Lecture 3: Asset Pricing II (CCAPM, ICAPM, APT models)

Question 1

Consumption CAPM (CCAPM):
- ?-factor model
Asset returns ~ growth rate in aggregate ? if parameters of t' linear relationship are ?over time. 
- avoid ? critique.

Answer 1

Consumption CAPM (CCAPM):
- Single-factor model
Asset returns ~ growth rate in aggregate consumption if parameters of t' linear relationship are constant over time. 
- avoid Roll critique.

Question 2

Consumption CAPM (CCAPM):

• Amount of risk = extent to which ?? moves with consumption growth.
• The higher the ? bet. asset returns & consumption growth, t ? we perceive t’ asset.

Answer 2

Consumption CAPM (CCAPM):

• Amount of risk = extent to which risk premium moves with consumption growth.
• The higher the covariance bet. asset returns & consumption growth, t riskier we perceive t’ asset.

Question 3

CCAPM:
E(Ri) = ?*?
where
C = a consumption-tracking portfolio
Ri = return on asset i
RP_C = risk premium associate with consumption uncertainty
= RP_C = E(R_C ) = E(r_C )-rf

Answer 3

CCAPM:
E(Ri) = 𝛽_i,C * RP_C
where
C = a consumption-tracking portfolio
Ri = return on asset i
RP_C = risk premium associate with consumption uncertainty
= RP_C = E(R_C ) = E(r_C )-rf

Question 4

CCAPM:

𝛽_𝐶𝑖= ?/?

Answer 4

CCAPM:

𝛽_𝐶𝑖=(𝐶𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑅_𝑖 𝑎𝑛𝑑 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑔𝑟𝑜𝑤𝑡ℎ )/(𝐶𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑅_𝑀 𝑎𝑛𝑑 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑔𝑟𝑜𝑤𝑡ℎ)

Question 5

CCAPM:

β_M,C is not necessarily equal to ?.

Answer 5

CCAPM:

β_M,C is not necessarily equal to 1.

Question 6

CCAPM: Issues:

• ? issues
• ? empirical performance
• ? outperform CAPM.

Answer 6

CCAPM: Issues:

• Data issues
• Weak empirical performance
• Not outperform CAPM.

Question 7

Intertemporal CAPM (ICAPM)
- ?-period, ?-factor model. 
- Investors optimise ? over time when faced with uncertainty. 
=> investors will form multiple portfolios to ? against each of these risks – a ?-? CAPM.

Answer 7

Intertemporal CAPM (ICAPM)
- Multi-period, multi-factor model. 
- Investors optimise consumption over time when faced with uncertainty (e.g. prices of consumer goods, labor income, future investment opportunities).
=> investors will form multiple portfolios to hedge against each of these risks – a multi-beta CAPM

Question 8

ICAPM:
- Market portfolio is no longer t’ ? ? portfolio in t’ sense th’ it’s a single choice for investors along with combinations of ?? asset.
- In ICAPM equilibrium, investors will hold a combination of:
> ?? asset
> ? portfolio
> ? portfolios.

Answer 8

ICAPM:
- Market portfolio is no longer t’ optimal tangency portfolio in t’ sense th’ it’s a single choice for investors along with combinations of rf asset.
- In ICAPM equilibrium, investors will hold a combination of:
> risk-free asset
> market portfolio
> hedging portfolios.

Question 9

ICAPM:

“? variables”: any variables included in t’ model must have ? power as far as future asset ? are concerned.

Answer 9

ICAPM:
“State variables”: any variables included in t’ model must have predictive power as far as future asset returns are concerned.

Question 10

Arbitrage: exploitation of security mispricing => make risk-free profits.

Answer 10

Arbitrage: exploitation of security mispricing => make risk-free profits.

Question 11

Arbitrage Pricing Theory (APT) vs CAPM assumptions:
APT assumes:
1. ?? capital market
2. investors always prefer more ? to less ? with ?.
3. ? relationship bet risk & return.

APT does not assume but CAPM does:

1. a ?-? ? market portfolio
2. ?? security returns.
3. ? utility function.

