Podcast
Questions and Answers
What is the primary goal of portfolio diversification?
What is the primary goal of portfolio diversification?
- To maximize returns regardless of risk.
- To spread risk by constructing portfolios with a large number of securities. (correct)
- To eliminate all risk from a portfolio.
- To construct portfolios with a small number of securities to concentrate gains.
What characterizes the efficient frontier?
What characterizes the efficient frontier?
- The set of portfolios that offer the lowest possible return for a given level of risk.
- The set of portfolios with the highest risk.
- The set of portfolios that offers the highest expected return for a given level of risk. (correct)
- The set of portfolios that are impossible to achieve.
What is the effect of increasing the number of assets in a portfolio on diversifiable risk?
What is the effect of increasing the number of assets in a portfolio on diversifiable risk?
- Diversifiable risk initially decreases but then increases after a certain number of assets.
- Diversifiable risk decreases, approaching zero as the number of assets increases. (correct)
- Diversifiable risk increases linearly with the number of assets.
- Diversifiable risk remains constant regardless of the number of assets.
What is the impact of individual asset risk in a well-diversified portfolio?
What is the impact of individual asset risk in a well-diversified portfolio?
Which of the following is an accurate description of diversification?
Which of the following is an accurate description of diversification?
What is the key characteristic of an efficient portfolio?
What is the key characteristic of an efficient portfolio?
What is the shape of the efficient frontier when plotted with expected return on the y-axis and standard deviation on the x-axis if short-selling and riskless lending/borrowing are not allowed?
What is the shape of the efficient frontier when plotted with expected return on the y-axis and standard deviation on the x-axis if short-selling and riskless lending/borrowing are not allowed?
What is the shape of the efficient frontier when plotted with expected return on the y-axis and standard deviation on the x-axis if short-selling is allowed, but riskless lending/borrowing is not?
What is the shape of the efficient frontier when plotted with expected return on the y-axis and standard deviation on the x-axis if short-selling is allowed, but riskless lending/borrowing is not?
What is the shape of the efficient frontier when plotted with expected return on the y-axis and standard deviation on the x-axis if both short-selling and riskless lending/borrowing are allowed?
What is the shape of the efficient frontier when plotted with expected return on the y-axis and standard deviation on the x-axis if both short-selling and riskless lending/borrowing are allowed?
In the context of portfolio theory, what does 'short-selling' refer to?
In the context of portfolio theory, what does 'short-selling' refer to?
How does precluding short-selling affect the constraints in portfolio optimization?
How does precluding short-selling affect the constraints in portfolio optimization?
What is a riskless asset in the context of portfolio theory?
What is a riskless asset in the context of portfolio theory?
What does riskless lending refer to?
What does riskless lending refer to?
What characterizes riskless borrowing?
What characterizes riskless borrowing?
In a portfolio consisting of a risky asset and a risk-free asset, how is the portfolio's risk level determined?
In a portfolio consisting of a risky asset and a risk-free asset, how is the portfolio's risk level determined?
What is the tangency portfolio?
What is the tangency portfolio?
Which of the following best describes the One-Fund Theorem?
Which of the following best describes the One-Fund Theorem?
In Modern Portfolio Theory (MPT), what is the primary role of utility theory?
In Modern Portfolio Theory (MPT), what is the primary role of utility theory?
What are the key assumptions of Modern Portfolio Theory (MPT)?
What are the key assumptions of Modern Portfolio Theory (MPT)?
According to Modern Portfolio Theory (MPT), how do investors make portfolio choices?
According to Modern Portfolio Theory (MPT), how do investors make portfolio choices?
What condition makes the mean-variance approach optimal within utility theory?
What condition makes the mean-variance approach optimal within utility theory?
What does variance measure in the context of portfolio theory?
What does variance measure in the context of portfolio theory?
What do indifference curves represent in the context of investor preferences?
What do indifference curves represent in the context of investor preferences?
