Asset Allocation 12-14 Flashcards
government focuses on clarifying mission, creating a plan, and reviewing progress toward achieving long-and -short-term objectives.
the election of plan
achieve the agreed on goals and objectives
3 levels with governance hierarchy
covering investment committee
investment staff
3rd pary resources
effective governance models perform:
- articulate the long and short term objectives of the investment program
- allocate decision, rights and responsibilities among the fundamental units
- specify process for developing and approving investment policy statement
- specify processes for developing and approving the strategic asset allocation
- establish a reporting framework to monitor the program’s progress toward the agreed-on goals and objectives
- periodically undertake a governance audit
reporting framework
clear & concise, accurately answering questions
address performance evaluation, compliance with inv. guidelines
progress toward achieving the stated goals and objectives
benchmark
management reporting
governance reporting -address strength and weakness in a program execution
governance audit
to ensure that the established policies, procedures, and governance structure are effective
performed by 3rd independent party
effective investment governance ensures
durability/survivability of the investment program
weak to avoid decision-reversal risk
economic balance sheet
financial A/L
+ extended portfolio A/L
Financial asset
equity
FI
human capital
pv of trues earnings, inheritances, futures intellectual property
liability ST borrwowing mortgage debt pv of future consumption pv of prospective payout for foundations
asset only
grow asset
high return/volatility
focus on asset side of b/s, exp(r), risk, correlations
*target an overall required return
MVO mean variance optimization is the most familiar and deeply standard asset-only approach
maximize sharpe ratio for acceptable level of volatility
liability-relative/liability driven investing LDI
funding liability
objective of funding liabilities
provide money to pay liability when due
modell legal/quasi-liability
fund ability and invest excess asset and growth
penalty for not meeting liability (banks, DB, insurers)
goal-based /GBI
support needs
AA for sub-portfolio
each of which is aligned to specified goals
aspirational objective
model goals with specified required probability of success - individual investors
drawback: sub-portfolio add complexity
goals maybe ambiguous/may change overtime
mental accounting
bottom-up strategic AA
strategic asset allocation - Quant approach Utility theory
effect achieving IPS
optimal asset allocation
expected to provide the highest utility to the investor at the investors investment time horizon
power utility function
underlies mean-variance optimization
risk aversion does not depend on level of wealth
optimal asset allocation w* =
(U-rf)/(variance)*1/degree of risk aversion
Sharpe ratio
higher the greater its contribution to the sharpe ratio of the overall portfolio holding.
however this condition is not usually true. Diversification potential in a portfolio may differ. Portlio risk may decrease through favorable correlation characteristics of the strategies.
global market value weighted portfolio
on the line tangent to efficient frontier
- sum all investable asset hold by investors, reflects the balancing of supply and demand across world markets
- in financial theory, it minimizes diversification risk, which in principle is uncompensated
- makes the most efficient use of the risk budget
- serve as a starting point and ensure investor articulates a clear justification for moving away from global capitalization market weights
2 phases:
- allocate asset in proportion to global portfolio of stocks, bond, real asset
- disaggregate each of these broad asset classes in region, country, security weights using capitalization weights
implementation hurdle
- estimating the size of each asset class on a global basis is an imprecise exercise given the uneven availability of info on non-publicly traded assets
- the practicality of investing proportionately in residential real asset, much of which is held in individual homeowners’ hands has been questioned
- private commercial real estate and global private equity assets are not easily carved into pieces of a size that is accessible to most investors
liability relative
portfolio value match the liability with a buffer
FI primarily because int rates are a major financial driver of both liability and bond value.
Bond can be important in hedging liabilities but equities can be relevant for liability hedging too.
underfunded pension due to liability increase
- optimal AA in general is sensitive to changes in the fund status of the plan
- increase fund statues by decrease surplus risk overtime
- as FS change, proportion of liability hedging asset and return seeking asset and duration of liability hedged change
sensitive to int. rate, duration, inflation, credit risk
tactical asset allocation TAA
active
ST
approaches:
1. discretional TAA
discretional relies in a qualitative interpretation of political, economic and financial market condition
2. Systematic TAA
systematic relies on quantitative signals to capture documented return anomalies that maybe inconsistent with market efficiency (value, momentum)
involves deliberate ST deviations from the strategic asset allocations by taking ST economic/financial market conditions that appear more favorable to certain asset classes
-investment return in short term is predictable
- ST tilt away from the strategic asset mix
- responsive to price momentum, perceived asset class valuation, stage of business cycle
Drawback:
- may incur additional cost higher trading cost and taxes
- TAA increases the concentration of risk relative to the policy portfolio
generating alpha through TAA decisions is dependent on successful market or factor timing rather than security selection
Evaluation (3 ways) between TAA and SAA
- sharpe ratio
- information ratio
- scatter plots
Dynamic asset allocation DAA
multi-period
deviation that are motivated by long-term valuation signals or even views
Barriers: monitory and trading cost (tax CGT)
should evaluate cost-benefit lens
GDP-weighted global bond index involves both active/passive choices
passive presented by the overall selection of the universe of global bonds
active choice is represented by the weighting scheme, which is to use the GDP rather than capital market weights. Tilting away from FI to real economy
Risk budgeting
variance, std of return, concern for tail risk, be quantified by VAR or drawdown, absolute/relative term
Active risk budgeting addresses the question of how much benchmark related risk an investor is willing to take in seeking to outperform a benchmark.
