Asset allocation Flashcards
The objective of risk budgeting in asset allocation
use risk efficiently in the pursuit of return.
What is Marginal Contribution to Total Risk
MCTR identifies the rate at which risk would change with a small (or a marginal) change in the current weights.
MCTR = (beta of asset class)(portfolio return volatility)
Optimal allocation from a risk budgeting perspective: when the ratio of excess return (over the risk-free rate) to MCTR is the same for all assets.
What is Absolute Contribution to total risk
How much it contributes to portfolio return volatility
ACTR = Weights * MCTR
Solutions to allocating to less liquid assets
1) Exclude less liquid asset classes from the SAA (MVO); use funds to implement
2) Include the asset class but attempt to model the specific risks (factor-based allocation)
3) Include the asset class but attempt to model the specific highly diversified characteristics associated with the true asset class
- better estimates of E(R), risk and correlation
- can use listed real estate indexes, that have characteristics close to their R.E. counterparts.
Mean-Variance Optimization formula
Um=E(Rm)−0.005λσ2m
λ - risk aversion coefficient
Large λ, results in large penalty for risk, leading to conservative asset mix.
Smaller λ, smaller penalty for risk, aggressive penalty mix
Key limitations of MVO
- Outputs (asset allocations) are highly sensitive to small changes in the inputs
- The asset allocations tend to be highly concentrated in a subset of the available asset classes
- Many investors are concerned about more than mean & variance of returns
- Although the asset allocations may appear diversified across assets, the sources of risk may not be diversified
- Most portfolio exists to pay for liability or consumption series, and MVO allocations are not directly connected to the what influences that value of the liability or consumption series
- MVO is a single period framework that does not take account of trading/rebalancing risks.
Reverse Optimization
Remedies for 2 constraints:
- Outputs (asset allocations) are highly sensitive to small changes in the inputs
- The asset allocations tend to be highly concentrated in a subset of the available asset classes
Reverse optimization - start with an assumed set of optimal weights + Covariances + λ and solve for expected returns
Starting weights: observed market-cap value of the asset classes that form the opportunity sets.
corner portfolio
a point on the efficient frontier where one asset class either enters or leaves the efficient mix.
Black Litterman Model
Allows for an investor’s own distinctive views from those produced by reverse optimization
Expected return, volatility and correlations in MVO
In MVO, the composition of efficient portfolios is typically more sensitive to expected return estimates than it is to estimates of volatility and correlations. Furthermore, expected returns are generally more difficult to estimate accurately than are volatilities and correlations. Thus, in addressing the first criticism of MVO—that outputs are highly sensitive to small changes in inputs.
Issues with illiquid asset classes
1) lack of accurate indexes to base CMEs on
2) lack of investment vehicles in which to track theses indexes even if they were accurate.
from risk-budgeting perspective, what is an optimal asset allocation
when the ratio of excess return to MCTR is the same for all assets and matches the Sharpe Ratio of the tangency portfolio
Asset class-based asset allocation vs risk factor based asset allocation
Risk factor-based asset allocation optimizes in excess return while asset class-based asset allocation optimizes in the total return space.
If the expected return of a particular asset mix, E(R) was 10%, and the utility of the asset mix was 6%, this would mean
the investor value a risky return of 10% and a risk-free return of 6% equally.
Overcome MVO’s limitation of asset allocation tend to be highly concentrated,
Adding constraints beyond the budget constraint
specify a set allocation to a specific asset specify an allocation range for an asset specify an upper limit to an asset class specify a relative allocation between asset classes
Liability-relative asset allocation approaches
1) Surplus optimization / an extension of MVO
2) Hedging return seeking portfolio
3) Integrated asset-liability approach
Differences in asset allocation between suplus optimization and asset only (liability relative asset allocation)
In conservative portfolio
Surplus optimization has more corporate bonds as a hedging vehicle while asset-only strategies has large allocation to cash
Surplus optimization approach in liability relative asset allocation
- optimize over all assets and liabilities
- liabilities are included as a “negative asset”
- Institution is constrained to hold this ‘negative asset’
- outcome optimizes over asset surplus
Hedging/return seeking portfolio
Basic when SURPLUS AVAILABLE - two portfolio combo for conservative investors or when the size of PV(L) is large in relation to the size of the firm
1) hedging portfolio
2) return seeking portfolio
Variants / (deficit) - allotment to hedging portfolio increases as the funding ratio increases
1) partial hedged portfolio
2) return seeking portfolio
If the funding ratio <1, cannot create a fully hedged portfolio
Integrated asset-liability approach
When decisions regarding the composition of liabilities must be made in conjunction with the asset allocation decision.
often implemented in the context of multi-period models
decisions about the asset allocation will affect the amount of business