Optimal Portfolio Choice and CAPM

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Questions and Answers

What is the portfolio weight of an investment of $10,000 in a portfolio totaling $40,000?

0.50

0.10

0.75

0.25 (correct)

Which formula correctly represents the expected return of a two-stock portfolio?

E[RP] = xF * E[RF] + xH * E[RH] (correct)

E[RP] = xF * E[RF] - xH * E[RH]

E[RP] = (xF + xH) * E[R]

E[RP] = (xF + xH) / 2

What effect does diversification have on a portfolio's risk?

It eliminates all risks associated with the assets.

It helps mitigate certain risks by combining assets that have common risks. (correct)

It reduces risk by combining assets with correlated returns.

It can increase risk if the assets are negatively correlated.

What is the role of beta in assessing a stock's risk relative to the market?

Beta estimates how much the stock's price movements correlate with market movements. Signup and view all the answers

Which of the following represents the average return of an investment portfolio?

The weighted sum of expected returns based on portfolio weights. Signup and view all the answers

What is the weight of Intel stock in a portfolio that consists of 30% in Bore and 70% in a portfolio containing 50% Intel and 50% Coca-Cola?

35% Signup and view all the answers

Combining Bore with Intel and Coca-Cola improves what characteristic of a portfolio?

Risk and return possibilities Signup and view all the answers

If a portfolio only contains Intel and Coca-Cola, it will likely have what type of curve compared to combinations including Bore?

A black curve indicating lower efficiency Signup and view all the answers

In a portfolio that includes another portfolio, how are the weights of the individual stocks determined?

By multiplying the portfolio weights Signup and view all the answers

What is the role of the market portfolio in portfolio theory?

It includes all risky assets in the market. Signup and view all the answers

What does beta measure in the context of portfolio management?

Market risk of a single stock relative to the market Signup and view all the answers

Which type of position refers to the purchase of stocks with the expectation that they will rise in value?

Long position Signup and view all the answers

What impact does adding more stocks to an equally weighted portfolio have on its volatility?

Volatility decreases with more stocks. Signup and view all the answers

How does the volatility of a portfolio compare to the weighted average volatility of the individual stocks within it?

The portfolio's volatility is less than the weighted average volatility. Signup and view all the answers

What does the equation SD(RP) = ∑ xi SD(Ri) Corr(Ri, RP) indicate about portfolio risk?

It highlights the effects of correlation on portfolio risk. Signup and view all the answers

What is an efficient portfolio primarily aimed at achieving?

Balancing expected return with acceptable levels of risk. Signup and view all the answers

What role does diversification play in portfolio management?

It spreads risk across different securities to reduce overall volatility. Signup and view all the answers

Which of the following concepts is primarily related to the relationship among stocks in a portfolio?

Beta Signup and view all the answers

If two stocks have a perfect positive correlation of +1, what does this imply for a portfolio containing those stocks?

The portfolio's volatility will equal the weighted average volatility of the stocks. Signup and view all the answers

In portfolio theory, what does the term 'weights' refer to?

The proportion of total investment allocated to each asset. Signup and view all the answers

Study Notes

Optimal Portfolio Choice and the Capital Asset Pricing Model

Investors can choose efficient portfolios by understanding mean-variance portfolio optimization.
This technique is used routinely by professional investors and financial institutions.
The Capital Asset Pricing Model (CAPM) is the most important model for the relationship between risk and return.
In CAPM, the efficient portfolio is the market portfolio of all stocks and securities.
Expected returns of securities depend on their beta with the market portfolio.
Volatility of a portfolio is measured by standard deviation.
Calculating portfolio return involves weighting average returns of investments in the portfolio with their respective weights.
Diversification reduces risk in a portfolio.
Covariance is the expected product of deviations from the means of two returns.
Correlation measures the relationship between two returns, and values range from -1 to +1.
Calculating a portfolio's variance involves weighted averages of the variances of individual stocks and covariances between pairs.
Efficient portfolios maximize expected return for a given level of volatility.
Portfolios with 20% or more in stock Intel are efficient options.
By combining stocks into a portfolio, risk is reduced through diversification.
Stocks that tend to move together have a higher correlation.
Risk is lessened when investments have less tendency to move together.
Adding more stocks diversifies further, lessening risk.
Diversification is most beneficial with a small number of stocks.
Short sales (selling a security one does not own) are possible and can increase investment return but also increase overall portfolio volatility.
The Sharpe ratio is a measure of a portfolio's risk-return tradeoff.
The portfolio with the highest Sharpe ratio is called the tangent portfolio or efficient portfolio.
Investors choosing the most efficient portfolio depend on their risk tolerance.
The efficient portfolio depends on the market portfolio.
Determining which securities to sell or buy is based on their expected returns in relation to their required return.

The Volatility of a Large Portfolio

The return of a portfolio of n stocks is equal to the weighted average of the returns of individual stocks.
When portfolios of many stocks are considered, the variance is determined primarily by the average covariance of component stocks.
Volatility decreases as more stocks are included in portfolios.

Risk-Free Saving and Borrowing

Investing in risk-free securities, such as Treasury bills, reduces overall portfolio volatility.
Investing in stocks via margin may increase expected portfolio return (but also volatility).
Expected return of a portfolio with risk-free securities is the weighted average of the risk-free investment and the risky portfolio.
Volatility of a portfolio holding a combination of risk-free investments and a risky portfolio is lower than the variance of the risky portfolio as a percentage.

The Capital Asset Pricing Model (CAPM)

The market portfolio is the efficient portfolio in the market.
Investors with homogeneous expectations identify the market portfolio as the portfolio of highest Sharpe ratio regardless of their risk preferences.
In the CAPM, the risk premium of a security is proportional to its beta.
The risk premium for a security is its market risk multiplied by the market risk premium.
The Capital Market Line (CML) describes the relationship between risk and return for efficient portfolios, combined with risk-free return.

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Description

Test your knowledge on optimal portfolio choice and understand the key concepts of the Capital Asset Pricing Model (CAPM). This quiz covers mean-variance optimization, diversification, risk-return relationships, and the mathematical principles underlying portfolio management. Sharpen your financial acumen and evaluate your grasp of these crucial investment strategies!