Equity Valuation & Asset Allocation

Question 1

Cobb-Douglas production function (neoclassical model)

Answer 1

• Y is the total real economic output
• A is the total factor productivity
• K is the capital stock
• α is the output elasticity of K
• L is the labor input
• β is the output elasticity of L

Question 2

Constant return to scale

Answer 2

A given percentage increase in capital stock and labor input results in an equal percentage increase in output

Question 3

The percentage growth in real output

Answer 3

Question 4

Solow residual

Answer 4

Synonym for total factor productivity

Question 5

H-model

Answer 5

Question 6

The Fed model

Answer 6

• US stocks are undervalued if the forward earnings yield on the S&P 500 is greater than the yield on US Treasury bonds
• US stocks are overvalued if the forward earnings yield on the S&P 500 is less than the yield on US Treasury bonds

Question 7

Gordon growth model

Answer 7

Question 8

Gordon growth model for the forward earning yield

Answer 8

• p is the earnings payout ratio
• (1 - p) is the earnings retention rate

Question 9

Yardeni model (based on the growth rate) - forward earnings yield

Answer 9

Question 10

Yardeni model (based on bond yields) - justified (forward) earnings yield

Answer 10

• y_B = corporate bond yield
• LTEG = long-term earnings growth
• d = a weighting factor measuring the importance the market assigns to the earnings projections

Question 11

Cyclically Adjusted P/E Ratio (CAPE)

Answer 11

Real S&P 500 price / MA₁₀ of the real reported earning

Question 12

• Real stock price index_t
• Real earnings_t

Answer 12

• = Nominal stock price index_t * CPI_{reference year} / CPI_t
• = Nominal earnings_t * CPI_{reference year} / CPI_t+1

Question 13

Tobin’s q

Answer 13

= market value of debt and equity / replacement cost of assets

Question 14

Equity q

Answer 14

= equity market cap / (replacement cost of assets - liabilities)

Question 15

Forward (justified) P/E

Answer 15

Question 16

Horse race system

Answer 16

Funds spread among a group of managers whose performance is going to be measured against each other

Question 17

ALM approaches

Answer 17

• Cash flow matching (exact matching)
• Immunization (duration matching)
• Dynamic
• Static

Question 18

Expected utility formula

Answer 18

Question 19

Roy’s safety first ratio

Answer 19

• Is the probability of exceeding a minimum return given a normal distribution of returns in a safety-first approach

Question 20

Bonds protection against inflation and deflation

Answer 20

Question 21

Corner portfolios efficient mix

Answer 21

• The efficient mixes between two adjacent corner portfolios are simply linear combinations of those portfolios
• Expected return = w * E_Pa + (1 - w) * E_Pb

Question 22

The three broad approaches to asset allocation

Answer 22

• Asset-only
• Liability-relative
• Goals-based

Question 23

The five criteria for effectively specifying asset classes

Answer 23

• Assets within an asset class should be relatively homogeneous
• Asset classes should be mutually exclusive
• Asset classes should be diversifying
• The asset classes as a group should make up a preponderance of world investable wealth
• Asset classes selected for investment should have the capacity to absorb a meaningful proportion of an investor’s portfolio

Question 24

Bottom-up vs Top-down forecast contrast

Answer 24

• Bottom-up forecasts tend to be more optimistic than top-down forecasts
• Top-down models can be slow in detecting cyclical turns if the current statistical relationships between economic variables deviate significantly from their historic norms

Question 25

* Risk budgeting * Active risk budgeting

Answer 25

* Addresses the questions of which types of risks to take and how much of each to take * Addresses the question of how much benchmark-relative risk an investor is willing to take in seeking to outperform a benchmark

Question 26

* Strategic asset allocation * Tactical asset allocation * Dynamic asset allocation

Answer 26

* Incorporates an investor’s long-term, equilibrium market expectations * Involves short-term tilts away from the strategic asset mix in order to exploit perceived deviations from equilibrium * Incorporates deviations from the strategic asset allocation that are motivated by longer-term valuation signals or economic views

Question 27

The three "super classes” of assets

Answer 27

* Capital assets * Consumable/transformable assets * Store of value assets

Question 28

Capital allocation line

Answer 28

* The combinations of expected return and standard deviation of return available to an investor from combining the optimal portfolio (with the highest Sharpe ratio) of risky assets with the risk-free asset * Expected return = w \* E(R_{optimal portfolio}) + (1 - w) \* R_{risk-free asset} * Standard deviation = w \* σ_{optimal portfolio std}

