3.4 Valuing Common Stocks

Question 1

What is the relationship between number of assets and risk

Answer 1

As the number of assets in the portfolio increases the risk of the portfolio (in terms of standard deviation) falls.

• This does not reach zero (except in special circumstances, which do not occur in the real world).
• Mean return is the weighted averaged of returns, while the portfolio risk is a mix of the weighted average of variances adjusted by the covariances.

Question 2

Answer 2

Question 3

How does the StD of the portfolio change depending on ρ?

Answer 3

Question 4

Equation for portfolio returns with n assets

What happens as n approaches ∞?

Answer 4

Question 5

The average stock has a monthly standard deviation of 10% and the average correlation between stocks is 0.4. If you invest the same amount in each stock, what is the variance of the portfolio?

Answer 5

Question 6

Portfolio risk graphically

Answer 6

Question 7

Optimal protfolio selection

What is the optimisation problem we need to solve?

Answer 7

Question 8

Assumptions for expected return and risk

Answer 8

• We assume that the expected return and risk from historic data is representative.
• Assuming semi-strong form efficiency holds, market price and volatility are representative of the returns required in the past to reflect the risks of the business

Question 9

Efficient frontier portfolios diagrammatically

Answer 9

Question 10

Implications of a risk free asset

Answer 10

If we introduce a risk free asset (safe), each portfolio consists of both risk free and risky assets.

• A portfolio of risk free and risky assets can be viewed as a combination of two assets: the risk free asset and a portfolio of risky assets.
• Frontier portfolio with risk free assets must be a combination of the:
  
  • Risk free asset
  • A tangency portfolio (consisting of risky assets)

Question 11

What is the Sharpe ratio?

Answer 11