Research has narrowed the thousands of leadership behaviors into .docxketurahhazelhurst
1. Research has narrowed the thousands of leadership behaviors into two primary dimensions. Please list and discuss these two behaviors.
2. Distinguish between charismatic, transformational, and authentic leadership. Could an individual display all three types of leadership?
.
1. Research Topic Super Computer Data MiningThe aim of this.docxketurahhazelhurst
1. Research Topic: Super Computer Data Mining
The aim of this project is to produce a super-computing data mining resource for use by the UK academic community which utilizes a number of advanced machine learning and statistical algorithms for large datasets. In particular, a number of evolutionary computing-based algorithms and the ensemble machine approach will be used to exploit the large-scale parallelism possible in super-computing. This purpose is embodied in the following objectives:
1. to develop a massively parallel approach for commonly used statistical and machine learning techniques for exploratory data analysis
1. to develop a massively parallel approach to the use of evolutionary computing techniques for feature creation and selection
1. to develop a massively parallel approach to the use of evolutionary computing techniques for data modelling
1. to develop a massively parallel approach to the use of ensemble machines for data modelling consisting of many well-known machine learning algorithms;
1. to develop an appropriate super-computing infra-structure to support the use of such advanced machine learning techniques with large datasets.
Research Needs:
Problem definition – In the first phase problem definition is listed i.e. business aims and objectives are determined taking into consideration certain factors like the current background and future prospective.
Data exploration – Required data is collected and explored using various statistical methods along with identification of underlying problems.
Data preparation – The data is prepared for modeling by cleansing and formatting the raw data in the desired way. The meaning of data is not changed while preparing.
Modeling – In this phase the data model is created by applying certain mathematical functions and modeling techniques. After the model is created it goes through validation and verification.
Evaluation – After the model is created, it is evaluated by a team of experts to check whether it satisfies business objectives or not.
Deployment – After evaluation, the model is deployed and further plans are made for its maintenance. A properly organized report is prepared with the summary of the work done.
Research paper Policy
· APA format
. https://apastyle.apa.org/
. https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guide/general_format.html
· Min number of pages are 15 pages
· Must have
. Contents with page numbers
. Abstract
. Introduction
. The problem
4. Are there any sub-problems?
4. Is there any issue need to be present concerning the problem?
. The solutions
5. Steps of the solutions
. Compare the solution to other solution
. Any suggestion to improve the solution
. Conclusion
. References
· Missing one of the above will result -5/30 of the research paper
· Paper does not stick to the APA will result in 0 in the research paper
· Submission
. you have multiple submission to check you safe assignments
. The percentage accepted is 1%.
1. Research and then describe about The Coca-Cola Company primary bu.docxketurahhazelhurst
1. Research and then describe about The Coca-Cola Company primary business activities. Include: Minimum 7 Pages. Excluding reference page
2.
A. A brief historical summary,
B. A list of competitors,
C. The company's position within the industry,
D. Recent developments within the company/industry,
E. Future direction, and
F. Other items of significance to your corporation.
3. Include information from a variety of resources. For example:
A. Consult the Form 10-K filed with the SEC.
B. Review the Annual Report and especially the Letter to Shareholders
C. Explore the corporate website.
D. Select at least two significant news items from recent business periodicals
The report should be well written with cover page, introduction, the body of the paper (with appropriate subheadings), conclusion, and reference page.
.
1. Prepare a risk management plan for the project of finding a job a.docxketurahhazelhurst
1. Prepare a risk management plan for the project of finding a job after graduation.
and
2. Develop a reward system for motivating IPT members to do their jobs more conscientiously and to take on more responsibility.
[The assignment should be at least 400 words minimum and in APA format (including Times New Roman with font size 12 and double spaced), and attached as a WORD file.]
Plagiarism free
.
1. Please define the term social class. How is it usually measured .docxketurahhazelhurst
1. Please define the term social class. How is it usually measured? What are some ways that social class is affecting health outcomes for people who become ill with COVID-19?
2. What is the CARES Act? Has it been enough? What has happened to people's ability to pay their bills since it expired?
3. As things stand now, data is showing higher COVID-19 related mortality rates for African Americans. Given what you know from the textbook and from the attached articles, what are some explanations for the disparity?
