Week 2 - Portfolio Theory and Asset Pricing

Question 1

What is alpha?

Answer 1

Excess return an investment produces compared to a benchmark. We do not want a negative alpha.

Question 2

What is beta?

Answer 2

Correlation with market risk, measure sensitivity to market return/impact of systematic risk on stock return. Typically it is best for beta to be around 1.

Question 3

What is the difference between R and r?

Answer 3

R is the excess over risk free rate while r is the complete return

Question 4

What is missing from the utility functions?

Answer 4

1) Higher moments of return distributions are not accounted for (not always significant)
2) Liquidity is not accounted for - can assets be sold quickly
3) Income preference vs capital appreciation
4) Inflation hedging characteristics (current environment vs. 20-years ago)

Question 5

What is the relationship between risk appetite and wealth/age?

Answer 5

Risk appetite declines with wealth and as age goes on, risk appetite also decreases with age (and during retirement there is a greater focus on income preference)

Question 6

What is important to consider when considering overall risk?

Answer 6

Risk is not solely about assets, depends on liability profiles, probability of loss relative to liabilities. Risk is not the same as volatility

Question 7

What is the Capital Allocation Line (CAL)? What happens if there is a different rate of borrowing/lending?

Answer 7

Represents all the possibilities of combining a single risky asset P and a risk free asset F. To go beyond a certain level, borrowing is required. If the borrowing rate is higher than the lending rate then the slope is shallower

Question 8

What is the issue with superannuation and the CAPM model?

Answer 8

Superannuation funds cannot borrow, which is something that the is assumed in the CAPM

Question 9

What is the utility formula?

Answer 9

U = E(r)-(A*sigma^2)/2

Question 10

What is Markowitz Portfolio Optimisation?

Answer 10

Search for the CAL with highest reward-variability ratio (steepest CAL) or the highest Sharpe ratio

Question 11

What is the Sharpe ratio?

Answer 11

Excess return on portfolio divided by standard deviation of excess portfolio return

Question 12

What is the separation property?

Answer 12

The separation property states that portfolio choice can be separated into two independent tasks:

1) Determination of the optimal risky portfolio (same for everyone)
2) Allocation of the complete portfolio to risk-free vs. risky portfolio (depends on risk appetite)

Question 13

Describe some of the changes in risk portfolio optimisation across different risk levels. (Stable - Conservatively Balanced - Balanced - High Growth)

Answer 13

Infrastructure/Property remain constant
Cash and fixed interest decrease as risk appetite increases
Private equity and domestic/international shares increases as risk appetite increases

Question 14

Define the single factor and single index models. Why are they used?

Answer 14

Single factor:
r = E(r) + Bm +e (m=macroeconomic factor, e = firm specific surprises)
Single index:
R(p) = a(i) + BR(m) + e (R(m) = excess return on market and a(i) is the effect of the active manager)

Question 15

Describe the security characteristic line

Answer 15

The security characteristic line details a relationship between the excess return on a portfolio and the excess return on the market index. The intercept is alpha, gradient is beta and any variance from the line is explained by the error term for a particular time

Question 16

Explain the relationship between volatility and diversification

Answer 16

As the number of stocks increases (from a broad base), overall volatility decreases as idiosyncratic risk is eliminated and all that is left is systematic risk (captured by beta)

Question 17

What are active weights/positions?

Answer 17

Active weights are the difference in weights on stocks in the portfolio and the index, i.e. w(a) = w(p) - w(i)

Question 18

What is the implied proportionality formula for weighted positions?

Answer 18

w(i) = alpha/sd[e(i)]

To answer a question on this, find the respective value for each weight, find the ratio and then work out the position to invest

Question 19

Why is e[R(M)] > 0 but alpha is not?

Answer 19

Because we assume that return on the market is above the risk free rate - there is strong evidence to suggest this and it makes intuitive sense (if not, why would anyone bother with the market as a whole at all?).
However, portfolio management may not add value, either poor investors or fees may take away potential profits above the market

Question 20

What is tracking error?

Answer 20

Tracking error is the volatility of active return:

(T.E.)^2=(beta-1)^2[s.d.(M)]^2+ s.d.(alpha)^2. Typically it is greater than residual risk as beta deviates from 1.

Question 21

What are the CAPM assumptions about individual behaviour?

Answer 21

1) Investors are rational, mean-variance optimisers
2) Planning horizon is a single period
3) Investors have homogeneous expectations (same as each other)

Question 22

What are the CAPM assumptions about market structure?

Answer 22

1) All assets are publicly held and trade on public exchanges
2) All information is publicly available
3) No taxes
4) No transaction costs
Last two already do not hold in reality

Question 23

Name two large features of the CAPM model.

Answer 23

1) It relies heavily on market efficiency to reach the optimal outcome
2) It is a theory about non-observable expectations (and therefore cannot be verified by historical data)

Question 24

Name some model extensions to the CAPM model.

Answer 24

Borrowing constrained, taxes included, franking credits included, higher moments included (extramarket risk), intertemporal model (planning horizon is larger than one period)

Question 25

Should a reward be expected for individual securities?

Answer 25

No. Should not expect a stock specific reward for non-beta risk (as it can be diversified away)

Question 26

What are some of the advantages of the CAPM model?

Answer 26

1) Generally robust even with relaxed assumptions
2) Useful in capital budgeting decisions as the basis for required rate of return
3) Utility regulation (very large)
4) As a measure of risk - allowed to classify high beta as a bad thing

Question 27

Describe the security market line.

Answer 27

The security market line details an expected return-beta relationship. We have the formula:
E[r(i)] = r(f) + beta*[r(m) - r(f)]
Intercept is risk-free rate, gradient is the beta of the stock.