Answer 11

Arbitrage Pricing Theory (APT) vs CAPM assumptions:
APT assumes:
1. perfectly competitive capital market
2. investors always prefer more wealth to less wealth with certainty.
3. linear relationship bet risk & return.

APT does not assume but CAPM does:

1. a mean-variance efficient market portfolio
2. normally distributed security returns.
3. quadratic utility function.

Question 12

APT expression can be written as a linear stochastic process generating actual returns:
Ri = ???
where:
Ri = ? return on asset i during a specified time period
E(Ri) = ? return for asset i if all the risk factors have ? changes
b_ij = reaction in asset i’s returns to ? in a common factor j
δk = a set of ?? or ? with a ? mean that influences the ? on all assets
ε_i = a unique effect on asset i’s return that, by assumption, is ?? in large portfolios and has a mean of ?
N = number of assets

Answer 12

APT expression can be written as a linear stochastic process generating actual returns:
Ri = E(Ri) + b_i1 * δi + b_i2 * δi + … + b_ik*δk + ε_i
where:
Ri = actual return on asset i during a specified time period
E(Ri) = expected return for asset i if all the risk factors have zero changes
b_ij = reaction in asset i’s returns to movements in a common factor j
δk = a set of common factors or indexes with a zero mean that influences the returns on all assets
ε_i = a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero
N = number of assets

Question 13

δ forms the essence of the APT: ? ? factors expected to have an impact on all assets:
e.g. ? , Growth in ?, Major ? upheavals, Changes in ? rates, …

This is at odds with ? as the only relevant explanatory variable in the CAPM.

Thus APT contends that there are ? factors that influence ?.
But: In application of the theory, the factors are not identified.

Answer 13

δ forms the essence of the APT: multiple macroeconomic factors expected to have an impact on all assets:
e.g. Inflation, Growth in GNP, Major political upheavals, Changes in interest rates, …

This is at odds with beta as the only relevant explanatory variable in the CAPM.

Thus APT contends that there are MANY factors that influence returns.
But: In application of the theory, the factors are not identified.

Question 14

E(Ri) = ???
where:
λo = the expected return on an asset with ? ? risk
λj = the ?? related to the common jth factor
b_ij = the pricing relationship between the ?? and asset - that is how ? asset i is to jth common factor (often referred to as ?? or ?)

Answer 14

E(Ri) = λo + λ1b_i1 + λ2 * b_i2 + … + λkb_ik
where:
λo = the expected return on an asset with zero systematic risk
λj = the risk premium related to the common jth factor
b_ij = the pricing relationship between the risk premium and asset - that is how responsive asset i is to jth common factor (often referred to as factor betas or loadings)

Question 15

APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is ? when the unique effects are ? away.

Answer 15

APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is zero when the unique effects are diversified away.

Question 16

Riskless arbitrage conditions:
1. Requires no net ? invested ?: ∑_i ?= 0

2. Will bear no ? or ? risk: ∑_i▒ ? ? = 0 (For all K factors [i.e. no systematic risk] and w is small for all I [ unsystematic risk is fully diversified])
3. Still earns a profit: ∑_i ? ? > 0

(w_i = the percentage of ? in security i)

Answer 16

Riskless arbitrage conditions:
1. Requires no net wealth invested initially: ∑_i w_i = 0

2. Will bear no systematic or unsystematic risk: ∑_i▒w_i * b_ij = 0 (For all K factors [i.e. no systematic risk] and w is small for all I [ unsystematic risk is fully diversified])
3. Still earns a profit: ∑_i w_i * Ri > 0

(w_i = the percentage of investment in security i)

Question 17

ICAPM vs APT:

1. ICAPM hold for ? assets whereas APT only makes a statement about ? pricing of ?? portfolios.
2. No special role for the ? portfolio in the APT.
3. Motivation for ? is different.

Answer 17

ICAPM vs APT:

1. ICAPM hold for all assets whereas APT only makes a statement about relative pricing of perfectly diversified portfolios.
2. No special role for the market portfolio in the APT.
3. Motivation for factors is different.