Investment Management ACF 313 Part I
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Questions and Answers

What is the primary goal of an investor according to Markowitz’s solution?

  • Eliminate all risky securities from the portfolio
  • Minimize investment length and maximize securities
  • Maximize expected returns and minimize uncertainty (correct)
  • Maximize risk and minimize returns

According to the portfolio selection problem, all securities have certain outcomes.

False (B)

Who proposed the modern portfolio theory in 1952?

Harry M. Markowitz

The approach proposed by Markowitz can be regarded as a __________ approach.

<p>single period</p> Signup and view all the answers

Match the following concepts with their descriptions:

<p>Portfolio Selection Problem = Selecting the best combination of securities for investment Expected Returns = Projected gains from an investment Risk Aversion = Preference for lower risk investments Utility of Wealth = Satisfaction derived from wealth</p> Signup and view all the answers

What must an investor recognize regarding security returns during the holding period?

<p>They are unknown and must be estimated (B)</p> Signup and view all the answers

Nonsatiation means that investors always prefer more to less wealth.

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

What is the basic challenge faced by investors as mentioned in the portfolio selection problem?

<p>Determining which set of risky securities to invest in</p> Signup and view all the answers

What is the primary conflict faced by investors while attempting to maximize returns?

<p>Maximizing expected returns and minimizing risk (C)</p> Signup and view all the answers

The Markowitz model provides a qualitative approach to balancing returns and risk.

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

What formula can be used to calculate the rate of return on a portfolio?

<p>rp = (w1 - w0) / w0</p> Signup and view all the answers

The initial wealth is denoted by _____ and the terminal wealth by _____.

<p>w0; w1</p> Signup and view all the answers

Which of the following statements about random variables is true?

<p>They can be described by their moments, such as expected return and standard deviation. (D)</p> Signup and view all the answers

An investor can accurately predict the future rate of return for all portfolios.

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

What must an investor decide at time t=0?

<p>Which portfolio to invest in</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Expected Return = The average return anticipated from an investment Standard Deviation = A measure of the dispersion of returns Initial Wealth = The aggregate purchase price at time t=0 Terminal Wealth = The market value at time t=1</p> Signup and view all the answers

According to Markowitz, investors should base their portfolio decisions on which two parameters?

<p>Expected returns and Standard deviations (B)</p> Signup and view all the answers

Investors are assumed to prefer lower levels of terminal wealth over higher levels.

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

What is the assumption that investors prefer portfolios with smaller standard deviations called?

<p>Risk Aversion</p> Signup and view all the answers

The two assumptions in the discussion of portfolio selection are ______ and ______.

<p>Nonsatiation, Risk Aversion</p> Signup and view all the answers

What characterizes a 'fair gamble' for an investor?

<p>A situation with an expected return of 0 (C)</p> Signup and view all the answers

Utility is solely about financial gain and does not consider personal satisfaction.

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

How do investors maximize their utility according to the provided information?

<p>By rationally allocating their resources.</p> Signup and view all the answers

What does a correlation coefficient of +1 indicate?

<p>Perfect positive correlation (C)</p> Signup and view all the answers

A correlation coefficient of 0 signifies that the returns of two securities are perfectly correlated.

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

What is the formula for calculating the correlation coefficient?

<p>r_ij = Cov_ij / (σ_i * σ_j)</p> Signup and view all the answers

When the covariance is zero, the correlation coefficient will also be __________.

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

What is the range of values for the correlation coefficient?

<p>-1 to +1 (B)</p> Signup and view all the answers

With perfectly negatively correlated assets, one can create a portfolio with almost no risk.

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

What statistical measure is closely related to covariance?

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

A correlation coefficient of -1 indicates a __________ correlation.

<p>perfect negative</p> Signup and view all the answers

Which of the following best describes negative covariance?

<p>Variables move in opposite directions (A)</p> Signup and view all the answers

What is the primary objective of the Markowitz portfolio selection problem?

