TOPIC THREE Chapter 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 of a variable

The variance (σ 2 ) 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 from the 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 the ex 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 the ex 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-averse 2.risk-neutral 3.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 participating is 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 they will 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 on the 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