Reading 4 Flashcards
MVO
Most common approach to asset allocation. Assumes investors are risk averse, so they prefer more turn for same level of risk.
Given an opportunity set of investable assets, their expected returns and variances, as well as pairwise correlations between them, MVO identifies the portfolio allocations that maximizes the turn for every level of risk
Utility Maximization
Um = E(Rm) - (0.005 x Lambda x variance of m)
- if in % terms eg 8% is 8.0, then use 0.005
if in decimal like 0.08, use 0.5
What is lambda
Captures each individual investor’s preference for trading off risk and return.
It is unique to each individual and is based on the investor’s willingness and capacity to take on risk
risk-neutral: Lamba = 0
typically between 1 and 10
risk average: level of 4
What is MVO budget constraint / unity constraint
asset weights must add up to 100%
MVO non-negativity constraint
all weights in the portfolio should be positive and between 0% and 100%; no short positions
What is the MVO Process
Inputs: expected returns, variances, covariances (Correlations), risk aversion factor, constraints
MVO: maximize utility, subject to constraints
Outputs: asset allocations (portfolio weights), portfolio expected return, portfolio variance
Criticisms of MVO
- GIGO: garbage in, garbage out
- concentrated asset class allocations
- skewness and kurtosis
- risk diversification
- ignores liabilities
- single period framework
What is reverse optimization?
Instead of starting with expected returns (and other inputs) and deriving optimal portfolio weights, start with what we assume to be “optimal” portfolio weights from the global market portfolio and derive the expected returns consistent with those weights.
Then we use these return estimates (Called implied returns) to do a traditional MVO and derive optimal portfolio weights for our particular investor.
What does reverse optimization process look like?
- Inputs: assumed optimal asset allocations, variances, covariances (correlations), risk aversion factor, constraints
- Reverse MVO: maximize utility, subject to constraints
- Outputs: implied returns
- Inputs: implied returns, variances, covariances (correlations), risk aversion factor, constraints
- MVO: maximize utility, subject to constraints
- Outputs: revised asset allocations, portfolio expected return, portfolio variance
What is the benefit of starting with a market portfolio in reverse MVO?
derived returns already reflect a highly diversified portfolio and you avoid the tendency of MVO to come up with highly concentrated asset allocations
Black-Litterman Model
Extension of reverse optimization in which the implied returns (actually implied excess returns) from a reverse optimization are subsequently adjusted to reflect the investor’s unique views of future returns
eg. derives an expected return for EM equities as 6.5%, but you think its too low, you could adjust the expected return by 75 bps to 7.25% and rerun MVO using adjusted return estimates
What is the Black-Litterman Model Process?
Inputs: assumed optimal asset allocations, variances, covariances (correlations), risk aversion factor, constraints
Reverse MVO: maximize utility, subject to constraints
Outputs: implied returns
Black Litterman
Inputs: reverse implied returns, variances, covariances (correlations), risk aversion factor, constraints
MVO: maximize utility, subject to constraints
Outputs: revised asset allocations, portfolio expected return, portfolio variance
How does inclusion of human capital and real estate property impact individual investor’s portfolio?
increases capacity to bear risk
Why are less liquid asset classes difficult to include in MVO?
- there are few indexes available that accurately track these illiquid investments, making it harder to find data to use for estimating return, risk and correlations
- Even where indexes exist to provide return data, they are generally not investable as a passive alternative to active management of these asset classes.
- the risk-return characteristics of a specific real estate, private equity, or infrastructure investment are different from those of its asset class. Eg any one infra fund is not fully diversified, and therefore, its risk and return characteristics reflect both systematic and nonsystematic risk
How do you address illiquidity in MVO?
- Exclude illiquid asset classes when running an MVO, but use them to meet separately set target asset allocations.
- Include the illiquid asset classes in MVO and model the inputs of the specific (not asset class) investments you plan to use (ie the risk estimate will be based on both nonsystematic and systematic)
- include illiquid asset classes in MVO using highly diversified asset class inputs, recognizing that the actual investments made may have different characteristics.
Marginal Contribution to Portfolio Risk
Change in total portfolio risk for a small change in the asset allocation to a specific asset class
Marginal Contribution to Total Risk: Formula
MCTR = (beta of asset class wrt portfolio) x (total portfolio risk measured by sd)
Absolute contribution to total risk
ACTR - weight x MCTR
% of risk contribution by position
ACTR / total portfolio risk
How do you know you have reached optimal allocation to each asset class?
When ratio of excess return to MCTR is equal for all asset classes and is equal to Sharpe of the total portfolio
Plan Surplus
Market Value of investment portfolio assets - PV of pension liabilities
Funding ratio
market value of assets / PV of liabilities
A pension plan is fully funded if funding ratio = 1 (ie surplus = 0)
Quasi Legal Liabilities
Not legal obligations, but are cash outflows expected to occur in the future and are essential to the mission of the institution
What are the 3 approached to liability-relative asset allocation?