<p>Maximize expected utility of terminal wealth (C)</p> Signup and view all the answers

All investors have the same utility of wealth function.

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

What does 'diminishing marginal utility of wealth' mean?

<p>It means that as a person becomes wealthier, each additional unit of wealth provides less additional utility than before.</p> Signup and view all the answers

The __________ equivalent is the guaranteed amount of money that provides the same utility as a riskier option.

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

Which investment option would a risk averse investor likely prefer?

<p>Option A with a certain return of 5% (C)</p> Signup and view all the answers

A rich investor values an extra unit of wealth more than a poor investor.

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

What motivates risk averse investors to choose less risky investments?

<p>Risk averse investors prefer less risk even if it means sacrificing some expected terminal wealth.</p> Signup and view all the answers

What does an indifference curve represent?

<p>A set of combinations of risk and return that provide the same amount of utility. (B)</p> Signup and view all the answers

An indifference curve can intersect with another indifference curve.

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

What does the slope of an indifference curve indicate about an investor's risk aversion?

<p>The steeper the slope, the more risk averse the investor is.</p> Signup and view all the answers

All investors have an infinite number of indifference curves, resulting in an indifference curve _____ representing their preferences.

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

Match the risk aversion level with the description:

<p>Highly risk averse = Steeper slope of indifference curve Moderately risk averse = Moderately steep slope of indifference curve Slightly risk averse = Gentler slope of indifference curve</p> Signup and view all the answers

What assumption causes indifference curves to be positively sloped and convex?

<p>Nonsatiation and risk aversion (B)</p> Signup and view all the answers

All investors are assumed to have identical degrees of risk aversion.

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

What should an investor do to select the optimal portfolio from their indifference curve map?

<p>Select the portfolio that lies farthest northwest.</p> Signup and view all the answers

Flashcards

Portfolio Selection Problem

The process of figuring out which combination of risky assets (like stocks and bonds) to invest in to achieve the best financial outcome.

Expected Return (ER)

The average return an investor expects to earn from an asset, calculated by considering all possible outcomes and their likelihoods.

Uncertainty

The uncertainty or variability of potential returns from an investment. A higher risk means greater potential gains and losses.

Maximize ER and Minimize Uncertainty

A theory that suggests investors should aim for the highest possible expected return while simultaneously minimizing the risk associated with their investments.

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Markowitz's Solution

A mathematical model developed by Harry Markowitz to determine the optimal portfolio of assets based on their individual returns, risk, and correlations.

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Nonsatiation

The idea that investors always prefer more wealth to less wealth, meaning they are always looking to increase their holdings.

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Risk Aversion

The tendency for investors to prefer a certain outcome (lower risk) to an uncertain one, even if the expected return is the same.

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Utility of Wealth

A graphical representation showing how much happiness or satisfaction an investor derives from different levels of wealth, illustrating their attitude towards risk.

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Markowitz Portfolio Theory

Investors prioritize making decisions based on expected returns (ER) and standard deviations (STD) to choose the best portfolio.

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Nonsatiation Assumption

Investors always choose the portfolio with the highest expected return, even if the standard deviation is similar to another portfolio.

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Risk Aversion Assumption

Investors are generally averse to risk. They prefer portfolios with lower standard deviations, avoiding fair gambles.

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Investor Utility

The satisfaction or enjoyment individuals derive from economic activities like consumption, work, or investment.

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Fair Gamble

A gamble where the expected return (ER) is zero. Risk-averse investors avoid such situations.

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Utility

The relative satisfaction gained or lost from an economic activity.

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Same ER, Different STD

A situation where two portfolios have identical expected returns (ER) but different standard deviations (STD).

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Terminal Wealth

The future value of an investment at a specific point in time.

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Rate of Return

The gain or loss on an investment over a specific period, expressed as a percentage of the initial investment.