rebalancing
discipline of adjusting portfolio weights to more closely align with the strategic asset allocation
never rebalance implies rising risk/return
countercyclical
contrarian 逆势的 investment approach
align strategic asset allocation
percent-range rebalancing setting rebalancing thresholds or trigger points
target weight 50%
trigger point 45, 55%
range 10%
strategic consideration for rebalancing
using derivatives as a rebalancing tool to lower costs
widen: 正比： transaction cost correlation momentum facto tax consequences liquidity risk tolratce
Narrow corridor: high volatility mean reversion less correlation risk averse investor
- higher transaction costs imply wider rebalancing ranges
- more risk-averse investors will have tighter rebalancing ranges
- less correlated assets also have tighter rebalancing ranges
- beliefs in momentum factor widen rebalancing ranges
- mean reversion encourages tighter ranges
- tax discourage rebalancing and encourage asymmetric and wider rebalancing ranges
mean-variance optimization MVO markowitz
most concentrated
Um=E(Rm) - 0.005(risk aversion coefficient)* Variance m
coefficient = 4 moderate risk averse investor
maximize the expected return for an expected level of risk
provide a framework to determine how much to allocate to each asset class to create optimal asset mix
inputs: return, risk (std), pair-wise correlation
A single portfolio with specific asset class weights at each level of return describes traditional mean variance optimization.
reverse optimization
solve output high sensitivity of input of MVO
input determined by market cap weights, cov, and risk aversion coefficient.
more diversified
result in a much more diversified allocation since it uses global market portfolio as baseline.
COV - Reverse MVO - E(r)
start with optimal portfolio o weight from the global market and drive E(r)
run a traditional MVO based on E(r)
Criticism of MVO
inputs are historical data
- output sensitivity to input (garbage-in-garbage-out)
- concentrated allocation
- focus of skewness and kurtosis is ignored
indirectly incorporate skewness kurtosis or both into the utility function and use an asymmetric definition or risk such as conditional value at risk instead of variance
- highly granular and narrowly defined asset classes
solve: redefine the asset class more broadly and follow rules for well specified asset classes. - MVO is a single-period framework that does not take account of costs and taxes
- MVO does not model liability and goals (single period approach)
Resampled MVO
Solves input sensitivity and high concentration
Monte carlo similation
Monte carlo similation used to generate thousands of random variations of the inputs around the initial estimates, resulting thousands of simulated efficient frontiers.
Mont carlo simulation solves single period framework with all possible outcomes.
The resampled efficient frontier is an average of all the simulated frontiers
used to create an efficient frontier at each return level and run thousands of times resulting in an efficient frontier that is the result of an averaging process. The efficient frontier becomes a blur rather than a single sharp curve. At each level of return, the most efficient of the simulated efficient portfolios is at the center of the distribution.
risk aversion coefficient = 0
risk neutral investor
optimal AA is 100% invested in EM.
Exp Utility = Exp(r)
To achieve better-diversified efficient frontier:
reverse optimization black-litterman model concentrated asset class weight
Solve input sensitivity: Address MVO's sensitivity to small differences in expected return estimates by archiving expected returns to those implied by the asset class weights of a proxy for the global market portfolios
reverse optimization
black-litterman model
highest prob of exceeding 4% return
calculate sharpe ratio
= E(r)-target / std
E(r) = E(r) - 0.005*risk aversion coefficient * variance
the higher, the higher problem exceeding the threshold
Non-nominal optimization
solves skewness and kurtosis, mean and variance only of MVO
Traditional MVO ignores non-normal distribution
use 1. mean-semi variance optimization
- mean-conditional var optimization
- mean-variance-skewness optimization
- mean-variance-skewness-kurtosis
Monte carlo simulation solves single period framework with all possible outcomes.
