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Questions and Answers
What does covariance measure in a financial context?
What does covariance measure in a financial context?
Correlation values can range from -1 to +1.
Correlation values can range from -1 to +1.
True
Define the difference between positive correlation and inverse correlation.
Define the difference between positive correlation and inverse correlation.
Positive correlation occurs when two variables change together, while inverse correlation occurs when they change in opposite directions.
Covariance is positive when both variables __________ or __________ together.
Covariance is positive when both variables __________ or __________ together.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What is the primary goal of portfolio theory?
What is the primary goal of portfolio theory?
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A risk-averse investor is willing to take on increased risk without expecting a higher return.
A risk-averse investor is willing to take on increased risk without expecting a higher return.
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What should an Investment Policy Statement (IPS) specify?
What should an Investment Policy Statement (IPS) specify?
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A risk-neutral investor is indifferent to the degree of risk as long as the expected return is ______.
A risk-neutral investor is indifferent to the degree of risk as long as the expected return is ______.
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Match the types of investors with their characteristics:
Match the types of investors with their characteristics:
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What is an example of an absolute risk objective?
What is an example of an absolute risk objective?
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Portfolio construction should only occur once and not need any adjustments thereafter.
Portfolio construction should only occur once and not need any adjustments thereafter.
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What is the challenge faced by rational investors when selecting assets?
What is the challenge faced by rational investors when selecting assets?
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Which measure of risk considers only deviations below the mean?
Which measure of risk considers only deviations below the mean?
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An efficient portfolio can offer higher returns with the same level of risk compared to another portfolio.
An efficient portfolio can offer higher returns with the same level of risk compared to another portfolio.
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What is the primary formula used to calculate the expected rate of return on a portfolio?
What is the primary formula used to calculate the expected rate of return on a portfolio?
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Variance is depicted by the symbol ______.
Variance is depicted by the symbol ______.
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Match the terms with their definitions.
Match the terms with their definitions.
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Which of the following is NOT an advantage of using standard deviation as a risk measure?
Which of the following is NOT an advantage of using standard deviation as a risk measure?
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Covariance measures the degree to which two random variables vary together.
Covariance measures the degree to which two random variables vary together.
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What is the purpose of using variance in finance?
What is the purpose of using variance in finance?
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What is the main purpose of diversification in portfolio management?
What is the main purpose of diversification in portfolio management?
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Naive diversification means investing in securities with varying weights based on their performance.
Naive diversification means investing in securities with varying weights based on their performance.
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What does the number of securities in a portfolio affect?
What does the number of securities in a portfolio affect?
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Optimal allocation is very sensitive to small changes in the input ____________.
Optimal allocation is very sensitive to small changes in the input ____________.
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Match the number of securities with the reduction in specific risk:
Match the number of securities with the reduction in specific risk:
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Who was the initiator of Modern Portfolio Theory?
Who was the initiator of Modern Portfolio Theory?
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Investors prefer lower returns for a given risk level according to Modern Portfolio Theory.
Investors prefer lower returns for a given risk level according to Modern Portfolio Theory.
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What is the primary purpose of diversification in a portfolio?
What is the primary purpose of diversification in a portfolio?
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The measure of risk in investments is represented by the __________ of the investment return.
The measure of risk in investments is represented by the __________ of the investment return.
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What does the term 'opportunity set' refer to in Modern Portfolio Theory?
What does the term 'opportunity set' refer to in Modern Portfolio Theory?
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Investors base their decisions only on expected return and risk.
Investors base their decisions only on expected return and risk.
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What is the mean-variance optimisation model used for?
What is the mean-variance optimisation model used for?
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Match the following concepts with their descriptions:
Match the following concepts with their descriptions:
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What effect does low correlation between assets have on portfolio risk?
What effect does low correlation between assets have on portfolio risk?
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Combining two assets with +1.0 correlation will reduce the portfolio standard deviation.
Combining two assets with +1.0 correlation will reduce the portfolio standard deviation.
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What is the optimal portfolio for an investor?
What is the optimal portfolio for an investor?
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The efficient frontier represents a set of portfolios with the maximum rate of return for a given level of ___ risk.
The efficient frontier represents a set of portfolios with the maximum rate of return for a given level of ___ risk.
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Match the correlation values with their effects on portfolio risk:
Match the correlation values with their effects on portfolio risk:
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How does adding more assets to a portfolio affect risk?
How does adding more assets to a portfolio affect risk?
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Estimation risk refers to potential errors in portfolio allocation based on accurate statistical inputs.
Estimation risk refers to potential errors in portfolio allocation based on accurate statistical inputs.
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What does the slope of the efficient frontier curve indicate as you move upward?
What does the slope of the efficient frontier curve indicate as you move upward?
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An investor’s utility curve specifies the trade-offs between expected return and ___.
An investor’s utility curve specifies the trade-offs between expected return and ___.
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How many correlation estimates would be needed with 100 assets?
How many correlation estimates would be needed with 100 assets?
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Study Notes
Portfolio Theory
- Portfolio theory is a mathematical framework for selecting investments that maximize returns while minimizing risk.
- Key learning objectives include explaining the concept, identifying optimal portfolios, and understanding advantages/ disadvantages of the theory.
Portfolio Management Process
- Preparing the Policy Statement (IPS): Defines investment objectives and constraints.
- Analyzing Financial Conditions: Evaluating current and projected financial and economic factors to inform strategies.
