Exam 7: Investor Preferences and Portfolio Concepts

A risk-free asset is defined as one whose cash flows are not certain across all possible states of the world.

$\text { Investment }$ $\quad$$\quad$$\quad$$\quad$$\text { A }$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { B }$ \ State description Bad state Good state Bad state Good state Probability 0.5 0.5 0.5 0.5 Payoff 200 220 400 435 -Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?

Investment A B State description Bad state Good state Bad state Good state Probability 0.25 0.75 0.25 0.75 Payoff 200 220 400 435 -Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What is the expected utility of asset A?

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Investiment } A$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text { Investment } B$ Good year Bad year Good year Bad year Probability 0.80 0.2 0.90 0.1 Pay-off 140 45 110 70 -Under a concave quadratic utility preference function with a constant term of 0.0001,a wealth level of 100 will have a utility of:

$\text { Investment }$ $\quad$$\quad$$\quad$$\quad$$\text { A }$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { B }$ \ State description Bad state Good state Bad state Good state Probability 0.5 0.5 0.5 0.5 Payoff 200 220 400 435 -The share market is currently returning 18% p.a. ,while the risk-free asset return is 6%.If an investor wishes to earn a return of 10%,what weight should the investor hold in the risk-free asset?

The variance of a portfolio is a non- linear function of the weight invested in the risky asset.

Which of the following is an input into the Markowitz (1959)optimal portfolio determination?

In estimating the covariance matrix,the Markowitz approach for ten assets involves how many calculations?

A feature of indifference curves is a positive slope.

Given a log utility function,a risk-averse investor will favour an asset that pays $100 with certainty over an asset that pays $90 with certainty.

Investors are generally assumed to be:

Individual portfolios can consist of human capital,furniture,the family home,car,bank deposits,shares,bonds and other financial assets.The bank deposits are always considered as risk free assets.

In estimating the covariance matrix,the Sharpe diagonal approach for 10 assets involves how many calculations?

Which of the following measures the spread or volatility of uncertain future returns?

According to Markowitz (1959),if all of the portfolios that satisfy the mean-variance criterion are identified,and investor preferences can be modelled,then the portfolio chosen by an investor is that combination of __________ that maximises expected utility.

Calculate the return on an optimal portfolio where the return on the risky asset is 5%,the return on the risk-free asset is 4%,and where the investor invests has a weight of 75% in the risky asset.

Given a portfolio of 95 shares,what is the total number (variances and covariances)of estimates using the Sharpe's (1963)simple model of asset returns?

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Investiment } A$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text { Investment } B$ Good year Bad year Good year Bad year Probability 0.80 0.2 0.90 0.1 Pay-off 140 45 110 70 -A portfolio comprising two assets can be formed with zero variance,provided the correlation between the securities is:

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Investiment } A$ $\quad$$\quad$$\quad$$\quad$$\quad$$\text { Investment } B$ Good year Bad year Good year Bad year Probability 0.80 0.2 0.90 0.1 Pay-off 140 45 110 70 -Once a portfolio becomes sufficiently large,the __________ is of greatest importance with respect to risk.

Investment A B State description Bad state Good state Bad state Good state Probability 0.25 0.75 0.25 0.75 Payoff 180 240 ?? 190 -Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?