Advantages relative to MVO:
- It has a multi-period framework
- Incorporate cost of rebalancing
- solves path-dependent issue by adjusts for change in cash flows
- incorporates statistics outside the normal distribution, skewness and excess kurtosis
Intepret and critique an AA in relation to an investor’s economic B/S
investor with stable jobs with consistent capital
model CF with
human capital as an inflation-linked bond.
investor with less certain and more volatile future wage:
model human capital
as a mix of inflation-linked bond, equity and corp. bonds
including human capital & residential RE along with traditional investment vehicles increase investors capacity to bear risk.
Liquidity in Asset Allocation
Less liquid asset classes such as direct real estate, infrastructure, and private equity - cannot be readily diversified to eliminate idiosyncratic risk, so representing overall asset class performance is problematic. - far fewer indexes that attempt to represent aggregate performance for these less liquid asset classes than indexes of traditional highly liquid asset classes. - Finally, the risk and return characteristics associated with actual investment vehicles are typically significantly different from the characteristics of the asset classes themselves.
- it’s more challenging to make capital market assumption due to the lack of accurate index for less liquid assets
- even if there are accurate index, there are no low-cost passive investment vehicles to track them.
practical options:
- exclude less liquid asset classes from the MVO and consider RE funds as potential when fulfilling the target strategic AA.
- include them in MVO and model the inputs to represent the specific risk characteristics
- include then in MVO and model the inputs to represent the highly diversified characteristics associated with the true asset classes.
3 aspects of risk budgets:
- identifies the total amount of risk and allocates the risk to a portfolio’s constituent parts
- an option risk budget allocates risk efficiently
- the process of finding the optimal risk budget is risk budgeting
absolute/relative risk budget
The goal of risk budgeting is to 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.
absolute contribution to total risk (ACTR)
measure how much it contributes to portfolio return volatility for an asset class i
ACTRi = wi * MCTR = wi * beta * std
optimal asset allocation
excess return /MCTR = Sharpe ratio = (E(r)-rf)/MCTRi
is optimal AA from a risk budgeting perspective
when the ratio of excess return to MCTR is the same for all assets and is equal to sharpe ratio of the portfolio.
Fama French
factor based AA
solves non diversified risk of MVO
factors are typically observed based on market premiums and anomalies
the factor represents what is referred to as a zero(dollar) investment or self-financing investment.
factors generally have low correlations with the market and with one another
typically similar to the fundamental/structural factors used in multi-factor models
developing liability-relative AA
plan surplus = MV(A) - PV(L)
funding ratio = MV(A)/PV(L) =1 fully funded and surplus =0
3 approaches to liability relative asset allocation
1. surplus optimization
an extension of MVO that manages the portfolio surplus against the surplus volatility.
Um = E(Rs,m) - 0.005 * risk aversion coefficient * Variance (Rs,M)
Rsm =Surplus return = change in asset - change in liability / initial asset value
minimize risk of underlying by insurance companies and overfunded pension
most appropriate for conservative investors
increasing allocation to the hedging portfolio as the funding ratio and the surplus increase.
- links asset and pv of liability through a correlation coefficient.
- 1 step
- simplicity
- linear correlation
- all level of risk
- any funding ratio
- single period
allocation to corp bond declines with increase in plan surplus return can be explained by
positive correlation of bond prices with the pv of liability.
the hedging asset is employed to a greater degree at the low end of the surplus efficient frontier.
3 approaches to liability relative asset allocation
- Surplus optimization
- two portfolio approach
- integrated asset-liability approach (ALM)
forming hedging portfolio
asset and liability must be drive by the same factor
pv of future CF =mv of asset
date of valuation of asset = date of that for liabilities
discount rate assumption
higher discount lead to higher funding ratio
require lower contribution from sponsors
limitation: 1. funding ratio <1 mv(c)/pv(l)<1 basis form is not applied 2. loses due to the nature disasters cannot be hedged buy insurance
3 approaches to liability relative asset allocation
3. integrated asset-liability approach (ALM)
DFA dynamic financial analysis
jointly optimizes assets and liabilities, typically against future changes in multiple factors.