- Constructing the Portfolio: Allocating assets based on the IPS to minimize risk and meet objectives.
- Monitoring and Updating: Regularly measuring and evaluating performance, adjusting as needed.
Types of Investors
- Risk-Loving Investors: Prefer risk and higher returns.
- Risk-Averse Investors: Will only accept increased risk if the returns compensate for it.
- Risk-Neutral Investors: Are indifferent to risk levels as long as expected returns are the same.
Investment Policy Statement (IPS)
- Defines investment objectives and constraints.
- Clearly outlines client risk tolerance.
- Specifies portfolio risk objectives: absolute, relative, or a combination.
Challenge to Rational Investor
- Investors face a variety of assets/securities with different levels of risk and return.
- The goal is to select the optimal assets or combinations to maximize returns and utility while managing risks.
Modern Portfolio Theory (MPT)
- Risk is the uncertainty of future outcomes, measured by variance or deviation.
- Return is the reward from investing, the excess compensation an investor earns.
- Portfolio is a collection of assets (stocks, bonds, etc).
- Opportunity set is all available portfolio combinations.
- Diversification balances risk by mixing assets within a portfolio, neutralizing negative performance with positive performance, thereby smoothing out unsystematic risk.
MPT Intitiated by Harry Markowitz
- Developed in the early 1950s.
- Later awarded the Nobel Prize in 1990.
- Quantitative relationship between return and risk in investments.
- Quantifies the concept of diversification.
- Builds on mean-variance models with optimal portfolio.
Mean-Variance Optimisation
- Model built on the trade-off between risk and return for investment.
- Expected performance of investments and risk appetite of the investor are required as input.
Alternative Measures of Risk
- Variance/Standard deviation of expected return.
- Range of returns.
- Returns below expectations (semivariance).
Characteristics of Using Standard Deviation of Returns
- Intuitive measurement.
- Correct and widely recognized risk measure.
- Used in theoretical asset pricing models.
Expected Rates of Return for Individual Assets
- The sum of potential returns multiplied by their corresponding probability.
Portfolio Expected Return Calculation
- The weighted average of expected rates of return of investments in the portfolio.
Individual Investment Risk
- A measure of the spread of numbers between investments in a dataset.
- Measures how far each number is from the mean (average) and other numbers.
- Depicted by the symbol σ2.
- Used to establish market stability and volatility.
Covariance of Returns
- Measures the change in two random variables compared to each other when used in a financial or investment context.
- It is the relationship between the returns on two different investments over a time period.
Correlation (Degree of Movement)
- Measures the relationship between two variables, indicating if the change in one variable is accompanied by a corresponding change in another.
- Positive correlation shows variables moving in the same direction.
- Negative correlation shows variables moving in opposite directions.
Covariance vs. Correlation
- Covariance measures the direction and magnitude of how variables change together.
- Correlation quantifies the strength and direction of the relationship between variables.
Asset Class Correlation
- A measure depicting the correlation between different asset classes and the S&P 500 between January 2013 and December 2023.
Standard Deviation of a Portfolio
- Formula, which calculates it based on individual asset weights, variances, and covariances.
Standard Deviation Calculations of a Two-Stock Portfolio
- Expected rate of return and expected standard deviations of returns can characterise assets within a portfolio.
- Portfolio risk is impacted by the correlation (using covariance), which is measured between assets, affecting the portfolio's standard deviation.
- Low correlation in the asset reduces portfolio risk without affecting expected returns
Standard Deviation of a Three-Asset Portfolio
- Portfolio procedures remain the same; however, their complexity increases as more assets are factored in.
Estimation Issues
- Portfolio allocation depends on accurate statistical input, including expected returns, standard deviation, and correlation coefficient.
- Estimation risk refers to the potential errors arising from using these inputs.
- High sensitivity of optimal portfolio allocation to slight changes in input parameters.
- A large number of asset correlations reduces the accuracy of the portfolio.
The Efficient Frontier
- Portfolio frontier showing portfolios with maximum return for all levels of risk or minimum risk for all levels of return.
- Efficient frontier consists of investment portfolios rather than portfolios of individual assets.
- High returns and low risks are assets on the efficient frontier.
Efficient Frontier and Investor Utility
- Investor utility curves show trade-offs between return and risk.
- Slope of the efficient frontier curve gradually decreases as the return increases.
- Interaction of utility curves and efficient frontier determine the optimal portfolio for an investor and their given utility.
Efficient Frontier and Investor Utility - continued
- Optimal portfolios are found at the point of tangency between the efficient frontier and the investor utility curve.
Diversification
- The practice of investing in a variety of securities to mitigate risk associated with one particular security's performance.
- Less-correlated securities enhance portfolios.
- Diversification reduces specific risk while maintaining expected returns.
Benefit of Diversification
- Table showcasing the reduction in specific risk as the number of securities increases.
Diversified Holdings
- List and amount of assets in a portfolio.
- Type of investments in the portfolio are diversified.
Portfolio Theory Concerns
- Difficulty in accurately obtaining input parameters.
- High sensitivity of optimal allocation to minor changes in input variables.
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Description
Test your knowledge on key concepts of investment theory including covariance, correlation, and portfolio management strategies. This quiz will challenge your understanding of risk profiles, investment policy statements, and portfolio construction principles. Prepare to refine your investment acumen with these essential questions.