4. What is environmental racism (injustice)? How does environmental racism put some populations at higher risk for severe medical complications than others? (Vice article)
https://www.theatlantic.com/ideas/archive/2020/07/600-week-buys-freedom-fear/613972/
https://www.vox.com/2020/4/10/21207520/coronavirus-deaths-economy-layoffs-inequality-covid-pandemic
https://www.vice.com/en_us/article/pke94n/cancer-alley-has-some-of-the-highest-coronavirus-death-rates-in-the-country
https://www.theguardian.com/us-news/2020/apr/12/coronavirus-us-deep-south-poverty-race-perfect-storm
.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Ch5 Portfolio Theory -Risk and ReturnLiang (Kevin) Guo.docx
1. Ch5 Portfolio Theory -Risk and Return
Liang (Kevin) Guo
Learning Objectives
Be able to calculate ex post and ex ante risk and return
statistical measures, such as holding period return, average
returns, expected returns, and standard deviation.
Understand the difference between time-weighted and dollar-
weighted returns, geometric and arithmetic averages.
Be able to construct portfolios of different risk levels, given
information about risk free rates and returns on risky assets.
Be able to explain the CML theory.
Table of Contents
5.1 Rates of Return
5.2 Risk and Risk Premiums
2. 5.3 Inflation and Real Rates of Return
5.4 Asset Allocation Across Risky and Risk Free Portfolios
5.5 Passive Strategies and The Capital Market Line (CML)
5.1 Rates of Return
Considering one-single period investment: regardless of the
length of the period.
Holding period return (HPR): measuring Ex-Post (Past) Returns
over one-single period.
HPR = [PS - PB + CF] / PB
where
PS = Sale price (or P1)
PB = Buy price ($ you put up) (or P0)
CF = Cash flow during holding period ( Such as
dividend, interest)
Example: You put up $50 at the beginning of the year for an
investment. The value of the investment grows 4% and you earn
a dividend of $3.50. What is your HPR?
Annualizing HPRs
Annualize a holding period return: translate it into percentage
3. per year.
(1) Without compounding (Simple or APR):
HPRann = HPR/n
(2) With compounding: EAR
HPRann = [(1+HPR)1/n ]-1
where n = number of years held
Annualizing HPRs for holding periods of greater than one year
Example: Suppose you buy one share of a stock today for $45
and you hold it for two years and sell it for $52. You also
received $8 in dividends at the end of the two years. What is the
annual rate of return with and without compounding?
HPR =
(1) Annualized w/out compounding
(2) The annualized HPR assuming annual compounding is (n =2
):
4. (
Annualizing HPRs for holding periods of less than one year
Example: Suppose you buy one share of a stock today for $45
and you hold it for 3 months and sell it for $52. You also
received $8 in dividends at the end of the two years. What is the
annual rate of return with and without compounding?
HPR =
(1) Annualized w/out compounding
(2) The annualized HPR assuming annual compounding is (n
=0.25 ):
Investment Returns over multiple periods
The holding period return (HPR) is a simple measure of
investment return over a single period.
But how to measure the performance of a mutual fund over the
last ten-year period?
Several measures to find the average investment return for a
time series of returns .
(a) Arithmetic average return (simple Time-weighted average)
(b) Geometric average return (Geometric time-weighted
average)
5. (c) Dollar-weighted return
(a) Arithmetic Average Return (AAR)
(a) Arithmetic average (simple Time-weighted average)
Arithmetic means are the sum of returns in each period divided
by the number of periods.
Ignore compounding (Ignore reinvestment)
Used to forecast next-period return
n = number of time periods
(b) Geometric Average Return (GAR)
(b) Geometric average (Geometric time-weighted average
return)
Consider reinvestment (compounding)
6. n = number of time periods
Example: Continuing previous example, what is geometric
average return?
( c) Dollar-Weighted Return (DWR)
(c )Dollar-weighted return
It is the internal rate of return on an investment.
IRR method: (i.e. find the discount rate that makes the NPV of
the net cash flows equal zero.)
