Portfolio Theory

Question 1

Asset Allocation

Answer 1

An asset allocation decision has to be made at t=0.

The payoff in the future will depend on the asset allocation decision and this cannot be changed.

Question 2

Background Assumptions

Answer 2

• As an investor you want to maximise the portfolio risk for a give level of risk
• Your portfolio includes all of your assets and liabilities
• The relationship between asset returns is important for the optimal portfolio construction
• An efficient portfolio is not simply a collection of individual investments with good performance

Question 3

Risk Aversion

Answer 3

Given a choice between 2 assets with the same level of risk, most investors will select the asset with the higher rate of return.
(Yield on bonds increases with risk classification from AAA to AA)

Question 4

Risk

Answer 4

The condition in which there exists a quantifiable dispersion in the possible outcomes from any activity.
Outcomes can be both favourable and unfavourable and depends on managements/ shareholders risk appetite.

Question 5

Risk Perspectives

Answer 5

Downside risk: something goes wrong

Upside risk: outcome is better than expected

Question 6

Attitude to Risk

Answer 6

Risk averse- investors want to reduce risk.
Risk neutral- indifferent to level of risk
Risk seeking- seeking high risk

Question 7

Underlying Assumption

Answer 7

A rational investor will not take on additional risk unless there is additional reward.

• If risk increases an extra return will be required to satisfy the investor.
• An investors attitude to risk will affect how much additional return is required.
• Positive correlation between perceived risk of an investment and the return required by the investor

Question 8

Markowitz Portfolio Theory

Answer 8

• Markowitz Portfolio Theory (mean-variance portfolio optimisation) quantifies risk and derives the expected rate of return for a portfolio of N assets
• It shows that the variance of the rate of return is sensible performance metric of portfolio risk
• It derives the formula for computing the variance of a portfolio, showing how to effectively diversify a portfolio

Question 9

MPT Assumptions

Answer 9

1. Investors consider each investment asset as being derived by a probability distribution of expected returns over some certain holding period.
2. Investors maximise one-period expected utility function.
3. The risk of the portfolio is estimated on the basis of the variability of expected returns.
4. Investment decisions are based on the expected return and risk, so their utility is a function of mean returns and variance of returns only.
5. For a given level risk, investors would prefer higher returns to lower returns. Similarly, for a given level of expected returns, investors prefer less risk to more risk.

Question 10

Expected rates of return

Answer 10

For an individual asset:
Sum of the potential returns multiplied by the corresponding probability of returns.

For a N asset investment portfolio:
Weighted average of the expected rates of returns for the individual investments in the portfolio.

Question 11

Covariance of Returns

Answer 11

A measure of the degree to which two variables “move together” relative to their individual mean values over time.

A positive covariance means that 2 assets move together and a negative variance that return move inversely.

Question 12

Correlation

Answer 12

The correlation coefficient can vary only in the range -1 to +1.

A value of +1 would indicate perfect positive correlation. This means that returns for the two assets move “perfectly” together.

A value of –1 means that the returns for two assets have the same percentage movement, but in opposite directions.

Question 13

Portfolio Standard Deviation

Answer 13

Any asset of a portfolio may be described by two characteristics:

• The expected rate of return
• The expected standard deviations of returns

The correlation affects the portfolio standard deviation, hence low correlation reduces portfolio risk while not affecting the expected return.

Question 14

Combining stocks with different returns and risk

Answer 14

By combining assets with negative correlation it can help reducing portfolio risk significantly.

Combining two assets with correlation of -1.0 reduces the portfolio standard deviation to zero only subject to the condition that individual standard deviations are equal.

Question 15

The Efficient Frontier

Answer 15

The set of portfolios with the maximum rate of return for every given level of risk, or the minimum risk for every level of return.

The efficient frontier represents investment portfolios rather than individual securities.

Question 16

The Efficient Frontier Graph

Answer 16

Every portfolio that lies on the efficient frontier has either a higher rate of return for equal risk or lower risk for an equal rate of return than some portfolio beneath the frontier.

Question 17

Investor’s Utility & Efficient Frontier

Answer 17

• A utility curve describes the trade-offs each individual investor is willing to make between expected return and risk.
• The slope of the efficient frontier curve decreases steadily as you move upward.
• These two interactions between expected return and risk will determine the particular portfolio selected by an individual investor.
• The optimal portfolio has the highest utility for a given investor.
• It lies at the point of tangency between the efficient frontier and the utility curve with the highest possible utility.

Question 18

Systematic Risk

Answer 18

• The risk associated with the entire financial system or market
• Non-diversifiable, non-specific, unavoidable
• Market risk
• Reflects how returns are affected by systematic factors such as business cycles and economic factors.

Question 19

Unsystematic Risk

Answer 19

• Unsystematic risk is inherent in each company (investment) and is company-specific risk
• Diversifiable, specific, avoidable, residual risk
• The risk specific to a particular investment
• Can be reduced by spreading investment over a number of different shares

Question 20

Diversification- Domestic

Answer 20

Optimal domestic portfolio construction:
- An investor may just opt to choose among a
set of individual securities in the domestic
market
- The efficient frontier can be constructed by the
near-infinite set of portfolio combinations of
domestic securities
- The portfolio with the minimum risk along all
those possible combinations on the efficient
frontier is the minimum risk domestic portfolio

Question 21

Diversification- International

Answer 21

International Diversification:-
- Gains (diversification benefits) may arise by
adding additional (international) securities to
the existing domestic portfolio
- International securities do depend on different
factors than domestic securities and hence
there are opportunities for low correlation with
the domestic set.
- An internationally diversified portfolio
opportunity set shifts leftward of a domestic
opportunity set

Question 22

Domestic and International Markets

Answer 22

Markets do not often move together and their correlations may vary over time.
Reasons for the correlation differences:
– Different industrial structures exist in different
countries, thus different countries may
specialize into different sectors.
– Different economies (and countries) possibly
follow different business cycles

Question 23

Performance Metrics- Sharpe Ratio

Answer 23

It is defined as the average return over and above the risk-free rate divided by the standard deviation.

We choose the portfolio with the higher Sharpe ratio since it provides a better return for the same risk.

Question 24

Performance Metrics- The Treynor Ratio

Answer 24

It computes the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk per each unit of market risk assumed.

Question 25

Comparing Perfomance Metrics

Answer 25

• The two metrics give similar rankings in case of perfectly diversified portfolios (zero unsystematic risk), due to the fact that the total portfolio risk is equivalent to the systematic risk.
• The Treynor ratio may give high rankings to poorly diversified portfolios, but the opposite happens in case of the Sharpe measure.
• As the difference is due to the low level of portfolio diversification, the two metrics therefore provide complimentary but different information.