Problem of an Individual MV Investor

Question 1

Risk measured as variance can be completely diversified with…

Answer 1

…a sufficient number of negatively correlated and independent assets

Question 2

Systematic risk is…

Answer 2

…risk that cannot be eliminated through diversification, existing because the economy is complex and assets are interrelated

Question 3

What are the two steps in solving the MV investor’s problem?

Answer 3

Derive the EPF, which will allow us to eliminate all portfolios that the investor will never choose (i.e. those that do not diversify away all non-systematic risk). Then, choose a portfolio along the EPF according to the investor’s level of risk aversion.

Question 4

An efficient portfolio…

Answer 4

…is one offering the maximum expected rate of return for a given rate of portfolio return variance (i.e. risk)

Question 5

The EPF is the…

Answer 5

…complete collection of all efficient portfolios. Every allocation of assets along the line is efficient, meaning that there is no way of reducing risk without reducing return by simply reshuffling assets.

Question 6

The slope of the portfolio frontier is…

Answer 6

…the Marginal Rate of Transformation (MRT) which is the change in the expected return divided by the change in the return variance. As we move along the portfolio frontier we are trading risk for return and vice versa, and the ratio between the two (i.e. the MRT) changes as we move along the portfolio. It is the rate at which the economy can transform risk into return

Question 7

The Two-Fund theorem (First-Mutual Fund theorem) says that…

Answer 7

…you only need to find two efficient portfolios (i.e. maximise the expected return for two given levels of variance) and then any linear combination of these two portfolios is another efficient portfolio that will lie on the EPF. Different linear combinations will then trace out the EPF.

Question 8

Where along the EPF will an investor choose the portfolio that will maximise their utility?

Answer 8

At the point where the their MRS of risk for return is equal to the MRT (i.e. where their indifference curve is tangent to the EPF)

Question 9

How do we approach the MV problem when there is a risk-free asset?

Answer 9

Derive the EPF with a risk-free asset (i.e. consider combinations of MV efficient portfolios with the risk free asset and check which of these portfolios are efficient), and then let the investor choose the portfolio that maximises their utility

Question 10

The standard deviation/variance of the return on the risk-free asset is…

Answer 10

0, because it bears no risk

Question 11

Is the MRT constant when there is no risk-free asset? Is is constant when there is a risk-free asset?

Answer 11

It is NOT constant when there is NO risk-free asset, but is constant when there is a risk-free asset

Question 12

What is the slope of the EPF with a risk-free asset?

Answer 12

It is the Sharpe Ratio

Question 13

What is the Sharpe ratio?

Answer 13

The expected return on an asset (or portfolio) j minus the risk-free rate, divided by the standard deviation (i.e. risk) of the asset/portfolio. It shows the expected excess return per unit of risk and shows the risk-adjusted performance. It describes the trade-off between expected return and risk.

Question 14

The efficient portfolio in the presence of the risk-free asset (that will be combined with RF asset) is going to be the one that has…

Answer 14

The highest feasible Sharpe Ratio, which is portfolio Z

Question 15

Is the Sharpe Ratio constant along the EPF with a risk-free asset?

Answer 15

Yes, it is constant

Question 16

How will an investor choose a portfolio in the presence of the RF asset?

Answer 16

They will choose one along the MV efficient frontier with the risk-free asset, a combination of the risky portfolio Z and the RF asset, where their MRS is equal to the MRT.

Question 17

Without the risk-free asset, will the investor’s level of risk aversion determine the portfolio of risky assets that they choose?

Answer 17

Yes, the portfolio of risky assets chosen will depend on their level of risk aversion.

Question 18

With the risk-free asset, will the investor’s level of risk aversion determine the portfolio of risky assets they choose?

Answer 18

No, all investors will hold the same portfolio of risky assets, Z, which yields the highest feasible Sharpe Ratio, and then depending on their level of risk aversion they will hold it in a certain proportion with the risk-free asset.

Question 19

What information do we need to create a portfolio for a MV investor?

Answer 19

The expected returns from different sectors, and the variances of the returns from these sectors

Question 20

How do we summarise the relationships between these assets from different sectors?

Answer 20

Variance-covariance matrix. We multiply the vector of returns by the variance-covariance matrix.

Question 21

When we lose the ability to short-sell assets, what asset will we demand more?

Answer 21

The risk-free asset, as we lose the ability to mitigate risk by short-selling

Question 22

Why may you invest in an asset with a relatively low Sharpe ratio?

Answer 22

It may be negatively correlated with other assets