Asset Allocation Flashcards
Reverse Optimization
helps fix first criticism of MVO (GIGO)
improves return estimates
instead of starting w Er and other inptus and deriving optimal weights, start with assumed “optimal” portfolio weights from the global mkt portfolio and derive Er consistent w those weights
those estimates (“implied returns”) are used to do traditional MVO and erive optimal weights for a particular investor
global portfolio good starting point bc provides optimal diversification –> avoids tendency of MVO to come up w highly concentrated allocations
can also use other starting points like weights from an existing IPS
Black-Litterman Model
extension of reverse optimization
implied returns (technically implied excess returns) from reverse optimization are adjusted to reflect investor’s unique views of future returns
eg if reverse MVO derives an Er for EM equities of 6.5% but you think that’s too low you can adjust the Er of that aseet class and re-run the MVO using your adjusted return estimates
KEY TAKEAWAY FOR ASSET ALLOCATION: tends to yield better diversification because the starting point of the analysis is the fully diversified world market portfolio (i.e., all asset classes are considered).
Resampling / Resampled MVO
basically just using normal MVO but with a lot of iterations from Monte Carlo
can be used to address GIGO and overconcentration concerns of MVO
starts/ w basic MVO, then monte carly generates thousands of random variations for inputs around initial estimates –> efficient frontier and associated asset allocations for each point on the frontier
resampled efficient frontier = avg of simulated efficient frontiers –> asset allocation for any point on the resampled frontier is an avg of possible portfolios for that point on the frontier
avg has to be more stable than any one set of guesses, so it’s more stable method
uses of monte carlo
Monte carlo essentially a random number generator, but random within user-defined boundaries –> used in resampling to generate a range of possible inputs for MVO, but HERE it’s used a different way – to simulate multiple future return paths for a portfolio over time (paths based on best guess of Er and risk for port)
Address limitations of MVO being single-period –> address rebalancing and taxes in multiperiod
Taxes easy to incorp into single-period and rebalancing is irrelevant –> multiperiod is reality, and rebalancing in multi involves buying & selling invmts –> taxable gains & losses
Also interim CF –> investors save (add) money into and spend $$ out of portfolio –> interim CF
Monte Carlo Simulation (MCS) = easy to do this at each future point in simulation
Guide individual investors to ID their risk tolerance level –> MCS can show range & likelihood of possible outcomes given various assumptions eg clients planning for retirement can visually see how often and when theyre likely to run out of $$$
Utility Calc
utility aims to maximize investor utility, an approach to finding optimal point on the efficient frontier
used in MVO
Utility of portfolio with asset allocation m = E(r) - 0.005 x (lambda) x VarM
Lamda = risk aversion coefficient, between 1 and 10, avg is 4
VarM = variance of portfolio w allocation M = stdev squared
NOTE: ALL THE ABOVE EXPRESSED AS APERCENT, I.e 5% = 5 –> If you use decimals, use 0.5 instead of 0.005!!!!!
MVO + its constraints
Allocating for optimal portfolio when you have the risky asset and the risk-free asset
MCTR & ACTR
marginal contribution to portfolio risk = change in total portfolio risk for a small change in allcoation to asset class i
= (beta of asset class i WRT the portfolio) x (total portfolio stdev)
so if an asset class has a higher beta, it’ll have a higher marginal contribution to portfolio risk (duh)
used in risk budgeting - figure out each change as you build up the portfolio from the ground up, how much risk are you adding and how much excess return are you getting from each choice
want the most excess return per unit of risk
Once you have MCTR, can get Absolute Contribution to Portfolio Risk (ACTR)
= asset class i’s contribution to portfolio VOLATILITY –> multiplying by its weight shows you actually how much it contributes
ACTRi = (weighti) x (MCTRi)
THE ULTIMATE GOAL:
1) all excess return/MCTR ratios are equal
and
2) they all equal the portfolio’s sharpe ratio
Excess return / MCTR is just the excess return (Return of asset i - RfR) divided by the MCTR
Liability-relative approaches:
Surplus Optimization
Hedging/Return-seeking
Integrated A/L approach
Goals-based Approaches:
Traditional Goals-based approach
+
Alternatives:
Allocation by Risk factors
60/40 rule
120-age
Endowment (Yale) model
Risk-parity
1/N
Traditional Goals based approach:
mostly for individuals
goals (future “liabilities”) are quantified, and grouped by required probability of success and time period until payout
advisors usually select from a standardized, pre-existing set of “modules” off the efficient frontier to meet the most common goals of clients, like funding college
select the module giving the HIGHEST RETURN for a goal’s TIMOE HORIZON and REQUIRED PROBABILITY OF SUCCESS (i.e. dont do sharpe like you have been doing on mocks)
discount the CF associated with that goal at the module’s return to determine allocation required to hit the goal
total asset allocation = sum of the allocations in the modules
When to use Wider or Narrower rebalancing corridors
Wider:
1) higher transaction costs
2) more risk-tolerant clients
3) momentum markets
Narrower:
1) more volatile asset classes (but note trade-off against higher transaction costs)
2) asset classes with LOWER correlations w/ the rest of the portfolio
3) in mean-reverting markets
stepwise regression
a factor model that helps minimize correlation risk
describe: avoids using highly correlated risk factors, thereby avoiding multicollinearity
