Chapter 5: Portfolio Theory

Question 1

Modern portfolio theory

Answer 1

Specifies a method for an investor to construct a portfolio that gives the maximum return for a specified risk, or the minimum risk for a specified return.

Question 2

Actuarial risk

Answer 2

Risk that the investor fails to meet his or her liabilities.

Question 3

7 Assumptions of Mean-variance Portfolio Theory

Answer 3

• All expected returns, variances and covariances of pairs of assets are known
• Investors make their decisions purely on the basis of expected return and variance
• Investors are non-satiated
• Investors are risk-averse
• fixed single-step time period
• no taxes or transaction costs
• Assets may be held in any amounts

Question 4

2 Assumptions of Efficient portfolio theory

Answer 4

• Investors are never staited

- Investors dislike risk

Question 5

Inefficient portfolio

Answer 5

If the investor can find another portfolio with the same/higher expected return and lower variance, or the same/lower variance and higher expected return.

Question 6

Efficient portfolio

Answer 6

If the investor cannot find a portfolio with a higher expected return and the same/lower variance or a lower variance and the same/higher expected return.

Question 7

Opportunity set

Answer 7

The set of points in E-V space that are attainable by the investor based on the available combinations of securities.

Question 8

Indifference curves

Answer 8

join points of equal expected utility in E-V space.

Question 9

Optimal portfolio

Answer 9

The portfolio that maximises the investor’s expected utility.

Question 10

7 Key factors that might influence the investment decision

Answer 10

• Expected return & variance
• Higher moments of the distribution of returns such as skewness and kurtosis
• Suitability of the asset for an investor’s liabilities
• taxes & investment expenses
• Marketability of the asset
• restrictions imposed by legislation
• restrictions imposed by the fund’s trustees

Question 11

State 2 conditions that need to be met in order for mean-variance portfolio theory to be consistent with utility theory.

Answer 11

• Investors have quadratic utility functions

- Investment returns are normally distributed (or elliptically symmetrically distributed)

Question 12

Explain 2 Benefits of diversification

Answer 12

• Return on the portfolio is less exposed to the specific risks of any one component.
• the correlation components become less important, therefore variance of return is minimised.

Question 13

Outline the limitations of CAPM

Answer 13

• Empirical studies don’t support it
• It does not account for taxes, inflation, or situations in which no riskless asset exists
• It does not consider multiple time periods or optimisation of consumption over time.

Question 14

Key defining properties of brownian motion

Answer 14

• Independent increments
• Stationary increments
• Gaussian increments
• Continuous sample paths
• B0 = 0
• Cov(Bs, Bt) = min(s, t)
• {Bt, t>= 0} is a Markov process
• {Bt, t>= 0} is a Martingale
• {Bt, t>= 0} returns infinitely often to 0 (or indeed to any other level)
• Scaling property
• Time inversion property