Finance Chapter 4: EGARCH and Portfolio Analysis
29 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the expected return from the risk-free asset?

  • 0.08
  • 0.03
  • 0.10
  • 0.05 (correct)

What is the formula for the return from the combined portfolio?

  • rc = q.Rp + (1-q).σf
  • rc = q.rf + (1-q).σp
  • rc = q.E[rf] + (1-q)E[σp]
  • rc = q.Rf + (1-q).rp (correct)

What does the standard deviation of the risk-free asset equal?

  • 0.05
  • 0.08
  • 0 (correct)
  • 0.10

How is the standard deviation of the combined portfolio calculated?

<p>σc = (1 - q).σp (A)</p> Signup and view all the answers

The riskier asset offers a higher expected return due to what characteristic?

<p>Inherent risk (C)</p> Signup and view all the answers

What does the utility of an investment depend on?

<p>The expected return and risk of the investment (A)</p> Signup and view all the answers

How does the coefficient of risk aversion (C) affect utility?

<p>Higher C increases the penalty for risk, reducing utility (D)</p> Signup and view all the answers

What best describes the relationship between risk aversion and investment choices?

<p>Higher risk aversion leads investors to prefer lower return but lower risk investments (D)</p> Signup and view all the answers

Which of the following is true about the Sharpe ratio?

<p>It measures excess return relative to risk (A)</p> Signup and view all the answers

Which investment alternative has the highest Sharpe ratio?

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

Which statement about inefficient investments is true?

<p>An inefficient investment can never yield the highest utility (A)</p> Signup and view all the answers

If two investment alternatives have close Sharpe ratios, what is likely to happen?

<p>Performance differences may be negligible (B)</p> Signup and view all the answers

What influences an investor's decision to add an asset to their portfolio?

<p>How much the asset contributes to the portfolio's total risk (C)</p> Signup and view all the answers

What happens to utility as risk aversion increases?

<p>Utility decreases due to higher penalties for riskier choices (A)</p> Signup and view all the answers

What is the consequence of having a higher risk aversion in an investment?

<p>More compensation is needed for taking on additional risk (D)</p> Signup and view all the answers

What characterizes an indifference curve in risk-return profiles?

<p>It shows the trade-off between risk and expected return at a fixed utility score (B)</p> Signup and view all the answers

Which of the following statements is true about asset D?

<p>It dominates alternative investments by offering a higher return at a lower risk (B)</p> Signup and view all the answers

Which investment strategy allows for both risky assets and risk-free assets?

<p>Capital allocation strategy (A)</p> Signup and view all the answers

What does it mean when an asset is weakly or negatively correlated with existing assets?

<p>It may still be worth adding to the portfolio despite low expected returns (D)</p> Signup and view all the answers

What key factor should not influence the assessment of an asset's addition to a portfolio?

<p>Personal taste for higher risks (A)</p> Signup and view all the answers

What must be fulfilled for an investor to consider the risk-return of different assets as equally useful?

<p>The utility score must be fixed with a specific risk tolerance (A)</p> Signup and view all the answers

What does a negative value of b in the EGARCH model indicate?

<p>Negative shocks have a greater impact on future volatility than positive shocks of the same magnitude. (C)</p> Signup and view all the answers

Which characteristic of the EGARCH model distinguishes it from other volatility models?

<p>It allows coefficients to be negative due to the log function. (A)</p> Signup and view all the answers

Which statement about the Sharpe ratio is correct?

<p>It helps to compare the expected reward for an additional unit of risk. (A)</p> Signup and view all the answers

In the context of portfolio selection, what does the Markowitz approach primarily address?

<p>Balancing individual preferences with objective portfolio choices. (B)</p> Signup and view all the answers

What can be inferred about the portfolio with the highest expected return among the provided options?

<p>The expected return of extremely high-risk portfolio is the same as the high-risk portfolio. (A)</p> Signup and view all the answers

Which portfolio exhibits the highest standard deviation of excess return?

<p>Portfolio E (D)</p> Signup and view all the answers

What does the quadratic utility function represent in the context of investment decisions?

<p>It provides a way to evaluate risk preferences relative to expected returns. (D)</p> Signup and view all the answers

If a portfolio has an expected return of 0.05 and a standard deviation of excess return of 0.09, what is its Sharpe ratio?

<p>0.56 (C)</p> Signup and view all the answers

Flashcards

Fraction invested in risk-free asset (q)

The percentage of an investor's wealth allocated to the risk-free asset, like a government bond.

Fraction invested in risky asset (1-q)

The percentage of an investor's wealth allocated to the risky asset, like stocks.

Combined Portfolio Return (rc)

The return on the combined portfolio, calculated as the weighted average of the returns from the risk-free and risky assets.

Expected Combined Portfolio Return (E[rc])

The expected value of the combined portfolio return, calculated using the fractions invested in each asset and their respective expected returns.

Signup and view all the flashcards

Standard Deviation of Combined Portfolio (σc)

The standard deviation of the combined portfolio, determined by the fraction invested in the risky asset and its standard deviation.

Signup and view all the flashcards

EGARCH Model

A model that captures asymmetry in the volatility process, where negative shocks have a larger impact on future volatility than positive shocks of the same magnitude.

Signup and view all the flashcards

Persistence in Volatility

The impact of past volatility on current volatility. A higher value indicates that past volatility has a stronger influence on the current level.

Signup and view all the flashcards

Sharpe Ratio

Measures the risk-reward trade-off of an investment. A higher Sharpe ratio indicates a better return for the level of risk taken.

