Investment Theory and Portfolio Management Quiz

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Questions and Answers

What does covariance measure in a financial context?

  • The risk associated with a single investment
  • The direction and degree of movement between two variables (correct)
  • The average return of an investment
  • The total market value of a portfolio

Correlation values can range from -1 to +1.

True (A)

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.

<p>increase, decrease</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Covariance = Measures the direction and degree of relationship between two variables Positive Correlation = Both variables change together Inverse Correlation = Variables change in opposite directions Correlation = Measures the strength of the relationship between two variables</p> Signup and view all the answers

What is the primary goal of portfolio theory?

<p>Achieve an optimal balance between risk and return (B)</p> Signup and view all the answers

A risk-averse investor is willing to take on increased risk without expecting a higher return.

<p>False (B)</p> Signup and view all the answers

What should an Investment Policy Statement (IPS) specify?

<p>Investment objectives and constraints</p> Signup and view all the answers

A risk-neutral investor is indifferent to the degree of risk as long as the expected return is ______.

<p>the same</p> Signup and view all the answers

Match the types of investors with their characteristics:

<p>Risk-Loving Investor = Prefers high-risk, high-return investments Risk-Averse Investor = Avoids risk unless compensated by higher returns Risk-Neutral Investor = Indifferent to risk given the same expected return</p> Signup and view all the answers

What is an example of an absolute risk objective?

<p>Not to suffer any loss of capital (A)</p> Signup and view all the answers

Portfolio construction should only occur once and not need any adjustments thereafter.

<p>False (B)</p> Signup and view all the answers

What is the challenge faced by rational investors when selecting assets?

<p>Finding the optimal balance between risk and return</p> Signup and view all the answers

Which measure of risk considers only deviations below the mean?

<p>Semivariance (B)</p> Signup and view all the answers

An efficient portfolio can offer higher returns with the same level of risk compared to another portfolio.

<p>False (B)</p> Signup and view all the answers

What is the primary formula used to calculate the expected rate of return on a portfolio?

<p>E(R_portfolio) = Σ Wi * E(Ri)</p> Signup and view all the answers

Variance is depicted by the symbol ______.

<p>σ2</p> Signup and view all the answers

Match the terms with their definitions.

<p>Standard Deviation = Widely recognized risk measure Variance = Statistical measurement of spread Covariance = Measure of how two variables move together Expected Rate of Return = Weighted average of potential returns</p> Signup and view all the answers

Which of the following is NOT an advantage of using standard deviation as a risk measure?

<p>It measures risk in all investments accurately. (B)</p> Signup and view all the answers

Covariance measures the degree to which two random variables vary together.

<p>True (A)</p> Signup and view all the answers

What is the purpose of using variance in finance?

<p>To determine volatility and market stability.</p> Signup and view all the answers

What is the main purpose of diversification in portfolio management?

<p>To invest in a variety of securities to reduce risk (D)</p> Signup and view all the answers

Naive diversification means investing in securities with varying weights based on their performance.

<p>False (B)</p> Signup and view all the answers

What does the number of securities in a portfolio affect?

<p>Specific risk reduction</p> Signup and view all the answers

Optimal allocation is very sensitive to small changes in the input ____________.

<p>parameters</p> Signup and view all the answers

Match the number of securities with the reduction in specific risk:

<p>1 = 0% 2 = 46% 4 = 72% 8 = 81% 16 = 93% 32 = 96% 64 = 98% 500 = 99%</p> Signup and view all the answers

Who was the initiator of Modern Portfolio Theory?

<p>Harry Markowitz (B)</p> Signup and view all the answers

Investors prefer lower returns for a given risk level according to Modern Portfolio Theory.

<p>False (B)</p> Signup and view all the answers

What is the primary purpose of diversification in a portfolio?

<p>To smooth out unsystematic risk.</p> Signup and view all the answers

The measure of risk in investments is represented by the __________ of the investment return.