This measure of return considers both security performance and
changes in investment (accounting for cash flow).
If different amounts of money were managed in the portfolio for
each period it may be useful to see the Dollar weighted returns.
The DWR gives you an average return based on the stock’s
performance and dollar amount invested each period.
Tips on Calculating Dollar Weighted Returns
Initial Investment is an outflow
Ending value is considered as an inflow
Additional investment is an outflow
Security sales are an inflow
7. Dollar-Weighted Return (Example)
Example: You initially buy one share of mutual fund AAA at
$50, in one year collect a $2 dividend, and you buy another
share at $53. In two years you sell the stock for $54, after
collecting another $2 dividend per share. What is dollar-
weithted return?
NPV = $0 = -$50 - $51/(1+IRR) + $112/(1+IRR)2
Solve for IRR:
IRR is average annual dollar weighted return.
Dollar-weighted return vs Time-weighted return
Example: You initially buy one share of mutual fund AAA at
$50, in one year collect a $2 dividend, and you buy another
share at $53. In two years you sell the stock for $54, after
collecting another $2 dividend per share. What are the time-
weighted average return (Arithmetic Average Return and
Geometric Average Return )? What makes it different from
dollar-weighted return?
Time-weighted return (TWR) assumes you buy ONE share of
8. the stock at the beginning of each period and sell ONE share at
the end of each period. TWRs are thus independent of the
dollar amount invested in a given period.
DWR vs TWR (cont.)
TWR cash flows:
HPR for year 1 = HPR for year 2 =
To calculate TWRs:
(1) Arithmetic Average Return =
(2) Geometric Average Return =
Q: When should you use the DWR and when should you use the
TWR?
- If you want to measure the performance of your investment
in a fund, including the timing of your purchases and
redemptions you should calculate the DWR instead of TWR.
Year 0-1Year 1-20112-$50$ 2-$53$ 2+$53+$54
Arithmetic Average Return (AAR) vs Geometric Average
Return (GAR)
9. Q: When should you use the GAR and when should you use the
AAR?
A1: 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.
A2: When you are trying to estimate an expected return (ex-ante
return):
Use the Arithmetic Average Return (AAR)
Class Discussion
(1) If you want to measure the performance of your investment
in a fund, including the timing of your purchases and
redemptions you should calculate the __________.
(2) If you desire to forecast performance for next period, the
best forecast will be given by the ________.
(3) If you always reinvest your dividends and interest earned
on the portfolio. Which method provides the best measure of the
actual average historical performance of the investments you
have chosen?
10. A. Dollar weighted return
B. Geometric average return
C. Arithmetic average return
D. Index return
5.2 Risk and Risk Premiums
Risk = Uncertainty or potential variability in future cash flows
How likely/closely will the realized return be to the expected
return?
To quantify risk, we can begin with the question: What holding
period return are possible? And how likely are they?
To determine the variability, we calculate the standard deviation
of the distribution of realized returns.
Indicates the dispersion around the expected (historical average)
return
Two approaches to estimate the standard deviation.
Scenario Analysis
- Requires analysts’ estimates for probability & outcomes
(b) Using historical data
Assume the past data will extend into the future
Scenario Analysis
11. (a) Scenario Analysis: Describes a probability distribution of
future returns
List all possible economic outcomes (scenarios)
Specify both the probability (likelihood) of each scenario and
the HPR the security will realized in that scenario.
Example: The stock of Business Adventures sells for $40 a
share. Its likely dividend payout and end-of-year price depend
on the state of the economy by the end of the year as follows.
Economic statesProbabilityDividendStock priceHPRBoom
1/3250Normal conomy 1/3143Recession 1/30.534
The list of possible HPRs
with associated prob is
called the probability
Distribution of HPRs.
Scenario Analysis (Formula)
Scenario analysis
Requires analysts’ estimates for probability & outcomes
Subjective Expected Return (mean) is the weighted average of
all the possible returns, weighted by the probability that each
return will occur.
Subjective Variance is the expected value of the squared
deviation from the mean.
Standard deviation is square root of variance, describing the
expected value of deviation from the mean.