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Initial Wealth

The total value of an investment at the beginning of a period.

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Uncertainty in Returns

The possibility that the actual return on an investment will be different from the expected return.

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Expected Return

The average return that an investor expects to earn from an investment.

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Standard Deviation

A measure of the variability or dispersion of returns around the expected return.

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Markowitz Model

A mathematical model that helps investors balance risk and return by finding the optimal portfolio allocation.

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Portfolio

A collection of different investments held by an investor.

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Marginal Utility of Wealth (MUW)

The additional satisfaction an investor gains from an extra unit of wealth.

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Diminishing Marginal Utility of Wealth

The tendency for the added utility gained from each extra unit of wealth to decrease as wealth increases.

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Certainty Equivalent

The guaranteed amount of money that would make an investor as happy as taking a riskier investment with the same expected benefit.

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Risk Premium

The extra return an investor requires to compensate for taking on risk.

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Risk Averse Investors

Investors who are more comfortable with certainty and prefer to avoid risk.

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Markowitz Portfolio Selection

A strategy to maximize the expected utility associated with an investor's terminal wealth.

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Indifference Curve

A graphical representation of different combinations of risk and expected return that provide an investor with the same level of satisfaction. All points on the curve represent equally desirable portfolios.

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Investor's Preference

An investor's preference for higher expected returns and lower risk. This means they would like to maximize returns while minimizing uncertainty.

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Risk Aversion Level

The degree to which an investor dislikes risk. This is reflected in the steepness of their indifference curve.

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Indifference Curve Map

A set of indifference curves representing an investor's preferences for different risk and return combinations. Each curve represents a different level of utility.

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Optimal Portfolio

The selection of the portfolio that provides the highest level of utility, located on the highest indifference curve that touches the efficient frontier.

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Efficient Frontier

The set of portfolios that offer the highest expected return for a given level of risk. These portfolios are efficient because they maximize return for a given level of risk.

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Covariance

A statistical measure that describes the tendency of two variables to move together. A positive covariance means the variables tend to increase or decrease together, while a negative covariance means they tend to move in opposite directions.

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Negative Covariance

A type of covariance where the two variables move in opposite directions. When one variable increases, the other tends to decrease, and vice versa.

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Zero Covariance

A type of covariance where there is no relationship between the movements of the two variables. They are not related.

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Correlation

A statistical measure, represented by the correlation coefficient, that indicates the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.

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Correlation Coefficient

A measure of the linear relationship between two variables. It is calculated by dividing the covariance by the product of the standard deviations of the two variables. It ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation).

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Correlation Coefficient Formula

The formula used to calculate the correlation coefficient. It is derived by standardizing the covariance by the product of the individual standard deviations of the two variables.

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Diversification Benefits

The potential for risk reduction in a portfolio by combining assets that are imperfectly correlated. The lower the correlation between assets, the greater the potential for diversification benefits.

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Portfolio Risk-Return Plots

A graphical representation that shows the relationship between the expected return and standard deviation of a portfolio for different combinations of assets.

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Perfectly Negatively Correlated Assets

The situation where two assets have a correlation coefficient of -1. This means their returns move perfectly in opposite directions.

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Perfectly Positively Correlated Assets

A situation where two assets have a correlation coefficient of +1. This means their returns move perfectly in the same direction.

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Study Notes

Investment Theory (Part I)

