Financial Economics – Gamma
Expected Returns Theory
- An application of the von Neumann-Morgenstern Theory
- A set of positive methods → what would the state of the world be if investors behaved rationally and optimised
the mean-variance trade off
- Assumes:
o Financial markets are compromised of mainly rational decision makers
o Uncertainty of outcomes is addressed with the mean-variance analysis
Building positive from normative finance
1. Start with the normative method
• Need to specify the behaviour of the individual investor by noting their preferences from their utility
function
• Assume that the investor/agent is rational and makes a single decision to address investment
uncertainty for investments that future outcomes with distributions that are all explained by the first
two moments
2. Assume that a collection of agents use this method when interacting with one another
3. Examine what happens if this ‘real world’ behaves this particular way
CAPM
- The model allows investors to ‘free-ride’ on the analysis of other investors if its assumptions hold:
- Assumptions:
o All investors are price takers → not price makers; assumed to be too small to influence price
o They pick portfolios based on the standard mean-variance analysis → i.e. they behave rationally
o They have common beliefs about the statistics of returns → this needs to hold on average; some
deviations can exist
o They can borrow and lend at the risk free rate → not necessarily true; assumption can be relaxed
o There are no nontraded assets → very big assumption
o There are no taxes or transaction costs
Consequences of CAPM
- If the assumptions hold:
o Investors hold a mean-variance efficient portfolio
o They all agree on which portfolios lie on the efficient frontier
- Due to Tobin’s mutual fund theorem:
o All efficient mean-variance portfolios combine the riskless asset with a fixed portfolio on the efficiency
frontier (a.k.a. tangency portfolio) (fixed portfolio only contains risky assets)
o Thus the weights of every asset inn each investor’s risky portfolio is exactly the same as the weight
that every other investor places on the same asset
- Since in equilibrium, demand = supply:
o The portfolio weights of the tangency portfolio are those of the market portfolio
o Market portfolio is the value-weighted index that contains all risky assets in proportion to their market
value
o Thus the market portfolio is mean-variance efficient
▪ Beating the market means finding a portfolio that is more efficient than the market portfolio
→ i.e. need to find a portfolio with a better risk-return relationship → however,
efficient/market portfolio gives the minimum risk for a given return → therefore not
possible/difficult to beat the market.
o Investors can use this knowledge to determine the their optimal capital allocation line as simply the
capital market line (the one that connects the risk-free asset to the market portfolio)
Expected Returns Theory
- An application of the von Neumann-Morgenstern Theory
- A set of positive methods → what would the state of the world be if investors behaved rationally and optimised
the mean-variance trade off
- Assumes:
o Financial markets are compromised of mainly rational decision makers
o Uncertainty of outcomes is addressed with the mean-variance analysis
Building positive from normative finance
1. Start with the normative method
• Need to specify the behaviour of the individual investor by noting their preferences from their utility
function
• Assume that the investor/agent is rational and makes a single decision to address investment
uncertainty for investments that future outcomes with distributions that are all explained by the first
two moments
2. Assume that a collection of agents use this method when interacting with one another
3. Examine what happens if this ‘real world’ behaves this particular way
CAPM
- The model allows investors to ‘free-ride’ on the analysis of other investors if its assumptions hold:
- Assumptions:
o All investors are price takers → not price makers; assumed to be too small to influence price
o They pick portfolios based on the standard mean-variance analysis → i.e. they behave rationally
o They have common beliefs about the statistics of returns → this needs to hold on average; some
deviations can exist
o They can borrow and lend at the risk free rate → not necessarily true; assumption can be relaxed
o There are no nontraded assets → very big assumption
o There are no taxes or transaction costs
Consequences of CAPM
- If the assumptions hold:
o Investors hold a mean-variance efficient portfolio
o They all agree on which portfolios lie on the efficient frontier
- Due to Tobin’s mutual fund theorem:
o All efficient mean-variance portfolios combine the riskless asset with a fixed portfolio on the efficiency
frontier (a.k.a. tangency portfolio) (fixed portfolio only contains risky assets)
o Thus the weights of every asset inn each investor’s risky portfolio is exactly the same as the weight
that every other investor places on the same asset
- Since in equilibrium, demand = supply:
o The portfolio weights of the tangency portfolio are those of the market portfolio
o Market portfolio is the value-weighted index that contains all risky assets in proportion to their market
value
o Thus the market portfolio is mean-variance efficient
▪ Beating the market means finding a portfolio that is more efficient than the market portfolio
→ i.e. need to find a portfolio with a better risk-return relationship → however,
efficient/market portfolio gives the minimum risk for a given return → therefore not
possible/difficult to beat the market.
o Investors can use this knowledge to determine the their optimal capital allocation line as simply the
capital market line (the one that connects the risk-free asset to the market portfolio)