E(R) = Expected Return
12. VAR(R) = Variance
Pi = probability of a state
Ri = return if a state occurs
Example (Scenario Analysis)
The stock of Business Adventures sells for $40 a share. Its
likely dividend payout and end-of-year price depend on the state
of the economy by the end of the year as follows. Calculate the
expected HPR and standard deviation of the HPR.
Economic state ProbDividendStock priceHPRColumn B *
Column EDeviation from Mean ReturnColumn B * squared
deviationBoom 1/3250Normal Economy 1/3143Recession
1/30.534Column sums
Expected return =Variance =Square root of variance = Standard
deviation =
Using historical data
(b) Using historical data
Assume the past data will extend into the future
Estimating Expected HPR (E[r]) from ex-post data. Use the
arithmetic average of past returns as a forecast of expected
future returns
Expected return is arithmetic mean of historical realized return
Variance is the expected value of the squared deviation from the
mean.
Standard deviation is square root of variance, describing the
13. expected value of deviation from the mean.
Example (Using historical data)
Compute the Facebook’s expected daily return and the standard
deviation using its realized return from May 18, 2014 to June
30,2017.
How to interpret Standard Deviation?
Standard deviations are useful for ranking the investments from
riskiest to least risky.
High standard deviation indicates the high risk
About two-thirds (68.26%) of all possible outcomes fall within
one standard deviation above or below the average
About 95% of all possible outcomes fall within two standard
deviations above and below the average.
Example: How to interpret the standard deviation of precious
example? (Expected return =10.8% and S.D.=16.37%)
23
14. Normal Distribution
Risk is the possibility of getting returns different from
expected.
mean.
Returns > E[r] may not be considered as risk, but with
Frequency distributions of annual HPRs
Which is the most risky and which is the least risky?
Risk Premium
Risk Premium is additional return we must expect to receive for
assuming risk.
The risk premium is the difference between the expected return
of a risky asset and the risk-free rate.
Excess Return or Risk Premium= E[r] – rf
The risk free rate is the rate of return that can be earned with
certainty.
Risk premium depends on level of risk associated with the
assets. As the level of risk associated with asset increases, we
will demand additional expected returns.
15. Risk Aversion
Risk aversion is an investor’s reluctance to accept risk.
The degree to which investors are willing to invest risky asset
depends on their risk aversion.
Risk premium on risky assets is to induce risk-averse investor
to hold these assets.
Risk premium an investor demands of a risky portfolio also
depends on their risk aversion.
Quantifying risk aversion:
E(rp) = Expected return on portfolio p
rf = the risk free rate
0.5 = Scale factor
A = risk aversion, between 2 to 4
The larger (lower) A is, the more risk averse (tolerant) the
investors are, the larger (smaller) will be the investor’s added
return required to bear risk.
16. Sharpe (reward-to-volatility) Ratio
Sharpe (reward-to-volatility) Ratio: Risk-return trade-off,
measure risk-adjusted performance
The Sharpe ratio tells us whether a portfolio's returns are due to
smart investment decisions or a result of excess risk.
Class discussion: Considering two portfolios. Portfolio A
generated a return of 15% and a 25% standard deviation last
year while Portfolio B generated a return of 18% and a 32%
standard deviation last year. T-bills were paying 4% last year.
Which portfolio do you prefer?
Higher Sharpe measure indicates a more efficient portfolio
5.3 Inflation and Real Rates of Return
The average inflation rate for the last 40 years was about 4%.
17. For the last 40 years, this relatively small inflation rate reduces
the terminal value of $1 invested in T-bills from a nominal
value of $10.08 to a real value of $1.63.
Nominal rate of interest determines how much more money you
will have while real rate of interest represents the rate of
increase in your actual purchasing power, after adjusting
inflation.
inflation rate
We can express their precise relationship as follows (exact
Fisher effect): :
( 1+ nominal interest rate) = (1+ real rate of interest) (1+ rate
of inflation)
Class discussion (Interest rate)
Example: what is the nominal rate of interest if real interest
rate is 10% and inflation rate is 4%?
Example: what is the real rate of interest if nominal interest
rate is 10% and inflation rate is 4%?