Question 29

Factors Related to Optimal Corridor Width

Answer 29

* Factors Positively Related to Optimal Corridor Width * Transaction costs * Risk tolerance * Correlation with the rest of the portfolio * Factors Inversely Related to Optimal Corridor Width * Volatility of the rest of the portfolio

Question 30

Single vs multi period asset allocation method

Answer 30

Resampled efficient frontier and Black-Litterman are **single period** approaches to optimization that do not consider uncertainty in cash flows into or out of the portfolio over time. Monte Carlo simulation can be used to consider this sort of cash flow uncertainty

Question 31

Resampled efficient portfolio

Answer 31

The portfolio defined by the average weights on each asset class for simulated efficient portfolios

Question 32

Alternatives to MVO

Answer 32

* Reverse optimization * Black-Litterman model * Constrained asset class weights

Question 33

Criticisms of MVO

Answer 33

* The outputs (asset allocations) are highly sensitive to small changes in the inputs * The asset allocations are highly concentrated in a subset of the available asset classes * Doesn't consider skewness and kurtosis * The sources of risk may not be diversified * May have no direct connection to the factors affecting any liability or consumption streams * Is a single-period framework that tends to ignore trading/rebalancing costs and taxes

Question 34

MVO sensibility to inputs

Answer 34

MVO portfolios are more sensitive to measurement errors in the expected return than to measurement errors in correlation and risk

Question 35

Minimum surplus variance (MSV) portfolio

Answer 35

The efficient portfolio with the least risk from an ALM perspective

Question 36

Reverse optimization

Answer 36

Uses inputs for risk and correlation (or covariance) to solve for expected return

Question 37

Approaches to liability-relative asset allocation

Answer 37

* Surplus optimization * Hedging/return-seeking portfolios approach * Integrated asset–liability approach

Question 38

Surplus optimization expected utility

Answer 38

* U_m^LR = the surplus objective function’s expected value for a particular asset mix m * E(R_{s, m}) = expected surplus return for asset mix m, with surplus return defined as (change in asset value – change in liability value) / (initial asset value) * σ²(R_{s, m}) = variance of the surplus return for the asset mix * λ = the investor’s risk aversion

Question 39

When is an asset allocation optimal from a risk-budgeting perspective?

Answer 39

When the ratio of excess return to MCTR is the same for all assets

Question 40

* Marginal contribution to total risk (MCTR) * Absolute contribution to total risk (ACTR) * Ratio of excess return to MCTR

Answer 40

* MCTR_i = (Beta of asset class *i* with respect to portfolio) \* (Portfolio return volatility) * ACTR_i = (Weight_i) \* (MCTR_i) * (Expected return - Risk-free rate) / MCTR

Question 41

Risk parity asset allocation

Answer 41

* The notion that each asset (asset class or risk factor) should contribute equally to the total risk of the portfolio * w_i = the weight of asset i * Cov(r_i,r_P) = the covariance of asset i with the portfolio * n = the number of assets * σ²_P = the variance of the portfolio

Question 42

Heuristic approaches to asset allocation

Answer 42

* 120 minus your age * 60/40 stocks/bonds * The endowment model * Risk parity * 1/N rule

Question 43

Endowment model (also know as the Yale model)

Answer 43

An approach to asset allocation that emphasizes large allocations to non-traditional investments, including equity-oriented investments driven by investment manager skill

Question 44

Norway model

Answer 44

An approach to asset allocation is highly committed to passive investment in publicly traded securities (subject to environmental, social, and governance [ESG] concerns), reflecting a belief in the market’s informational efficiency

Question 45

The expected after-tax standard deviation

Answer 45

* σ_at = (1 - t) \* σ_pt * σ_at = the expected after-tax standard deviation * σ_pt = the expected pre-tax standard deviation

Question 46

The equivalent rebalancing range for the taxable investor

Answer 46

* R_at = the after-tax rebalancing range * R_pt = the pre-tax rebalancing range

Question 47

Factor-model-based benchmark

Answer 47

Question 48

Return-based benchmark

Answer 48

(Example) 40% small-cap growth + 60% small-cap value

Question 49

Custom security-based benchmark (also called strategy benchmark)

Answer 49

Reflects the investment discipline of a particular investment manager

Question 50

Present value of a growing annuity

Answer 50

* g can also be the inflation rate

Question 51

Modeling with a private equity index

Answer 51

Captures neither the risk nor the return attributes of private equity accurately

Question 52

Ex post risk being a biased measure of ex ante risk

Answer 52

* In interpreting historical prices and returns, we need to evaluate whether asset prices reflected the possibility of a very negative event that did not materialize during the period * Looking backward, we are likely to underestimate ex ante risk and overestimate ex ante anticipated returns