Equity Valuation & Asset Allocation Flashcards
Cobb-Douglas production function (neoclassical model)
- 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
Constant return to scale
A given percentage increase in capital stock and labor input results in an equal percentage increase in output
The percentage growth in real output
Solow residual
Synonym for total factor productivity
H-model
The Fed model
- 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
Gordon growth model
Gordon growth model for the forward earning yield
- p is the earnings payout ratio
- (1 - p) is the earnings retention rate
Yardeni model (based on the growth rate) - forward earnings yield
Yardeni model (based on bond yields) - justified (forward) earnings yield
- yB = corporate bond yield
- LTEG = long-term earnings growth
- d = a weighting factor measuring the importance the market assigns to the earnings projections
Cyclically Adjusted P/E Ratio (CAPE)
Real S&P 500 price / MA10 of the real reported earning
- Real stock price indext
- Real earningst
- = Nominal stock price indext * CPIreference year / CPIt
- = Nominal earningst * CPIreference year / CPIt+1
Tobin’s q
= market value of debt and equity / replacement cost of assets
Equity q
= equity market cap / (replacement cost of assets - liabilities)
Forward (justified) P/E
Horse race system
Funds spread among a group of managers whose performance is going to be measured against each other
ALM approaches
- Cash flow matching (exact matching)
- Immunization (duration matching)
- Dynamic
- Static
Expected utility formula
Roy’s safety first ratio
- Is the probability of exceeding a minimum return given a normal distribution of returns in a safety-first approach
Bonds protection against inflation and deflation
Corner portfolios efficient mix
- The efficient mixes between two adjacent corner portfolios are simply linear combinations of those portfolios
- Expected return = w * EPa + (1 - w) * EPb
The three broad approaches to asset allocation
- Asset-only
- Liability-relative
- Goals-based
The five criteria for effectively specifying asset classes
- 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
Bottom-up vs Top-down forecast contrast
- 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
- Risk budgeting
- Active risk budgeting
- 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
- Strategic asset allocation
- Tactical asset allocation
- Dynamic asset allocation
- 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
The three “super classes” of assets
- Capital assets
- Consumable/transformable assets
- Store of value assets
Capital allocation line
- 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(Roptimal portfolio) + (1 - w) * Rrisk-free asset
- Standard deviation = w * σoptimal portfolio std
Factors Related to Optimal Corridor Width
- 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
Single vs multi period asset allocation method
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
Resampled efficient portfolio
The portfolio defined by the average weights on each asset class for simulated efficient portfolios
Alternatives to MVO
- Reverse optimization
- Black-Litterman model
- Constrained asset class weights
Criticisms of MVO
- 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
MVO sensibility to inputs
MVO portfolios are more sensitive to measurement errors in the expected return than to measurement errors in correlation and risk
Minimum surplus variance (MSV) portfolio
The efficient portfolio with the least risk from an ALM perspective
Reverse optimization
Uses inputs for risk and correlation (or covariance) to solve for expected return
Approaches to liability-relative asset allocation
- Surplus optimization
- Hedging/return-seeking portfolios approach
- Integrated asset–liability approach
Surplus optimization expected utility
- UmLR = the surplus objective function’s expected value for a particular asset mix m
- E(Rs, 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(Rs, m) = variance of the surplus return for the asset mix
- λ = the investor’s risk aversion
When is an asset allocation optimal from a risk-budgeting perspective?
When the ratio of excess return to MCTR is the same for all assets
- Marginal contribution to total risk (MCTR)
- Absolute contribution to total risk (ACTR)
- Ratio of excess return to MCTR
- MCTRi = (Beta of asset class i with respect to portfolio) * (Portfolio return volatility)
- ACTRi = (Weighti) * (MCTRi)
- (Expected return - Risk-free rate) / MCTR
Risk parity asset allocation
- The notion that each asset (asset class or risk factor) should contribute equally to the total risk of the portfolio
- wi = the weight of asset i
- Cov(ri,rP) = the covariance of asset i with the portfolio
- n = the number of assets
- σ2P = the variance of the portfolio
Heuristic approaches to asset allocation
- 120 minus your age
- 60/40 stocks/bonds
- The endowment model
- Risk parity
- 1/N rule
Endowment model (also know as the Yale model)
An approach to asset allocation that emphasizes large allocations to non-traditional investments, including equity-oriented investments driven by investment manager skill
Norway model
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
The expected after-tax standard deviation
- σat = (1 - t) * σpt
- σat = the expected after-tax standard deviation
- σpt = the expected pre-tax standard deviation
The equivalent rebalancing range for the taxable investor
- Rat = the after-tax rebalancing range
- Rpt = the pre-tax rebalancing range
Factor-model-based benchmark
Return-based benchmark
(Example)
40% small-cap growth + 60% small-cap value
Custom security-based benchmark (also called strategy benchmark)
Reflects the investment discipline of a particular investment manager
Present value of a growing annuity
- g can also be the inflation rate
Modeling with a private equity index
Captures neither the risk nor the return attributes of private equity accurately
Ex post risk being a biased measure of ex ante risk
- 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