Historical Real Returns & Sharpe Ratios
18. Real returns have been much higher for stocks than for bonds
Sharpe ratios measure the excess return to standard deviation.
The higher the Sharpe ratio the better.
Stocks have had much higher Sharpe ratios than bonds.
Real Returns%Sharpe RatioSeriesWorld Stock6.000.37US Large
Stock6.130.37Small Stock8.170.36World Bond2.460.24Long
term Bond2.220.24
Motivation (Portfolio Theory)
What is a Portfolio and Why is it useful?
A portfolio is simply a specific combination of securities,
usually defined by portfolio weights that sum to 1:
Weights can be positive (long positions) or negative (short
positions).
19. Example
Your investment account of $100,000 consists of three stocks:
200 shares of stock A, 1,000 shares of stock B, and 750 shares
of stock C. Your portfolio is summarized by the following
weights:
AssetSharesPrice/ShareDollar
InvestmentPortfolio
WeightA200$50 $10,000 10%B1000$60 $60,000 60%C750$40
$30,000 30%Total$100,000 100%
Motivation (Portfolio Theory)
Why not Pick the Best Stock instead of forming a portfolio?
We don’t know which stock is best!
Portfolios provide diversification, reducing unnecessary risks.
Portfolio can enhance performance by focusing bets.
Portfolios can customize and manage risk/reward trade-offs.
How do we construct a “Good” portfolio?
What does “good” mean?
What characteristics do we care about for a given portfolio?
Risk and return trade-offs
Investors like higher expected returns
Investors dislike risk
Question: How can we choose portfolio weights to optimize the
risk/reward characteristics of the overall portfolio?
Mean Variance Analysis
Objective:
20. Assume investors focus only on the expected return and
variance (or standard deviation) of their portfolios: higher
expected return is good, higher variance is bad
Develop a method for constructing optimal portfolios
Portfolio Returns and Risk
The expected return on a portfolio is the weighted average of
the expected returns of the individual assets in the portfolio.
The portfolio’s risk is measured by its return variance (Variance
is more complicated:
36
Portfolio Return Variance
Portfolio variance is the weighted sum of all the variances and
21. covariances:
There arenvariances, and n2 −n covariances�Covariances
dominate portfolio variance�Positive covariances increase
portfolio variance; negative covariances decrease portfolio
variance (diversification)
5.4 Asset Allocation Across Risky and Risk Free Portfolios
Possible to split investment funds between safe and risky assets
Risk free asset rf : proxy; T-bills or money market fund
Risky asset portfolio rp: risky portfolio
Example. Your total wealth is $10,000. You put $2,500 in risk
free T-Bills and $7,500 in a stock portfolio invested as follows:
Stock A you put 2,500
Stock B you put 3,000
Stock C you put 2,000
$7,500
Allocating Capital Between Risky & Risk-Free Assets
Weights in risky portfolio rp :
22. WA =
WB =
WC =
The complete portfolio includes the riskless investment and rp.
Wrf = 25% Wrp = 75%
Weights in the complete portfolio
WA =
WB =
WC =
Allocating Capital Between Risky & Risk-Free Assets
How much should be invested in the risky asset and risk free
asset respectively?
Examine risk & return tradeoff
Demonstrate how different degrees of risk aversion will affect
allocations between risky and risk free assets
Depending on your level of risk you must merely choose
between your weights of the risk free and the risky portfolio
23. Combined Portfolio Expected Return and Risk
Example: The information about T-bill and risky portfolio runs
as follows:
Expected Return rate for T-bill, rf= 5%
Standard deviation for T-
Expected Return rate for risky portfolio, rp= 14%
Suppose you invest y of your total wealth in the risky portfolio
What is the expected return and standard deviation for the
complete or combined portfolio?