<p>variance</p> Signup and view all the answers

What does the term 'opportunity set' refer to in Modern Portfolio Theory?

<p>The set of available portfolios based on risk and return (B)</p> Signup and view all the answers

Investors base their decisions only on expected return and risk.

<p>True (A)</p> Signup and view all the answers

What is the mean-variance optimisation model used for?

<p>To provide the optimal portfolio.</p> Signup and view all the answers

Match the following concepts with their descriptions:

<p>Risk = The uncertainty of future outcomes Return = The reward earned from investing Portfolio = A collection of assets Diversification = Mixing different assets to reduce risk</p> Signup and view all the answers

What effect does low correlation between assets have on portfolio risk?

<p>Reduces portfolio risk (D)</p> Signup and view all the answers

Combining two assets with +1.0 correlation will reduce the portfolio standard deviation.

<p>False (B)</p> Signup and view all the answers

What is the optimal portfolio for an investor?

<p>The portfolio that has the highest utility for a given investor.</p> Signup and view all the answers

The efficient frontier represents a set of portfolios with the maximum rate of return for a given level of ___ risk.

<p>risk</p> Signup and view all the answers

Match the correlation values with their effects on portfolio risk:

<p>+1.0 = No reduction in risk -1.0 = Potential reduction to zero risk 0.0 = Moderate reduction in risk -0.5 = Some reduction in risk</p> Signup and view all the answers

How does adding more assets to a portfolio affect risk?

<p>Decreases risk (D)</p> Signup and view all the answers

Estimation risk refers to potential errors in portfolio allocation based on accurate statistical inputs.

<p>True (A)</p> Signup and view all the answers

What does the slope of the efficient frontier curve indicate as you move upward?

<p>It decreases steadily.</p> Signup and view all the answers

An investor’s utility curve specifies the trade-offs between expected return and ___.

<p>risk</p> Signup and view all the answers

How many correlation estimates would be needed with 100 assets?

<p>4,950 (D)</p> Signup and view all the answers

Flashcards

Risk-Loving Investor

An investor who prefers taking on more risk, even if it means potentially losing more money.

Risk-Averse Investor

An investor who wants to minimize risk. They only accept higher risk if the potential reward is significantly greater.

Risk-Neutral Investor

An investor who is indifferent to risk and only focuses on expected return. They don't care if the investment is risky or stable as long as the projected return is the same.

Investment Policy Statement (IPS)

A document that outlines an investor's investment goals, risk tolerance, and any constraints on their portfolio.

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Portfolio Management

The process of selecting and managing assets with the aim of achieving an optimal balance between risk and return.

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Risk Objectives

A set of investment guidelines specified in the IPS that reflects an investor's willingness to take on risk.

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Challenge to a Rational Investor

A challenge faced by investors in choosing the best combination of assets to maximize returns while minimizing risk.

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Asset Allocation

The process of determining the proportion of assets to be allocated to different asset classes (e.g., stocks, bonds, real estate).

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Risk (in investment)

The uncertainty of an investment's future outcomes. Measured by the variance or deviation from expected returns.

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Return (in investment)

The reward an investor receives for investing their capital. Calculated as the return on investment over a specific period.

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Portfolio

A collection of assets like stocks, bonds, property, or currencies held by an investor.

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Opportunity Set

The set of all possible portfolios an investor can choose based on their combination of risk and return.

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Diversification

The process of mixing different assets in a portfolio to reduce unsystematic risk. It spreads risk by balancing the negative performance of one asset with the positive performance of others.

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Modern Portfolio Theory (MPT)

A model that aims to find the 'optimal' portfolio by considering the trade-off between an investment's expected return and risk. It quantifies diversification and forms the foundation for asset allocation.

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Assumption 1 of MPT: Probability Distribution

Investors consider each investment's potential outcomes as a probability distribution of expected returns within a specific time period.

