TOPIC THREEChapter 4: Understanding

Risk and Return

By Diana Beal and

Michelle Goyen

What is return?

• A return is the gain or loss achieved by making an investment

• Companies issue debt and equity and use the funds raised to increase the earnings of the firm.

• The cash flows from the investments a company makes are used to pay debt and equity holders their return

Measuring returns

• Ex post or realised returns are those returns that relate to past periods.

• They are observable and easily measured

• Past dividends and any price change are used to measure ex post returns on a share

• The holding period return is the return an investor would earn if the share was purchased at the start of the period and sold at the end of the period

• All Ordinaries Accumulation Index – takes the share prices of a group of companies listed on the ASX

• weights them according to their relative size in the market

• assumes that dividends paid by the companies are reinvested, so they increase the index

• Ex ante returns are those that investors expect to receive in the future

• They are not observable and measurement is more subjective than for ex post returns.

• expected return – the probability-weighted average of possible outcomes

• possible outcomes each have a probability assigned to them. The probability of all possible outcomes equals 100%

• can be a different number to any of the identified possible outcomes

What is risk?

• Risk is the chance that the actual outcome from an investment will be different from the expected outcome

• The risk of an asset is shown in the dispersion of its expected returns

• a wide distribution of returns indicates high risk

• a narrow distribution of returns indicates lower risk

Measuring risk

• a random variable is a possible outcome that is drawn from the distribution of possible outcomes for that variable

• if that distribution is normal, we can draw some useful conclusions about the data

• The normal distribution is a symmetric and bell-shaped curve centred on the expected value ofa variable

• The variance (σ2) is the squared deviation of the variable from its expected value

• The standard deviation (σ) is the square root of the variance

• For normal distributions:

the mean plus or minus– one standard deviation (σ) will cover

approximately 68% of possible outcomes– two standard deviations (2σ) covers about

95% of outcomes– three standard deviations (3σ) covers

around 99.7% of outcomes

• The ex ante variance is the probability-weighted average of deviations of possible returns fromthe expected return

• The ex ante standard deviation is the square root of the ex ante variance

• The ex post variance is the weighted average of the deviations of observed returns from the mean return

• The mean return of observed outcomes is used to calculate theex post variance

• The ex post standard deviation is the square root of the ex post variance.

• the larger the standard deviation, the greater the chance that theex post outcome will not equal the expected outcome

• the standard deviation of ex post outcomes is sometimes used as a substitute for the ex ante risk measure

• Different people have different views on how much risk they will tolerate

• A risk preference represents a person’s attitude to risk

• people are categorised into three groups:1. risk-averse2. risk-neutral3. risk-seeking

based on their risk preferences

• A risk-averse person will not participate in a fair game

• A fair game is one where the expected value of participatingis zero

• A risk-neutral person is indifferent to participating in a fair game

• this person will sometimes participate in a fair game and sometimes not

• won’t have a firm rule about playing fair games

• A risk-seeking person will reject a certain outcome in favour of a riskier game that has an equal or lower expected return

• might play a game where it is a reasonable expectation that theywill lose their money

• thinks it is fun to take risks

• Traditional finance theory is based on the assumption that market participants are risk-averse

• Differing degrees within the category of risk-aversion are used to explain differing preferences for assets with varying levels of risk

Risk-return relationship

• Risk-averse investors are willing to take on more risk if the expected return is high enough to compensate them for the risk

• Leads to the conclusion that there is a positive relationship between risk and expected return

• The required rate of return on an investment

– is the minimum level of return that is acceptable to an investor

– given the level of risk associated with that investment

• People making investment decisions compare the expected return to the required return

– If the expected return is higher, they will invest

– If the required return is higher, they will not invest as the expected return is insufficient to compensate them for that level of risk

Reducing risk

• A portfolio is a collection of different assets

• Diversification is the spread of different assets held in a portfolio

• The objective of holding a diversified portfolio is to reduce risk

• Correlation is a measure of the way two variables move relative to each other

– perfect positive correlation means the assets move in the same direction by the same amount (zero risk reduction)

– perfect negative correlation means they move in opposite directions by the same amount (maximum risk reduction)

• Systematic risk is the risk that is common to all businesses– cannot be reduced by diversification

• Unsystematic risk comes from the way a particular business conducts its activities – can be eliminated with diversification

• Total risk includes both systematic and unsystematic risk

• A well-diversified portfolio only contains systematic risk

• The unsystematic risk of each asset is offset by the unsystematic risks of the other assets in the portfolio

• Theoretically, investors cannot expect to gain higher returns by increasing unsystematic risk

Capital asset pricing model

• Portfolio theory – the optimal portfolio consists of an

investment in the market portfolio of all risky assets

– and an investment in the risk-free asset

• The Capital Asset Pricing Model (CAPM) – a quantifiable relationship between expected return and systematic risk

• The return on the market portfolio – a benchmark share price index

• The risk-free rate – the return on government-issued bonds

• The equity risk premium indicates how much additional return can be expected by moving from the risk-free asset to the market portfolio of risky assets.

• The asset’s beta – the level of systematic risk

• Beta – relative measure that describes how the return on the asset is related to the return onthe market portfolio

• CAPM has been challenged on theoretical grounds and has not received unanimous support when tested for its predictive ability

• Arbitrage Pricing Theory states that systematic risk comes from a number of factors

• No model has yet been developed that is capable of replacing the CAPM in a practical sense

People dimensions

• Allais Paradox – making decisions, we cancel what is the same and focus on what is different

• Changing the scale of measurement should not change the choice

• Experiments show that certainty is preferred to uncertainty, even if it means choosing the lower expect value