Topic 8: Efficient Portfolios

Question 1

What do Portfolio Weights do?

Answer 1

Fraction of the total investment in the portfolio held in each individual investment in the portfolio

Question 2

Formula for Portfolio weights

Answer 2

Question 3

What must the portfolio weight add up to?

Answer 3

1.00 or 100%

Question 4

Formula for expected return of a portfolio

Answer 4

Question 5

Volatility of a Two-Stock Portfolio

Answer 5

By combining stocks into a portfolio, we reduce risk through diversification

The amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face common risks and their prices move together

To find the risk of a portfolio, one must know the degree to which the stocks’ returns move together

Question 6

Covariance

Answer 6

Question 7

Estimate of the Covariance from Historical Data

Answer 7

Question 8

If the Covariance is positive…

Answer 8

the two returns tend to move together

Question 9

If the covariance is negative….

Answer 9

The two returns tend to move in opposite directions

Question 10

Correlation

Answer 10

The correlation measures of the common risk shared by stocks that does not depend on their volatility

• The correlation between two stocks will always be between -1 and 1

Question 11

Variance of a Two-Stock Portfolio

Answer 11

Question 12

What is the Variance of a Large Portfolio

Answer 12

Question 13

What is an Equally weighted portfolio?

Answer 13

• A portfolio in which the same amount is invested in each stock
• An equally weighted portfolio of n stocks invests 1/n in each stock

Question 14

What is the Variance of an equally weighted portfolio of n stocks

Answer 14

Question 15

In an inefficient portfolio…

Answer 15

It is possible to find another portfolio that is better in terms of both expected return and volatility

Question 16

In an efficient portfolio…

Answer 16

there is no way to reduce the volatility of the portfolio without lowering its expected return

Question 17

Expected Return and Volatility Graph

• Long position?
• Short Position?
• Short Selling?

Answer 17

• Postive investment in a security
• Negative investment in a security
• Sell a stock that you do not own and buy the stock in the future

Question 18

How else can risk be reduced?

Answer 18

By investing a portion of a portfolio in a risk-free investment, like T-Bills

However, doing so will likely reduce the expected return

An aggressive investor who is seeking high expected returns might decide to borrow money to invest even more in the stock market

Question 19

What is a Sharpe Ratio?

Answer 19

Measures the ratio of reward-to-volatilty provided by a portfolio

Question 20

Sharpe Ratio Formula

Answer 20

Question 21

What is a Tangent Portfolio?

Answer 21

The portfolio with the highest Sharpe Ratio, where the line with the risk-free investment is tangent to the efficient frontier of risky investments

Question 22

Tangent Portfolio Need to Knows

Answer 22

• Tangent portfolio is efficient and all efficient portfolios are combinations of the risk-free investment and the tangent portfolio
• Combinations of the risk-free asset and the tangent portfolio provide the best risk and return tradeoff available to an investor
• The investor’s preferences will determine only how much to invest in the tangent portfolio versus the risk-free investment

Question 23

Conservative investors

Answer 23

Invest a small amount in the tangent portfolio

Question 24

Aggressive investors

Answer 24

Invest more in the tangent portfolio