Lecture 7

Question 1

What is the Certainty Equivalent?

Answer 1

The rate that a risk-free investment would need to offer to provide the same utility as the risky portfolio.

Question 2

Why do investors invest in multiple risky assets?

Answer 2

To reduce total risk. A well-diversified portfolio does not have firm-specific or idiosyncratic risk but only the systematic risk remains.

Question 3

What is the risk premium?

Answer 3

Portfolio return - Risk free rate

Question 4

What is the condition for investors to invest in a portfolio of risky assets?

Answer 4

The risk premium of the portfolio needs to be higher than the risk free rate. Also depends on their risk aversion.

Question 5

Explain why only covariance matters for the volatility of a portfolio. Also include the formula for portfolio variance with the assumption that all weights are constant and that every variance and covariance is equal to the average.

Answer 5

These assumptions give the formula;
Portfolio variance = (1/n * Average Variance) + ((n-1)/1) * Average covariance.
When you increase n to infinity, variance disappears and only covariance remains. Therefore, only covariance determines the volatility of a portfolio.

Question 6

Why does firm-specific risk or idiosyncratic risk is not important when determining portfolios?

Answer 6

Because firm-specific risk can be diversified away for free, only systematic risk remains.

Question 7

What numbers determines the volatility risk of a portfolio?

Answer 7

Covariances between assets

Question 8

Why do we use correlations instead of covariances?

Answer 8

Correlations can measure the strength and do it in a small interval (-1 - 1)

Question 9

What is the first step of the Markowitz Portfolio Theory?

Answer 9

Describe all risk-return combinations in a utility curve.

Question 10

What is the Expected Return of a Combined Portfolio with One Risky Asset and One Risk Free Asset?

Answer 10

E(Rc) = Risk Free Rate + weight * (Risk premium)

Question 11

The Combined Portfolio with One Risky Asset and One Risk Free Asset is expected to earn a risk premium that depends on the risk premium of the One Risky Asset because the Risk Free Asset has no volatility or risk premium.

Question 12

What is the formula for Volatility of the Combined Portfolio?

Answer 12

Volatility Combined Portfolio = Weight * Volatility Risky Portfolio

Question 13

How do you name the straight line in the Markowitz Graph?

Answer 13

Capital Allocation Line (CAL)

Question 14

What is the formula of the Share Ratio (Reward-to-volatility ratio) and what is it?

Answer 14

The Sharpe Ratio is the slope of the CAL in the Markowitz Portfolio Theory. It gives the expected risk premium per unit risk and you calculate it by;
Sharpe Ratio = Risk Premium / Volatility Risky Portfolio

Question 15

Can the reward-to-volatility ratio (Sharpe Ratio) of any
combination of the risky asset and the risk-free asset be different from the ratio for the risky asset taken alone?

Answer 15

No because the risk-free asset has no volatility or risk premium to change it.

Question 16

What happens when you use a levered portfolio?

Answer 16

The weight of risky asset becomes >1 and you have to multiply the volatility of the risky asset with that positive weight because leverage makes the volatility and risk higher.

Question 17

What happens to the Sharpe Ratio when the portfolio is levered?

Answer 17

Unaffected

Question 18

How to calculate a utility curve for the Markowitz Portfolio Theory?

Answer 18

U = Expected Return (Combined Portfolio) - 0.5 * Risk Aversion * Variance (Combined Portfolio)
This equals;
Risk Free Rate + (Expected Return Risk Portfolio - Risk Free Rate) - 0.5 * Risk Aversion * Variance (Combined Portfolio).

Take the derivative of this formula and solve for Y = Optimal point