Post on 31-Dec-2015
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