Finance Investment Strategies Quiz

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Questions and Answers

What does increasing marginal disutility of a bad suggest about risk compensation?

Each additional unit of risk requires less compensation.

There is no relationship between risk and compensation.

Risk compensation decreases as risk increases.

Each additional unit of risk requires increasingly more compensation. (correct)

Which formula represents the variance of a sample?

var = 1/n Σ(x²-xbar²)

var = 1/n Σ(x-xbar)²

var = 1/(n-1) Σ(x-xbar)² (correct)

var = 1/n² Σ(x-xbar)²

What characterizes the efficient frontier in investment portfolios?

It excludes portfolios with non-correlated assets.

It consists of portfolios that are dominated by other portfolios.

It contains all possible portfolios that maximize expected return for a given level of risk. (correct)

It represents portfolios with the highest variance.

Which of the following does not impact the calculation of expected returns and standard deviations?

Market efficiency Signup and view all the answers

In the context of mean-variance optimization, what is a non-dominated portfolio?

A portfolio that provides more return for the same risk as another. Signup and view all the answers

What does the symbol $R_p$ represent in finance?

The portfolio return Signup and view all the answers

Which of the following is true about the correlation coefficient?

It indicates the strength of the linear relationship between two assets Signup and view all the answers

How is the variance of portfolio return calculated?

It considers diversification depending on correlation of asset returns Signup and view all the answers

What does the formula $E(R_p) = \sum_{i=1}^{N} w_i E(R_i)$ represent?

The expected portfolio return Signup and view all the answers

Which expression represents the covariance between two assets?

Cov(R_i, R_j) = ρ_{ij}σ_iσ_j Signup and view all the answers

What is the primary purpose of calculating the standard deviation of a portfolio?

To describe the distribution of returns and measure risk Signup and view all the answers

What represents a non-dominated portfolio in investment terminology?

A portfolio that offers a higher return for a lower risk Signup and view all the answers

For two assets, the variance of the portfolio return is calculated using which formula?

$\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2Cov(R_1, R_2)$ Signup and view all the answers

What characterizes a dominated portfolio?

More or equal risk and less or equal expected return Signup and view all the answers

What does the Efficient Frontier represent?

Non-dominated portfolios only Signup and view all the answers

Why might limits on short positions be necessary?

To mitigate the impact of extreme allocations Signup and view all the answers

How can one address the problem of having too many parameters to estimate in portfolio optimization?

Utilize asset categories rather than individual securities Signup and view all the answers

What does the tangency of the indifference curve with the efficient frontier indicate?

The optimal portfolio for an investor Signup and view all the answers

What problem is associated with utility maximization in portfolio choice?

Indifference curves can be challenging to define consistently Signup and view all the answers

Which of the following parameters increases with the addition of each new asset in a portfolio?

Correlations between all pairs of assets Signup and view all the answers

What is the primary challenge when combining utility functions with the efficient frontier?

Obtaining real-world estimates for the utility function Signup and view all the answers

What do mean-variance rankings primarily emphasize in portfolio selection?

Diminishing marginal utility with respect to risk Signup and view all the answers

How is the utility function represented mathematically in the CFA framework?

U() = E(R) - 1/2Aσ^2 Signup and view all the answers

In the context of risk aversion, which of the following statements is accurate?

Risk-averse individuals prefer less volatile portfolios. Signup and view all the answers

What is the main concept of the asymmetry of distributions in mean-variance optimization?

Emphasizing losses more than gains when assessing portfolios Signup and view all the answers

If an investor has a risk aversion coefficient (A) of 2, which portfolio would they prefer given the following options?

Portfolio Y with E(r) = 4% and σ = 10% Signup and view all the answers

What must be true for an individual with a risk aversion coefficient of 2 to be indifferent between assets X and Y?

The standard deviation of Y must be adjusted to reduce its utility to the same level as X. Signup and view all the answers

Which of the following best describes indifference curves in mean-variance optimization?

They depict portfolios that provide the same level of satisfaction. Signup and view all the answers

Which aspect is considered less favorable in traditional risk-return tradeoff assessments?

Higher standard deviations signify larger potential returns. Signup and view all the answers

Study Notes

Utility

Utility functions rank portfolios based on their distribution of returns.
Mean-Variance rankings are a common approach, emphasizing expected return and risk (standard deviation).
Diminishing marginal utility dictates that the benefit of additional returns decreases as we receive more.
Risk aversion reflects an individual's tendency to prefer less risk for a given return.
Indifference curves represent portfolios that an individual considers equally desirable.
Indifference curves are typically curved, reflecting diminishing marginal disutility of risk.

Mean-Variance Rankings

Risk-averse individuals dislike risk and seek higher returns for greater risk.
Risk-seeking individuals enjoy risk, willing to accept lower returns for greater risk.
Risk-neutral individuals are indifferent to risk, accepting any return for any risk level.

Other Approaches

Asymmetry of distributions acknowledges that losses may have a greater impact than gains, unlike normal distributions.
Downside risk measures the potential loss of return below a desired target or a benchmark, such as zero.
Prospect theory suggests that individuals are more sensitive to losses relative to their starting point (reference point) than gains.

Utility Functions: As Functions

CFA model: U(R) = E(R) - (1/2) * A * σ^2
- A represents the risk-aversion coefficient, varying across individuals.
Utility functions are challenging to apply in practice, as determining individual utility functions is difficult.

Utility Functions: Indifference Curves

Indifference curves depict a set of portfolios with equivalent utility.
Individuals prefer portfolios to the northwest on the risk-return graph, indicating higher returns and lower risk.

Efficient Frontier

Represents the set of all possible portfolios with the highest expected return for each level of risk.
To calculate the efficient frontier, we need to estimate asset returns, standard deviations, and correlations.
Dominated portfolios are those with lower or equal expected returns than other portfolios for the same or higher risk levels.
The efficient frontier is an upward sloping line segment, representing non-dominated portfolios.

How to Calculate Expected Returns and Standard Deviations

Portfolio return: Weighted average of individual asset returns.
Expected portfolio return: Weighted average of individual asset expected returns.
Variance of portfolio return:
- Not the weighted average of standard deviations.
- Affected by asset correlations.
- Formula involves a summation of weighted covariances.

Practical Issues in Mean-Variance Optimization

Unrealistic allocations:
- Extreme short positions or large positions are problematic.
- May result from using atypical distributions or require limits on positions.
Too many parameters:
- Estimating many parameters (returns, standard deviations, correlations) becomes challenging, especially as the number of assets increases.
- Solutions include combining estimates with priors, simplifying to asset categories, or using return generating models.

Utility Maximization and Portfolio Choice

Optimal portfolio: Tangency point between the indifference curve of the investor and the efficient frontier.
Investors with higher risk aversion will have steeper (more concave) indifference curves and optimal portfolios closer to the minimum variance (risk-averse) portfolio.
Problems: Identifying the investor's true utility function (indifference curve) remains challenging.

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Description

Test your knowledge on utility functions, mean-variance rankings, and risk preferences in finance. This quiz explores how individuals rank portfolios based on their return distributions and risk aversion. Dive into concepts like diminishing marginal utility and indifference curves.