  • Investment Management course, ACF 313, Department of Accountancy, Faculty of Business Studies Finance, Wayamba University of Sri Lanka, Kuliyapitiya.
  • Successful completion of this topic enables students to understand the portfolio selection problem.
  • Students will understand why investors aim to maximize expected return (ER) and minimize uncertainty.
  • Crucial topics include Markowitz's solution, Nonsatiation, Risk Aversion, utility, and investor behavior.
  • Most investments carry uncertainty and risk.
  • Investors must determine the most suitable risky securities to invest in.
  • A portfolio comprises multiple securities.
  • Portfolio selection is similar to finding the optimal portfolio from various possible investment portfolios.
  • Harry Markowitz (1952) provided a solution to this portfolio selection problem, marking a significant point in modern portfolio theory.
  • The Markowitz approach assumes an investor with a specific amount to invest currently, held for a duration known as the holding period.
  • At the end of the holding period, the investor sells purchased securities.
  • The investment proceeds can be used for consumption or reinvestment.
  • The Markowitz model is a single-period approach.
  • Security returns during the holding period are typically unknown.
  • Investors estimate expected returns and aim to minimize uncertainty in future returns.
  • The investor attempts to maximize expected returns while minimizing risk.
  • The model seeks a balance between these competing objectives.
  • Initial wealth and terminal wealth calculations are crucial in portfolio theory.
  • Terminal wealth (at end of period) = Initial Wealth × (1 + return).
  • Portfolio return (rp) calculation: (End-of-period portfolio value – Beginning-of-period portfolio value) / Beginning-of-period portfolio value.
  • The investor must determine which portfolio is most suitable.
  • Investors must determine projected returns, and the standard deviation of the expected return for each portfolio.
  • Investor behavior assumes preferences for higher levels of terminal wealth.
  • Risk-averse investors choose portfolios with lower standard deviations.
  • A fair gamble has an expected return of zero.
  • Utility represents the satisfaction or enjoyment derived from economic activities like work, consumption, and investment.
  • People are assumed rational, maximizing their utility.
  • Utility of wealth function describes the link between utility and wealth.
  • Investors typically prefer more wealth to less wealth.
  • Marginal utility of wealth (MUW), the additional utility from each additional unit of wealth, usually decreases as wealth increases (diminishing marginal utility).
  • Wealthier investors generally place a lower value on additional wealth compared to poorer investors.
  • Certainty Equivalent is the guaranteed amount of money that makes an investor as happy as a riskier investment with the same expected result.
  • Risk premium is the expected increase in terminal wealth compared to a certain investment, accounting for the risk.
  • Risk-averse investors accept lower expected terminal wealth in exchange for lower risks.
  • Indifference curves display different combinations of expected terminal wealth and risk leading to the same level of utility.
  • Higher indifference curves represent a higher level of utility.
  • Investors choose the portfolio on the highest indifference curve and on the efficient frontier.
  • The degree of risk aversion affects the slope of indifference curves; more risk aversion leads to steeper slopes.
  • Expected return of a portfolio is calculated as a weighted average of the expected returns of individual assets within the portfolio.
  • Formula: E(Rp) = w₁E(R₁) + w₂E(R₂) + ... + wₙE(Rₙ)
  • Portfolio risk (standard deviation) isn't simply a weighted average of the individual securities' standard deviations.
  • Diversification reduces risk. The risk from covariance risk is minimized with higher diversification.
  • Standard deviation calculation formula:

[ \sigma_{p}^{2} = \sum_{i=1}^{n} \sum_{j=1}^{n} w_{i} w_{j} \sigma_{i} \sigma_{j} \rho_{i j} ] Where:   N = Number of securities in the portfolio wi  = weights of the ith security σi = standard deviation of returns for the ith security ρij= correlation of returns of security i and j

  • Covariance measures how much two securities' returns move together. Correlation coefficient of returns (r) is covariance divided by the product of the standard deviations:

[r_{i j} =\frac{Cov(R_{i}, R_{j})}{\sigma_{i} \sigma_{j}}]

  •  Correlation values lie between -1 and +1. (+1 = perfect positive correlation, -1=perfect negative correlation) , 0= no correlation.

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Investment Theory (Part I) PDF

Description

This quiz explores key concepts in Investment Management, focusing on portfolio selection and the theories posed by Harry Markowitz. Understand how investors balance expected returns against risks while considering risk aversion and utility. Engage with essential topics that form the foundation of modern portfolio theory.

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