Asset allocation

Question 1

The objective of risk budgeting in asset allocation

Answer 1

use risk efficiently in the pursuit of return.

Question 2

What is Marginal Contribution to Total Risk

Answer 2

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.

Question 3

What is Absolute Contribution to total risk

Answer 3

How much it contributes to portfolio return volatility

ACTR = Weights * MCTR

Question 4

Solutions to allocating to less liquid assets

Answer 4

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.

Question 5

Mean-Variance Optimization formula

Answer 5

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

Question 6

Key limitations of MVO

Answer 6

1. Outputs (asset allocations) are highly sensitive to small changes in the inputs
2. The asset allocations tend to be highly concentrated in a subset of the available asset classes
3. Many investors are concerned about more than mean & variance of returns
4. Although the asset allocations may appear diversified across assets, the sources of risk may not be diversified
5. 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
6. MVO is a single period framework that does not take account of trading/rebalancing risks.

Question 7

Reverse Optimization

Answer 7

Remedies for 2 constraints:

1. Outputs (asset allocations) are highly sensitive to small changes in the inputs
2. 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.

Question 8

corner portfolio

Answer 8

a point on the efficient frontier where one asset class either enters or leaves the efficient mix.

Question 9

Black Litterman Model

Answer 9

Allows for an investor’s own distinctive views from those produced by reverse optimization

Question 10

Expected return, volatility and correlations in MVO

Answer 10

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.

Question 11

Issues with illiquid asset classes

Answer 11

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.

Question 12

from risk-budgeting perspective, what is an optimal asset allocation

Answer 12

when the ratio of excess return to MCTR is the same for all assets and matches the Sharpe Ratio of the tangency portfolio

Question 13

Asset class-based asset allocation vs risk factor based asset allocation

Answer 13

Risk factor-based asset allocation optimizes in excess return while asset class-based asset allocation optimizes in the total return space.

Question 14

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

Answer 14

the investor value a risky return of 10% and a risk-free return of 6% equally.

Question 15

Overcome MVO’s limitation of asset allocation tend to be highly concentrated,

Answer 15

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

Question 16

Liability-relative asset allocation approaches

Answer 16

1) Surplus optimization / an extension of MVO
2) Hedging return seeking portfolio
3) Integrated asset-liability approach

Question 17

Differences in asset allocation between suplus optimization and asset only (liability relative asset allocation)

Answer 17

In conservative portfolio

Surplus optimization has more corporate bonds as a hedging vehicle while asset-only strategies has large allocation to cash

Question 18

Surplus optimization approach in liability relative asset allocation

Answer 18

• 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

Question 19

Hedging/return seeking portfolio

Answer 19

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

Question 20

Integrated asset-liability approach

Answer 20

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