- surplus optimization
- 2 portfolio approach
- Integrated asset-liability approach
Surplus Optimization Approach
Extension of MVO in which we determine an efficient frontier based on the surplus with its volatility as our measure of risk, stated either in money or percentage terms
Surplus Retuen
(change in asset value - change in liability value) / initial asset value
objective function of surplus maximization
maximize Um - E(return on surplus) - (0.005 * lambda * variance of surplus)
Two Portfolio Approach
Separate the asset portfolio into 2 sub-portfolios
1. hedging portfolio
2. return-seeking portfolio: using MVO to maximize utility and identify the optimal risk-return tradeoff
What are the limitations of the 2 portfolio approach?
- if the funding ratio is less than 1, it is difficult to create a hedging portfolio that completely hedges the liabilities
- a hedging portfolio may not be available to hedge certain kinds of risk (eg earthquakes)
Integrated Asset-Liability Approach
Banks, hedge funds with short positions and insurance companies make decisions about compositions of their liabilities jointly with their asset allocation decisions. There is a continuous feedback loop between the 2, which requires a multiperiod model. This is often referred to as an integrated asset-liability approach
What is the risk parity approach?
Diversification is achieved by ensuring that each asset class contributes the same amount to the total portfolio risk
How are asset correlations related to rebalancing frequency?
The higher the correlation of the asset class with the rest of the portfolio, the wider the corridor, because a portfolio tends to move with the asset class, and the allocations tend to stray more slowly from the target
How does volatility impact rebalancing frequency?
The higher the volatility of the asset classes, the narrower the optimal corridor because higher volatility increases the likelihood that the actual allocation will diverge over time from the target allocation
Benefit of MCS over MVO?
MCS is multi period
What is the goal of risk budgeting?
Maximize return PER UNIT of risk.
A risk budget identifies the total amount of risk and attributes risk to its constituent parts. an optimum risk budget allocates risk efficiently.
Name 1 common criticism of MVO
Model outputs, the asset allocations, tend to be highly sensitive to changes in the model.
Resulting asset allocations also tend to be highly concentrated in a subset of the available asset classes
which factors do you use in factor based approaches?
The factors commonly used in the factor-based approach generally have low correlations with the market and with each other. This results from the fact that the factors typically represent what is referred to as zero dollar investment or self-financing investment, in which the underperforming attribute is sold short to finance an offsetting long position in the better-performing attribute.
Constructing factors in this manner removes most market exposure from the factors because of the offsetting short and long positions, as a result, the factors generally have low correlations with the market and with one another.
Also, the factors commonly used in the factor-based approach are typically similar to the fundamental or structural factors used in multifactor models.
How is volatility related to rebalancing corridor?
The higher the volatility of the rest of the portfolio, excluding the asset class being considered, the more likely a large divergence from the strategic asset allocation becomes, which should point to a narrower optimal corridor, all else being equal
Describe Black-Litterman Model
Starts with excess returns produced from reverse optimization, which commonly uses the observed market capitalization value of the assets or asset classes of the global opportunity set. It then alters the reverse-optimized expected returns that reflect an investor’s own distinctive views yet still behaves well in an optimizer
How do you identify if MVO was used?
concentrated asset classes
List flaws of resampling
riskier asset allocations are over-diversified. However, the asset allocations do inherit the estimation errors in the original inputs
The 60/40 stock/bond heuristic optimizes the growth benefits of equity and the risk reduction benefits of bonds. true or false?
False.
It is not an optimization model. The 60/40 stock/bond heuristic allocates 60% of assets to equities, supplying long-term growth foundation and 40% to fixed income, supplying risk reduction benefits
The Norway model is a variation of the endowment model that actively invests in publicly traded securities while giving consideration to environmental, social, and governance issues.
True or false?
False
The Norway model PASSIVELY invests in publicly traded securities subject to environmental, social, and governance concerns. In comparison, the endowment model asset allocation emphasizes active management of large allocations to non-traditional investments, seeking to earn illiquidity premiums.
How do you achieve a hedging/return seeking portfolio?
first hedge the liabilities by allocating an amount equal to the PV of the fund’s liabilities to the hedging portfolio. Hedging portfolio must include assets whose returns are driven by the same factors that drive returns of liabilities.
The residual is surplus which would then be invested into a return-seeking portfolio.
Some of the issues with MVO can be corrected by using reverse optimization to solve for risk parameters based on inputs for expected return and correlation.
True or false?
False. Reverse optimization uses inputs for risk and correlation (or covariance) to solve for expected return
Easily tracked indexes in asset classes similar to that of an illiquid asset often do not represent the non-idiosyncratic risk of the illiquid asset very accurately.
True or false?
False
An idiosyncratic shock will affect only a single institution or asset and will not ripple out into the rest of the system. Systemic risk focuses on the danger of the entire financial system collapsing, causing a major downturn in the real economy.
easily tracked indexes for an asset class usually do not capture the idiosyncratic risk component of less liquid assets.
No low-cost passive investment vehicles are available to allow one to closely track the aggregate performance of less liquid asset classes. True or false?
True
Low-cost passive vehicles for tracking performance exist for publicly traded liquid assets but do not exist for illiquid assets.
Marginal contribution to total risk
Beta relative to portfolio * SD of the portfolio