If Investor X's indifference curves are steeper than Investor Y's, what does this imply?
If Investor X's indifference curves are steeper than Investor Y's, what does this imply?
What does covariance measure between two assets in a portfolio?
What does covariance measure between two assets in a portfolio?
How does the correlation between assets affect portfolio risk?
How does the correlation between assets affect portfolio risk?
Suppose a portfolio consists of 20% stock A and 80% stock B. If stock A returns 10% and stock B returns 5%, what is the portfolio return, assuming no other external factors?
Suppose a portfolio consists of 20% stock A and 80% stock B. If stock A returns 10% and stock B returns 5%, what is the portfolio return, assuming no other external factors?
Consider a 2-asset portfolio. Which of the following statements is true regarding the impact of correlation on the expected return and variance?
Consider a 2-asset portfolio. Which of the following statements is true regarding the impact of correlation on the expected return and variance?
If two securities are perfectly positively correlated ($\rho = 1$), what is the implication for portfolio risk?
If two securities are perfectly positively correlated ($\rho = 1$), what is the implication for portfolio risk?
If two securities are perfectly uncorrelated ($\rho = 0$), how is the portfolio variance calculated?
If two securities are perfectly uncorrelated ($\rho = 0$), how is the portfolio variance calculated?
If two securities are perfectly negatively correlated ($\rho = -1$), what is a key benefit for constructing a portfolio with these assets?
If two securities are perfectly negatively correlated ($\rho = -1$), what is a key benefit for constructing a portfolio with these assets?
An investor owns £200 of stock A and £800 of stock B. Another investor owns £2000 of stock A and £8000 of stock B. Assuming no shorting, is there any difference between their portfolios?
An investor owns £200 of stock A and £800 of stock B. Another investor owns £2000 of stock A and £8000 of stock B. Assuming no shorting, is there any difference between their portfolios?
What are the two specification choices that are required to implement Modern Portfolio Theory (MPT)?
What are the two specification choices that are required to implement Modern Portfolio Theory (MPT)?
Which of the following would be considered a practical method for diversifying an investment stock portfolio?
Which of the following would be considered a practical method for diversifying an investment stock portfolio?
An investor selects their portfolio based on reward and risk characteristics. What types of function would be optimal?
An investor selects their portfolio based on reward and risk characteristics. What types of function would be optimal?
Flashcards
Portfolio Diversification
Portfolio Diversification
Spreading investments across various securities to reduce risk.
Efficient Portfolio
Efficient Portfolio
A portfolio where no other portfolio offers less variance and higher expected return.
Efficient Frontier
Efficient Frontier
Graph of the set of efficient portfolios.
Short Selling
Short Selling
Signup and view all the flashcards
Riskless Lending and Borrowing
Riskless Lending and Borrowing
Signup and view all the flashcards
Tangency Portfolio
Tangency Portfolio
Signup and view all the flashcards
One-Fund Theorem
One-Fund Theorem
Signup and view all the flashcards
Investment Portfolio
Investment Portfolio
Signup and view all the flashcards
Modern Portfolio Goal
Modern Portfolio Goal
Signup and view all the flashcards
Risk Aversion
Risk Aversion
Signup and view all the flashcards
Indifference Curve
Indifference Curve
Signup and view all the flashcards
Covariance
Covariance
Signup and view all the flashcards
Portfolio correlations
Portfolio correlations
Signup and view all the flashcards
Study Notes
- Portfolio theory focuses on constructing portfolios with multiple securities to mitigate risk through diversification
N-Asset Portfolio Basics
- A portfolio consists of N securities, where N is greater than or equal to 2
- Rp represents the return of the portfolio
- μp signifies the expected return of the portfolio
- σp² denotes the variance of the portfolio
Diversification Explained
- Diversification involves spreading investments across a large number of securities to reduce risk
- This is achieved by investing equally in N securities