potential to improve the institutions overall return
- increase complexity
- linear-non-linear
- all level of risk
- any funding ratio
- multi-period
goal based approach
E(R) with specific prob. success over the required time-horizon
size of inv = pr(future goal) / (1+ E(r)^n
critique heuristic and other approach to AA
‘120 - YOUR AGE’
% allocation to equity = 120 - age
critique heuristic and other approach to AA
60/40 stock/bond heuristic
60% equities vs. 40% bonds
critique heuristic and other approach to AA
yale/endowment model
allocate larger amounts to alternative investment asset class
critique heuristic and other approach to AA
risk parity 1/n
wi * cov(ri, rp) = 1/n * variance p
each asset class contribute the same amount to the total portfolio risk
weigit = 1/n
overweight less risky asset
underweight more risky asset
asset size constraints - small assets
disadvantage subject to small asset:
- minimum requirement for some investment is not met
- lower governance capacity-sophistication and manpower resources
- higher internal management fees
- too small to diversify across asset classes
tax consideration
interest income taxed at a higher rate than dividends/capi gains
taxable assets have existing unrealized capital gains/losses which come with embedded tax liabilities.
r at = r pt(1-t)
rat = pa rat (1-td) + pa rpt (1-tcg)
std at= std pt(1-t)
3 potential ways current market value may be adj. to reflect the a/l:
- subtract the value of the embedded CGT from the current market value of the asset as if it were to be sold today
- assume the asset is to be sold in the future and discount the tax liability to its pv using the asset after-tax return as a discount rate
- assume asset is to be sold in the future and discount the tax liability to its pv using the after-rate rf rate.
taxes and portfolio rebalancing
Rat = Rpt/(1-t)
occur less frequently in the taxable portfolio due to reduction in volatility
reduce impact of taxation:
tax loss harvesting
trading to realized a capital loss to offset current/future realized capital gain, thereby reducing the taxes owned by the investor
reduce impact of taxation:
Strategic asset allocation
place less tax-efficient assets in accounts with more favorable tax treatment, such as retirement savings account.
tax deferred account
TDA
asset appreciate tax free but are taxes upon distribution
AF TDA = Vat = Vpt(1-t)
TEA
tax exempt assets
not subject to taxes
changes in investment objective/constraints from:
asset size business condition investor's personal circumstances interest rate cash flow regulation time horizon liquidity needs economic environment and capital market expectation change in committee members/trustees
Strategic asset allocation SAA
LT investment policy targets fr asset class weight
The Norway model
passively invests in publicly traded securities subject to environmental, social, and governance concerns.
5 criteria in effectively specify asset classes
- asset within an asset class should be relatively homogenous
- asset classes should be mutually exclusive
- asset class should be diversifying
- asset classes selected for investment should have the capacity to absorb a meaningful proportion of an investor’s portfolio.
impact of short sale on efficient frontier and asset allocation
- short sale constraint allows only positive asset weights, this may shift the efficient frontier downward and to the right, shifting the theoretical maximum possible return for a given level of risk downward
- in practice the constraint is not an issue because few investors would allow a “permanent” strategic allocation to short position.
Grinold-Kroner model for Equity market return
Expected repricing return = change in P/E ratio = 0.5%
Expected income return = dividend yield − increase in shares outstanding = 3.5% − ( −1.0%) = 4.5%
Expected nominal earnings growth = real earnings growth + inflation = 2.1% + 1.9% = 4.0%
r=(1+s)(1+i)(1+c)
s spending
i inflation
c cost of earning
Heuristics approach
refers to rules that provide a reasonable but not necessarily optimal solution, Some investors may skip the various optimization techniques and simply adopt an asset allocation mix (such as the “120 minus your age” rule or a 60/40 stock/bond mix).
Shortfall risk
is a liability-relative approach focused on the risk of having insufficient assets to pay obligations when due.
corridor width
- frequency of rebalancing from strategic asset allocation
narrow when rebalance often
increase in volatility
higher volatility makes large divergences from the strategic asset allocation more likely
wider when rebalance rarely
increase in transaction cost
higher risk tolerance
higher correlation
-when asset classes move in sync, further divergence from target weights is less likely
low volatility
the two portfolio model
a hedging portfolio + return seeking portfolio (mvo)
it allows the fund to create an asset portfolio that hedges its liabilities, while separately creating a portfolio that manages the remaining assets using mean-variance optimization (MVO) under a return-seeking approach.
- 2 steps
- linear/nonlinear
- conservative level risk
- positive funding ratio
- single period
Improvement to monte carlo simulations
- refine historical base asset class expectations for expected future economic conditions
- model the assets owned rather than generic asset classes.
Advantage of resample efficient frontier
- likely to be more stable, leading to less frequent turnover and lower transaction cost.
- allocation likely includes more asset classes from increased diversification, consistent with her reduced risk tolerance
advantage of black-litterman
adds in investors view of expected return
with constrain as strategic allocation to short is highly unusual.
Corner portfolio
MVO is required to find the corner portfolio
it’s must be on the efficient portfolio
shortcut to interpolate points along the efficient frontier
