Week 8 Flashcards
How do we work out the expected return on an asset, with multiple potential states of the world?
We multiply the probability of the state of the world by the potential return on the asset. We do this for every potential state of the world and add them up.
How do we work out the standard deviation of the expected return for an asset?
-Let p=probality of the state of the world.
-Let X1 be the expected return on an asset in that state of the world.
-Let E(X) be the expected overall return of the asset.
-We square root p(X1-E(X))^2 + the same for all the other states of the world, with E(X) remaining constant.
What is the Sharpe ratio?
(Expected return - risk free rate) / standard deviation. The higher the ratio, the more preferred the asset is as it has a greater return for a given amount of risk.
How do we measure absolute risk aversion (ARA)?
A(W) = -(U’‘(W) / U’(W)). As this increases, the level of risk aversion increases.
How do we measure relative risk aversion (RRA)?
R(W) = A(W) * W, where W is wealth.
What do A’(W) and R’(W) tell us about how an individual holds risky assets?
-If A’(W)/R’(W) > 0, an individual holds less/smaller % of wealth in risky assets, opposite when < 0. If = 0, then an individual holds the same/same % in risky assets.
Explain the indifference curve and budget line for a risk-averse individual.
The IC is upward-sloping and gives us the combination of the risk and expected returns which gives us the same level of utility. The greater the level of risk, the greater the level of additional expected returns a risk-averse individual will require, in order to maintain constant utility. The budget line gives us the ‘price’ of risk in terms of additional expected returns. The tangency between these two points is the equilibrium, where the MRS between risk and return is equal to the market price of risk.
What is the expected return of a portfolio with a risk-free and risky asset?
E(R) = kE(Rf) + (1-k)E(Ra), where k = fraction of portfolio in the risk-free asset.
What are the 3 puzzles of household finance (Campbell, 2006)?
-Failure to participate.
-Failure to diversify.
-Failure to re-mortgage.
What is the stockholding puzzle?
The majority of households hold no stocks despite the historically high expected-return premium on equity, in comparison to riskless assets. However, risk-averse households dislike riskiness in their consumption stream.
What is the equity risk premium (ERP) equation?
ERP = stock market return - risk-free return. Historically, there has been a positive risk premium, demonstrating that we should invest in risky assets.
What are the 4 potential explanations for an individual not investing in risky assets when they should?
-Fixed costs: There are both monetary and non-monetary costs involved with investing. Although fixed costs have decreased over time (due to digitisation, financial deregulation, etc), there are still many individuals who are discouraged from investing in risky assets due to fixed costs (administrative charges, cost of time, processing information, etc). Individuals who are more educated or have larger financial resources are more likely to overcome these costs.
-Financial literacy: This decreases with education, household wealth, income and gender (women invest less).
-Background risks: These can include health risks, future tax liabilities, labour market income, etc and all reduce the likelihood of someone investing in a risky asset.
-Behavioural reasons: If an individual is loss-averse they strongly prefer avoiding losses to acquiring gains. This pairs with myopic loss-aversion, in which short-run problems (e.g: financial crash) may overshadow the fact that in the long run, stocks normally outperform safer assets.