- On average, securities usually have a positive correlation
- Average variance is greater than average covariance
Portfolio Diversification Definition
- Investing in a portfolio with numerous securities reduces portfolio risk
Efficient Frontier
- An efficient portfolio means an investor cannot find another portfolio with less variance or higher expected returns
- The efficient frontier consists of the set of efficient portfolios
Key Observations with N Securities
- There exists a global minimum risk portfolio G
- There is a global maximum expected return asset M1
- There is a global minimum expected return asset M2
MPT Assumptions
- A single-period investment time horizon is present
- Asset risk is assessed using the mean and variance only
- Investors prefer non-satiation
- Investors are risk-averse
Practical Diversification Strategies
- Purchasing stocks from various countries
- Purchasing stocks from different industries
- Integrating different asset types into the stock portfolio
- Rebalancing portfolios regularly
- Monitoring and reassessing portfolios frequently
Optimal Portfolio Selection
- It lies on the efficient frontier
- It relies on an investor's risk aversion level
- The point on the efficient frontier should be tangential to the investors indifference curve
Short Selling
- Short selling refers to selling an asset not owned with the expectation of buying it back later at a lower price
- Short selling simplifies minimization because it only leaves one contraint
Riskless Lending and Borrowing
- A riskless asset has a fixed return over a period with zero risk
- Riskless lending involves investing in a riskless asset with a fixed interest rate Rf
- Riskless borrowing involves taking a loan at a fixed rate Rf
Efficient Frontier Cases
- Case I: No short-selling, no riskless lending or borrowing; the EF is a constrained hyperbola
- Case II: Short-selling is allowed, no riskless lending or borrowing; the EF is an unconstrained hyperbola
- Case III: Short-selling, riskless lending, and borrowing are allowed; the EF is a straight line
The 2-Asset portfolio
- Suppose asset 1 is risky, but asset 2 is risk free, then µp = x1µ1 + x2µ2, σp = x1σ1
- Renaming asset 2 as asset f (where f means risk-free asset) µp = x1µ1 + (1 − x1)*Rf, σp = x1σ1
- Does an investor prefer portfolios along RfA, RfB, or RfT : RfT is best
- An efficient investment consists of lending or borrowing at a risk-free rate Rf and investing the remaining wealth in a tangency portfolio T
One-Fund Theorem
- A single fund of assets T must be constructed for all investors efficient portfolios
- All efficient portfolios are combinations of T and Rf assets
Modern Portfolio Theory
MPT Learning Outcomes
- One will learn the fundamental assumptions underlying Modern Portfolio Theory (MPT)
- Gain familiarity with different portfolio definitions, such as a portfolio, an opportunity set, an efficient portfolio, and the efficient frontier
- Learn to calculate the expected return and variance and how correlation affects portfolio variance
- Understand why utility theory differs from the mean-variance and can give more specific portfolio choices
Investment Portfolio Definition
- A diversified securities collection in which xi is the weight and N is the total number of holdings
Return on a Portfolio
- Rp = ∑i xiRi
Specification of Opportunity Set
- specifying the investment universe, i.e., specifying the stocks i = 1, . . ., N that are available
- estimate securities’ risk characteristics, i.e. expected return and variance.
MPT Assumptions
- Investment decisions occur in a single time-period
- Asset risk can be represented by means and variance.
- Investors prefer non-satiation
- Investor risk aversion
What is An Efficient Portfolio
- Having less variance and higher expected returns
Expected Utility
- Indifference emerges when numerous assets have the same anticipated utility
- With indifference curves, higher expected utility are above and to the left
Correlation Effect
- Correlation doesn't affect projected returns, however it does affect risk
- The variance depends mostly on correlation of assets in a portfolio
- Perfect positive correlation = p is 1
- Perfect negative correlation = p is −1
Combining MPT and Utility Theory
- MPT will identify a number of efficient portfolios that can be used
- With utility theory applied, one single portfolio of investments is considered to be the most optimum
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
