Week 7- Household Finances Flashcards
Give 5 reasons why household finances are important?
- Household finance has received a significant increase in interest from both policy makers and researchers
- Increased emphasis on households to support themselves into retirement
- Households’ financial vulnerability has been highlighted by economic crisis
- Increase in financial products available to households
- Common consensus that many household do not save enough
What do we mean by uncertainty and risk?
We can attach an expectation to it, however there is a distribution around that which capture our risk.
What is assumption we make about the assets?
We have 1 safe asset vs 1 risky asset
How do we compare the risks and returns of assets?
Through 4 “state of the world” models, which all occur with equal probability.
How would you work out the probability of an asset (eg asset 2) with 4 states of world?
E(a2) = 0.25(return 1) + 0.25(return2) + 0.25(return 3) + 0.25(return 4)
How do you work out the standard deviation of an assets return?
σ(X) = √(π1 (X1 − E(X))²( + … + π𝑛 (Xn − E(X))²)
How would you work out the standard deviation of an asset (eg asset 2) with 4 states of world? Assume the probabilities are 2,4,6 and 8 with an estimated rate of return of 5.
σ(R2) = √(0.25 (2 − 5)² + 0.25(4 − 5)² + 0.25(6 − 5)² + 0.25(8 − 5)²)
How do we decide which asset is preferred when we take each asset’s risk and returns into account?
We use the Sharpe Ratio.
How do we calculate the Sharpe Ratio?
(Expected Returns-Risk Free Rate)/Standard Deviation
How can you use the Sharpe Ratio to decide which asset is preferred?
The asset with the higher Sharpe Ratio is preferred as there is a greater return for a given amount of risk.
What would risk averse people do when presented with a fair bet?
A risk averse person would decline a fair bet or would be required to be paid to take it
Which utility function will a risk loving person have?
Convex
Can we just use the second derivative of a utility function to find out how risk averse someone is?
Why?
No as an affine transformation of the utility function should represent the same
preferences as the original function, however the second derivative does not
How do we measure how risk averse someone is?
The measure of Absolute Risk Aversion
How do we denote the measure of Absolute Risk Aversion?
𝐴(𝑊) = −𝑈′′(𝑊)/𝑈′(W)
How can you use the measure of Absolute Risk Aversion to decide which asset is preferred?
A more positive value means a person is more risk averse.
So given a utility function: u(w)= aV(w)+b, what would the measure of Absolute Risk Aversion be?
-av’‘(w)/av’(w) = -v’‘(w)/v’(w)
What is an affine transformation?
A linear transformation so if we add a constant or multiply the utility function by a constant, the underlying preferences of that utility function should remain the same.
How do we work out how individual respond to a percentage change in wealth and what is this called?
R(𝑊) = −W𝑈′′(𝑊)/𝑈′(W) = W*A(W)
Relative Risk Aversion
What’s the difference between absolute and relative risk aversion?
Absolute risk aversion is absolute amounts, eg winning or losing £10, whereas relative risk aversion is about losing say 10% of your wealth.
What happens to your utility when you gain a pound?
There is always a positive effect.
So how can we work out how an individuals risk aversion changes with wealth?
1) Take the log utility function eg U(W) → ln(W) (W>1)
2) Find the absolute risk aversion of the log:
eg ln(W)→ A(W)= -(-1/W²/1/W) = 1/W
3) Take the derivative of the absolute risk aversion:
eg A(W)= 1/W → A’(W) = -1/W² <0
4) See if its more or less than 0, above for exmaple is decreasing absolute risk aversion.
What does decreasing absolute risk aversion mean?
As wealth increases, an individual becomes
less risk averse. This suggests that if wealth increases, an individual will increase (in absolute terms) the amount they invest in a risky asset
How do we work out our constant relative risk aversion?
R(W) = wA(W)
Then find the first derivative
What does constant relative risk aversion mean?
As wealth increases, an individual will maintain
their level of risk aversion. This suggests that as wealth increase they will invest the same % of their wealth
to the risky asset. Eg if I had £100 and invested 10%, if I had £200 I would still invest 10%.
What happens to a risk-averse person’s indifference curve?
It increases in slope as for a risk averse individual the greater the level of risk requires a greater additional level of expected return in order to maintain a
constant level of utility.
What does the budget line give?
The budget line gives the “Price” of risk expressed in terms of additional expected returns.
What does a steeper budget line indicate?
A steeper slope (B2) indicates a greater additional expected return for a given increase in risk.
Which ratio is the budget line effectively like?
The Sharpe Ratio
Where is the equilibrium outcome?
The equilibrium outcome is the tangency point between the budget line and the Indifference Curve.
What is significant about the marginal rate of substitution at equilibrium?
The marginal rate of substitution between risk and return is equal to the market price of risk.
What do we assume when working out equilibrium?
No borrowing or lending from an individual.
Consider the two asset F and A which are risk-free and risky, respectively. What is the expected return of a combination of asset holding, or the portfolio, given
as?
E(R)= kE(Rf)+(1-k)E(Ra)
What does k represent?
Where k is the percentage of the portfolio in the risk free asset and 1-k is the proportion invested in the risky asset.
Should risk averse people hold risky assets?
Yes
What is the variance of a portfolio?
The variance of a portfolio is a function of the variance of the each individual asset plus the covariance between them.
How is the variance of a portfolio calculated?
Portfolio Variance = k²σ²a+(1-k)²σ²b+2k(1-k)cov(A,B)
In the variance of a portfolio calculation, what do, k, σ²a and cov(A,B) represent?
- k is proportion invested in A
- σ²a is the variance associated with asset A
- cov(A, B) is the covariance between assets A and B.
Is σ²a squared standard deviation of asset A?
No, σ²a is the variance associated with asset A and isn’t squared!!!!!!!!!!!!!
What is another term for diversifiable risk, describe and give examples of this.
- Non systematic risk
- Only affect a limited number of assets.
- Parts shortages, Union action
What is another term for non-diversifiable risk, describe and give examples of this.
- Systematic risk
- Cause mass macro-economic changes
- Changes in GDP, Brexit Uncertainty, Inflation, interest rates etc
Why is there always risk with holding a riskt asset?
As we cannot eliminate systematic risk with a broad portfolio.
