Week 7- Household Finances

Question 1

Give 5 reasons why household finances are important?

Answer 1

• 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

Question 2

What do we mean by uncertainty and risk?

Answer 2

We can attach an expectation to it, however there is a distribution around that which capture our risk.

Question 3

What is assumption we make about the assets?

Answer 3

We have 1 safe asset vs 1 risky asset

Question 4

How do we compare the risks and returns of assets?

Answer 4

Through 4 “state of the world” models, which all occur with equal probability.

Question 5

How would you work out the probability of an asset (eg asset 2) with 4 states of world?

Answer 5

E(a2) = 0.25(return 1) + 0.25(return2) + 0.25(return 3) + 0.25(return 4)

Question 6

How do you work out the standard deviation of an assets return?

Answer 6

σ(X) = √(π1 (X1 − E(X))²( + … + π𝑛 (Xn − E(X))²)

Question 7

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.

Answer 7

σ(R2) = √(0.25 (2 − 5)² + 0.25(4 − 5)² + 0.25(6 − 5)² + 0.25(8 − 5)²)

Question 8

How do we decide which asset is preferred when we take each asset’s risk and returns into account?

Answer 8

We use the Sharpe Ratio.

Question 9

How do we calculate the Sharpe Ratio?

Answer 9

(Expected Returns-Risk Free Rate)/Standard Deviation

Question 10

How can you use the Sharpe Ratio to decide which asset is preferred?

Answer 10

The asset with the higher Sharpe Ratio is preferred as there is a greater return for a given amount of risk.

Question 11

What would risk averse people do when presented with a fair bet?

Answer 11

A risk averse person would decline a fair bet or would be required to be paid to take it

Question 12

Which utility function will a risk loving person have?

Answer 12

Convex

Question 13

Can we just use the second derivative of a utility function to find out how risk averse someone is?
Why?

Answer 13

No as an affine transformation of the utility function should represent the same
preferences as the original function, however the second derivative does not

Question 14

How do we measure how risk averse someone is?

Answer 14

The measure of Absolute Risk Aversion

Question 15

How do we denote the measure of Absolute Risk Aversion?

Answer 15

𝐴(𝑊) = −𝑈′′(𝑊)/𝑈′(W)

Question 16

How can you use the measure of Absolute Risk Aversion to decide which asset is preferred?

Answer 16

A more positive value means a person is more risk averse.

Question 17

So given a utility function: u(w)= aV(w)+b, what would the measure of Absolute Risk Aversion be?

Answer 17

-av’‘(w)/av’(w) = -v’‘(w)/v’(w)

Question 18

What is an affine transformation?

Answer 18

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.

Question 19

How do we work out how individual respond to a percentage change in wealth and what is this called?

Answer 19

R(𝑊) = −W𝑈′′(𝑊)/𝑈′(W) = W*A(W)

Relative Risk Aversion

Question 20

What’s the difference between absolute and relative risk aversion?

Answer 20

Absolute risk aversion is absolute amounts, eg winning or losing £10, whereas relative risk aversion is about losing say 10% of your wealth.

Question 21

What happens to your utility when you gain a pound?

Answer 21

There is always a positive effect.

Question 22

So how can we work out how an individuals risk aversion changes with wealth?

Answer 22

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.

Question 23

What does decreasing absolute risk aversion mean?

Answer 23

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

Question 24

How do we work out our constant relative risk aversion?

Answer 24

R(W) = wA(W)

Then find the first derivative

Question 25

What does constant relative risk aversion mean?

Answer 25

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%.

Question 26

What happens to a risk-averse person’s indifference curve?

Answer 26

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.

Question 27

What does the budget line give?

Answer 27

The budget line gives the “Price” of risk expressed in terms of additional expected returns.

Question 28

What does a steeper budget line indicate?

Answer 28

A steeper slope (B2) indicates a greater additional expected return for a given increase in risk.

Question 29

Which ratio is the budget line effectively like?

Answer 29

The Sharpe Ratio

Question 30

Where is the equilibrium outcome?

Answer 30

The equilibrium outcome is the tangency point between the budget line and the Indifference Curve.

Question 31

What is significant about the marginal rate of substitution at equilibrium?

Answer 31

The marginal rate of substitution between risk and return is equal to the market price of risk.

Question 32

What do we assume when working out equilibrium?

Answer 32

No borrowing or lending from an individual.

Question 33

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?

Answer 33

E(R)= kE(Rf)+(1-k)E(Ra)

Question 34

What does k represent?

Answer 34

Where k is the percentage of the portfolio in the risk free asset and 1-k is the proportion invested in the risky asset.

Question 35

Should risk averse people hold risky assets?

Answer 35

Yes

Question 36

What is the variance of a portfolio?

Answer 36

The variance of a portfolio is a function of the variance of the each individual asset plus the covariance between them.

Question 37

How is the variance of a portfolio calculated?

Answer 37

Portfolio Variance = k²σ²a+(1-k)²σ²b+2k(1-k)cov(A,B)

Question 38

In the variance of a portfolio calculation, what do, k, σ²a and cov(A,B) represent?

Answer 38

• 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.

Question 39

Is σ²a squared standard deviation of asset A?

Answer 39

No, σ²a is the variance associated with asset A and isn’t squared!!!!!!!!!!!!!

Question 40

What is another term for diversifiable risk, describe and give examples of this.

Answer 40

• Non systematic risk
• Only affect a limited number of assets.
• Parts shortages, Union action

Question 41

What is another term for non-diversifiable risk, describe and give examples of this.

Answer 41

• Systematic risk
• Cause mass macro-economic changes
• Changes in GDP, Brexit Uncertainty, Inflation, interest rates etc

Question 42

Why is there always risk with holding a riskt asset?

Answer 42

As we cannot eliminate systematic risk with a broad portfolio.