E(rc) =y E(rp) + (1 - y) rf
E(r)
24. E(rp) = 14%
rf = 5%
22%
0
P
F
Possible Combinations of asset allocation choices
s
E(rp) = 11.75%
16.5%
y =.75
y = 1
y = 0
5-42
Risk-return Trade Offs
42
Using Leverage with Capital Allocation Line
Borrow at the Risk-Free Rate and invest in stock
Using 50% Leverage, which means y = 1.5
E(rc) =
25. E(rC) =18.5%
33%
y = 1.5
E(r)
E(rp) = 14%
rf = 5%
= 22%
0
P
F
) Slope = 9/22
E(rp) -
rf = 9%
CAL
(Capital
Allocation
Line)
s
Complete portfolio offers a return per unit of risk of 9/22.
5-44
26. Capital Allocation Line (CAL) and its Slope
Capital Allocation Line plots all risk-return combinations
available by varying asset allocation between a risk free asset
and a risky portfolio
44
Risk Aversion and Allocation
How much should be invested in the risky portfolio and risk
free asset respectively? – depending on risk aversion and trade-
off between risk and return.
Greater levels of risk aversion lead investors to choose larger
proportions of the risk-free assets (risk free rate)
Lower levels of risk aversion (more risk tolerance) lead
investors to choose larger proportions of the portfolio of risky
assets
Willingness to accept high levels of risk for high levels of
returns would result in leveraged combination
If the reward-to-volatility ratio increases, investors might well
decide to take a greater position in the risky portfolio.
5.5 Passive Strategies and The Capital Market Line (CML)
How can investor choose the assets included in the risky
portfolio?
Using either passive or active strategies
27. Passive strategy
The investor makes no attempt to actively find undervalued
strategies nor actively switch their asset allocations.
Investment policy that avoids security analysis: securities are
fairly priced
Two advantages compared to active strategy
Avoids the costs involved in the undertaking security analysis
(active trading strategies may not guarantee higher returns )
free ride benefit: the activity of knowledge investors force
prices to reflect currently available information
Capital Market Line (CML)
A simple passive strategy (Indexing strategy): Investing in a
broad stock index (like S&P 500 index) and a risk free
investment.
Indexing has become an extremely popular strategy for passive
investors.
Capital Market Line: the Capital allocation line (CAL) provided
by combinations of one month T-bills and a broad index of
common stocks (or an index that mimics overall market
performance).
What does Portfolio theory suggest?
28. Investors should only invest two passive portfolios
Short-term T-bills
Fund of common stocks that mimics a broad market index
Vary combinations according to investor’s risk aversion.
å
=
=
n
1
T
T
avg
n
HPR
HPR
7
.1762)
.3446
.0311
.2098
.2335
.4463
(-.2156
HPR
avg
=
+
29. +
+
+
+
+
=
An example: You have the following rate
s of return on
a
stock
:
200
0
-
21.56%
200
1
44.63%
200
2
23.35%
2003
20.98%
2004
3.11%
36. = 22%
rp
= 22%
y = % in r
p
y = % in r
p
(1-y) = % in rf
(1-y) = % in rf
r
f
= 5%
r
f
= 5%
rf
= 0%
rf
= 0%
E(r
p
) = 14%
E(r
p
) = 14%
rp
= 22%
rp
= 22%
y = % in r
p
37. y = % in r
p
(1-y) = % in rf
(1-y) = % in rf
E(r)
E(r)
E(r
E(r
p
p
) = 14%
) = 14%
r
r
f
f
= 5%
= 5%
22%
22%
0
0
P
P
F
F
Possible Combinations
Possible Combinations
E(r
E(r
p
p
) = 11.75%
) = 11.75%
16.5%
38. 16.5%
E(r
E(r
p
p
) = 11.75%
) = 11.75%
16.5%
16.5%
y =.75
y =.75
y = 1
y = 1
E(r)
E(r)
E(r
E(r
p
p
) = 14%
) = 14%
r
r
f
f
= 5%
= 5%
22%
22%
0
0
P
P
F
F
Possible Combinations
39. Possible Combinations
E(r
E(r
p
p
) = 11.75%
) = 11.75%
16.5%
16.5%
E(r
E(r
p
p
) = 11.75%
) = 11.75%
16.5%
16.5%
y =.75
y =.75
y = 1
y = 1
E(r
E(r
C
C
) =18.5%
) =18.5%
33%
33%
E(r
E(r
C
C
) =18.5%
) =18.5%