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Assumption 2 of MPT: Utility Maximization

Investors prioritize maximizing their utility, which is their satisfaction from wealth, over a single period. Their utility curves exhibit decreasing marginal utility of wealth, meaning additional wealth brings less satisfaction as their wealth increases.

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Covariance (in Finance)

Measures how returns of two different investments move together over time. A positive covariance means they move in the same direction, while a negative covariance signifies opposite movements.

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Correlation

A statistical measure of how strongly two variables change in relation to each other. It shows how much one variable changes when the other changes.

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Positive Correlation

A type of correlation where variables move in the same direction. If one goes higher, the other also goes higher.

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Inverse Correlation

When variables move in opposite directions. If one increases, the other decreases.

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Covariance (Relationship direction)

The direction of the relationship between two variables and how much they change together. Positive when both increase/decrease, negative when moving oppositely.

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Efficient Portfolio

A portfolio is considered 'efficient' when no other portfolio offers a higher expected return for the same or lower risk, or lower risk for the same or higher expected return.

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Variance

Measures how much a variable deviates from its average value. Used to quantify risk by showing how much returns vary from their expected value.

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Semivariance

A measure of risk that only considers deviations below the expected return. It focuses on how much the portfolio might underperform.

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Covariance

The tendency of two assets or variables to move together. Positive covariance means they move in the same direction, negative means opposite directions.

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Expected Portfolio Return

The expected return of a portfolio is simply the weighted average of the expected returns of the individual assets in the portfolio. The weights are the proportions of each asset in the portfolio.

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Expected Individual Asset Return

The expected return of an individual asset is calculated as the sum of the potential returns multiplied by their respective probabilities.

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Individual Investment Risk

The risk of an individual asset is measured by its variance, which is the average squared deviations from the expected return. It captures how much the actual return might deviate from its expected value.

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Portfolio Expected Rate of Return Formula

The expected rate of return of a portfolio is a weighted average of the individual assets' expected rates of return, where the weights represent the proportions of the portfolio invested in each asset.

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Naïve Diversification

Diversification that involves investing equal amounts across a wide range of assets without considering their individual characteristics or correlations.

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Efficient Diversification

The process of constructing investment portfolios that optimize the balance between risk and return based on the correlations and variances of the assets within the portfolio.

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Benefits of Diversification

The theoretical benefit of diversification is that as the number of assets in a portfolio increases, the overall portfolio risk (specific risk) can be reduced significantly.

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Concerns with Portfolio Theory

The potential difficulty in accurately predicting future returns and correlations of assets, which can make constructing an optimal portfolio challenging.

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Portfolio Standard Deviation

The standard deviation of a portfolio reflects the overall risk of the investment. It measures how much the portfolio's returns are expected to deviate from their average, indicating the level of volatility.

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Correlation Coefficient

The correlation coefficient is a statistical measure that describes the relationship between the returns of two assets. It ranges from -1 to +1. Positive correlation means assets move in the same direction, while negative correlation means they move in opposite directions.

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Expected Rate of Return

The expected rate of return is the average return an investor anticipates receiving from an asset over a particular time period. This is a prediction, not a guarantee, based on historical data and future expectations.

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Standard Deviation of Returns

Standard deviation of returns measures the volatility or risk of an individual asset. It shows how much the asset's returns are expected to deviate from their average.

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Negative Correlation

Negative correlation between assets is a desirable characteristic in portfolio management. It means that when one asset's return falls, the other's return tends to rise. This helps reduce overall portfolio risk.

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Efficient Frontier

The efficient frontier is a graphic representation of the optimal portfolio combinations. It shows the highest expected return for each level of risk or the lowest risk for each level of return.

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Investor Utility

Investor utility represents an individual's preferences toward risk and return. It's their personal trade-off between these two factors. Different investors have different utility curves, reflecting their unique risk tolerance.

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Optimal Portfolio

The optimal portfolio for a given investor is the one that lies at the tangent point between the efficient frontier and the investor's utility curve. This portfolio offers the highest utility for that particular investor.

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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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