Question 28

What is the formula for beta?

Answer 28

Covariance[r(i), r(m)] / Variance[r(m)]

Question 29

What is a disequilibrium example with regards to the SML?

Answer 29

Expected alpha is the difference between expected return and SML return - if there is a disequilibrium then this will be a non-zero

Question 30

What is the main problem with CAPM testing?

Answer 30

1) Roll’s critique - test results are related to market definitions, as such testing CAPM is testing the efficiency of the market.
2) Typically H0: no relationship between beta and return and the test has weak statistical power to disprove it
3) CAPM does not assume stationary risk but tests do - CAPM based on expectations not empirical data

Question 31

What is the relationship between the following variables and beta. An increase in ______ will lead to what result for beta?

1) Variance of earnings
2) Variance of cash flow
3) Growth in EPS
4) Market capitalisation
5) Dividend yield
6) Debt-to-Equity ratio

Answer 31

1) Increase
2) Increase
3) Increase
4) Decrease
5) Decrease
6) Increase

Question 32

What are the 3 key assumptions of APT?

Answer 32

1) Security returns can be described by a factor model
2) Well-functioning security models do not allow for persistence of arbitrage opportunities
3) There are sufficient securities to diversify away idiosyncratic risk

Question 33

Explain what can be done in a scenario of disequilibrium for portfolios under APT assumptions.

Answer 33

If we have risky portfolio A spliced with cash to give us portfolio D but we have the same beta and portfolio at stock C but a lower expected return, we can long D and short C, giving us a net 0 exposure and a positive return at no risk!

Question 34

What is the difference between a single factor/index model and a multi-factor model? What factors can be used in a multi-factor model?

Answer 34

Simply put, a multi-factor model is reliant on more than one factor. They can be either:

1) Macroeconomic factors, e.g. interest rates, where factor returns are observable but factor exposures must be estimated
2) Micro or corporate factors, e.g. Price-to-book ratio, where factor exposures are observable but factor returns must be estimated

Question 35

What is the underlying assumption which makes a single factor model less viable?

Answer 35

A single factor model assumes each stock has the same relative sensitivity to underlying subfactors

Question 36

What is the Fama-French model?

Answer 36

R(i) = alpha(i) + beta(iM)R(M) + beta(iSMB)R(SMB) + beta(iHML)*HML + e(i)
Where SMB is the differential return balance between small and large stocks, HML is the differential return balance on firms with high book-to-market value and low book-to-market value (high B/M means likely to be in financial distress.
Also added momentum in 1997

Question 37

Compare the APT and CAPM

Answer 37

1) APT is not good at an individual stock level but performs well at an aggregated level
2) APT allows for stock mis-pricing
3) APT achieves the same result with fewer assumptions and can be extended to a multifactor universe
4) CAPM provides a unambiguous relationship between expected return and beta (in APT holds for most not all)

Question 38

What is the aim of active management?

Answer 38

The goal of active management is to identify factors with a significant positive expectation relative to their volatility and take greater exposure to them than the benchmark (e.g. value, momentum etc.)

Question 39

What is the covariance matrix of stock returns? What is the portfolio variance?

Answer 39

Matrix = stock factor exposures (n x f) * factor returns (f x f) * transpose stock factor exposures (f x n) + diagonal matrix of stock idiosyncratic variances

Portfolio variance = transpose portfolio weightings (1 x n) * Covariance matrix (n x n) * portfolio weightings (n x 1)

Question 40

What measures can be used to measure market risk premium?

Answer 40

1) ER - BY (Bond yield)
2) ER - BR (Bond return)
3) Geometric difference - (1+ER)/(1+BR)-1
4) ER - Inf (inflation)

Note: need to use LT bond yields, NOT short term. Better to use return than yield, and geometric difference is easier to work with

Question 41

What can be said about historic estimates of equity risk premium?

Answer 41

Compared to the rest of the world, Australian performance sits around average. Across 1959-1988, return is much higher, but the standard error is much higher when compared to 1989-2018. Suggests that decrease in volatility causes a decrease in risk premium and lower rate of return

Question 42

Explain the relationship between bond yield and bond return.

Answer 42

If bond yield is stationary, bond return is stationary. If bond yield increases/decreases from one period to the next, then all future cash flows will be discounted at a higher/lower rate and return is diminished/increased

Question 43

When should you use an arithmetic vs. geometric average? What is the relationship between the two?

Answer 43

E(geometric average) = E(arithmetic average) - [(sigma)^2]/2

ST - Arithmetic, LT - Geometric (over the long term, arithmetic leads to an upward projection of return)

Unbiased estimator for projection of H years based on T years of data is: (H/T)Geometric + (1-H/T)Arithmetic

Question 44

For Australian data, what are reasonable estimates of:

1) Geometric average equity premiums over bond returns
2) Equity volatility relative to bonds
3) ER-BR and standard error

Answer 44

1) Around a 3% geometric average of equity premiums over bond returns
2) Equity volatility relative to bonds is about 20% (yearly) over the last 50 years, but 15-20% in the last 30
3) ER-BR is roughly 4.5%-5% with a standard error of roughly 2%

Question 45

Are returns normally distributed? Does this change depending on frequency of data?

Answer 45

No. Particularly the case for more frequent data. At an annual level, non-normality distinctly improves (consistent with CLT) though it is clear there is some evidence of serial correlation. More reliable to estimate annual volatility than a higher frequency (not much use estimating anything with a lower frequency)

Question 46

What is the efficient frontier?

Answer 46

The efficient frontier is the set of optimal portfolios, offering the highest return on a defined level of risk (y-axis is rate of return and x-axis is volatility). A portfolio underneath the frontier is sub-optimal, while anything above the frontier is impossible