Signup and view all the flashcards

Expected Return

The expected return of an investment, calculated as the average of all possible returns.

Signup and view all the flashcards

Risk

A measure of how much riskiness is associated with an investment. It is typically measured by standard deviation.

Signup and view all the flashcards

Markowitz Portfolio Selection

A model that suggests investors choose portfolios based on their individual preferences for risk and return.

Signup and view all the flashcards

Quadratic Utility Function

The assumption that the decision-making process of investors is based on a quadratic utility function.

Signup and view all the flashcards

Expected Value

The expected value of an investment, factoring in the likelihood of different outcomes.

Signup and view all the flashcards

Risk-Return Trade-Off for Individual Investments

The relationship between risk and expected return for individual investments. An asset with a higher risk is expected to provide a higher return.

Signup and view all the flashcards

Risk-Return Trade-Off for Portfolios

The relationship between risk and expected return for a portfolio. An asset with a higher risk may still be beneficial if it lowers the overall portfolio risk.

Signup and view all the flashcards

Indifference Curve

A curve representing all combinations of risk and return that provide the same level of utility to an investor. Different investors with different levels of risk aversion will have different indifference curves.

Signup and view all the flashcards

Risk Aversion Coefficient

The slope of the indifference curve, reflecting the investor's willingness to accept more risk in exchange for a higher return. A higher coefficient indicates greater risk aversion.

Signup and view all the flashcards

Capital Allocation Line (CAL)

The line representing all possible portfolios that can be formed by combining a risky asset portfolio with a risk-free asset. The slope of this line reflects the risk-return trade-off of the risky asset.

Signup and view all the flashcards

Risk Premium

The return for taking on an additional unit of risk. It measures how much extra return an investor expects to receive for bearing more risk.

Signup and view all the flashcards

Correlation

A measure of how much an asset's return moves in relation to the overall market. A positive correlation implies movements in the same direction, while a negative correlation implies movements in opposite directions.

Signup and view all the flashcards

Systematic Risk

The systematic risk of an asset that cannot be diversified away. It is measured by beta, which represents the asset's sensitivity to market movements.

Signup and view all the flashcards

Risk Aversion (C)

A measure of how much an investor dislikes risk. Higher risk aversion means a greater preference for low-risk investments, even if they offer lower returns.

Signup and view all the flashcards

Excess Return

The expected return of an investment minus the risk-free rate. Measures the potential reward for taking on risk.

Signup and view all the flashcards

Risk (Standard Deviation)

The standard deviation of an investment's returns. Measures how much the returns are likely to fluctuate around the expected return.

Signup and view all the flashcards

Utility (U)

The way an investor's preferences for risk and return are represented mathematically. Higher utility means the investment is more desirable.

Signup and view all the flashcards

Inefficient Investment

In finance, an investment is considered inefficient (or 'mean-variance dominated') if another investment exists with a higher expected return for the same level of risk, or with lower risk for the same expected return.

Signup and view all the flashcards

Portfolio Optimization

The process of selecting investments based on the expected return and the risk of each investment, with the goal of maximizing utility (happiness) for the investor.

Signup and view all the flashcards

Risk Aversion and Investment Choice

The principle that investors with higher risk aversion will generally prefer investments with lower expected return but also lower risk.

Signup and view all the flashcards

Study Notes

EGARCH Model

  • The EGARCH model, similar to the GJR-GARCH model, reflects volatility asymmetry.
  • Negative shocks have a larger impact on future volatility compared to positive shocks of equal magnitude (if b < 0).
  • This model doesn't require constraints on coefficients, allowing them to be negative due to the log function.
  • EGARCH models account for leptokurtic conditional variance.

Chapter 4: Utility and Indifference Curves

  • Choosing between investment options is difficult.
  • The Sharpe ratio can indicate expected reward per unit of risk, but further personal preference needs to be assessed
  • The Markowitz portfolio selection method separates personal preferences from objective portfolio optimization.
  • Portfolio A to E provide examples with varying risk levels, expected return, excess return standard deviation, and respective Sharpe ratios

Portfolio Analysis

  • Investor preferences heavily influence investment choices.
  • Quadratic utility functions (U = E(r) - c.σ²) guide decision-making, where:
    • U = Utility
    • E(r) = Expected return
    • σ² = Variance of return
    • c = Risk aversion coefficient (higher c = higher risk penalty)
  • Utility depends on the expected return and its associated risk (measured by standard deviation).

Investor Preferences and Sharpe Ratios

  • Higher risk aversion leads investors to prefer investments with lower returns and lower risk.
  • The choice of investment does not solely depend on the Sharpe ratio, but also risk aversion
  • It is difficult to compare investment options that are close together in terms of risk and return
  • An investment with low Sharp ratio can still be preferred over another if its risk and return are more suitable to the investor

Capital Allocation Line

  • Investments can be in risk-free or risky assets.
  • A risk-free asset has a standard deviation of zero.
  • The expected return and standard deviation of a risky investment is calculated
  • Investors must decide how much of their wealth goes into risk-free and risky investments to optimize their portfolios.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Beleggingsleer 1 PDF

Description

Explore Chapter 4 discussing the EGARCH model's asymmetry in volatility and its implications for investment strategies. Learn about utility and indifference curves in portfolio selection, and see how different investment options can be evaluated using the Sharpe ratio. This quiz will test your understanding of key concepts in finance and investment analysis.

Use Quizgecko on...
Browser
Open
Browser
Browser