principle of AA Flashcards
MVO
Mean-variance optimization:
+ common approach to asset allocation
+ assume: investors are risk averse
+ identifies the portfolio allocations that maximize return for every level of risk
Um = E(Rm) − 0.005 × λ × Var
λ = the investor’s risk aversion coefficent
constrant of MVO
+ budget constraint or unity constraint: asset weights must add up to 100%
+ nonnegativity constraint: all weight must be positive between 0% to 100%
Constraints of MVO
(1) GIGO
(2) concentrate in some subset of asset class
(3) focus of mean/variance of return
(4) source of risk is not diversified
(5) single pediod, not take account taxes, cost
(6) not connect to liability, consumtion series
corner portfolios
all the set of portfolio in frontier line
6 Criticism of MVO
(1) The output (asset allocation) are highly sensitive to small changes in the input
(2) The asset allocations tend to be highly concentrated in a subset of available asset classes
REMEDI:
+ Reverse optimization
+ Black – Litterman Model
+ Resampled MVO
(3) Many investors are concerned about more than mean and variance of returns
(4) Although the asset allocations may appear diversified across assets, the source of risk may not be diversified
Remedy: USE FACTORS
(5) Most portfolios exist to pay for a liability or consumption series and MVO allocations are not directly connected to what influences that value of the liability or consumption series
Remedy: liability relative or goal-based asset allocation
(6) MVO is a single period framewok and it does not take into account trading/rebalancing cost and taxes
Remedy: simulation
ACTR
Absolute contributioin to risk (measures how much the asset class contributes to σp)
• ACTR = wi * MCTR = wi * βi * σp
Quasi
payments that are expected to be made but are not liabilities such as endowment
Characteristics of liabilities can effect asset allocation
(1) Fixed vs. contigent flows
(2) Legal vs quasi-liabilities
(3) Duration and convexity of liability cash flows
(4) Value of liabilities as compared with the size of the sponsoring organization
(5) Factors driving future liabilities cash flows such as inflations, economic conditions, interest rates, premiums
(6) Timing consideration such as longevity risk
(7) Regulations affecting liability cash flow such as rate`
variant 2-portfolio approaches
(1) Liability
(2) Surplus
longevity risk
live longer than forecast
+ annuity
+ pension
method for liability relative approach
(1) surplus optimization
(2) Hedging/Return seeking portfolio
(3) Integrated asset – liability approach
liability return
measures the time value of money for the liabilities plus any expected changes in the discount rate and future cash flows over the planning horizon
2 portfolios in Hedging/Return seeking portfolio
(1) hedging portfolio
(2) return seeking portfolio
the portion hedge in Hedging/Return seeking portfolio approach
+ fully hedge
+ partial hedge
Limitations of hedge/return seeking portfolio approach
(1) Could not creat a fully hedge portfolio if funding ratio < 1
(2) True hedging portfolio may not be available and if the portfolio is not perfectly hedged there will be basis risk
Dynamic in hedge/return seeking portfolio approach
means increase the allocation to hedging portfolio as funding ratio increases
more critical the goals, the ……… prob of success required
higher
The higher prob archieve goal = …….. discount rates
lower
The lower discount rates = …. capital allocation to that goal
greater
definition of Risk parity
each asset class should contribute equally to the total risk of the portfolio to be well diversified
Formula of risk parity
wi×Cov(ri rp)= 1/n σp^2
3 methods to incoprate client risk reference into asset allocation
(1) specifying additional constraints,
(2) specifying a risk aversion factor for the investor,
(3) using MCS
3 approach of liability-relative asset allocaiton
(1) Surplus efficient frontier approach
(2) Integrated asset-liability approach
(3) Two-portfolio approach.
encounter restriction
gặp hạn chế
commingled investment vehicle
like mutual fund, ETF, …
MCTR when portfolio optimal
= sharpe ratio
what is optimum risk budget
An optimum risk budget allocates risk efficiently
measuring the success of TAA relative to SAA
Sharpe ratio
3 steps in Process of MVO
S1: Do inputs:
+ expected return of each asset
+ Variances
+ Covariances (correlations) between asset (pairwise)
+ Risk averse factor
+ Constraints
S2: Do MVO:
+ Maximize Utility
+ Subject to constraint
S3: Do output
+ Asset Allocation (Port weight)
+ Port expected return
+ Port variance
Step of reverse optimization
- S1: do input:
+ Assumed optimal AA
+Variances
+ Covariances (correlations)
+ Risk averse factor
+ Constraints - reverse MVO
+ Maximize MVO
+ Subject to constraint - Output: implied returns
- Do MVO again
+ Implied returns
+ Variances
+ Covariances (correlations)
+ Risk averse factor
+ Constraints - Do MVO
+ Maximize utilities
+ Subject to constraint - Outputs:
+ revise AA
+ port expected return
+ port variance
step of Black Litterman do
It is extension of reverse MVO, not only implied return, but also reverse implied return
resample MVO
S1: start with basic MVO
S2: Do Monte Carlo, generate thousands of random variations for the inputs around the initial estimates, resulting in efficient frontier
S3: The resampled efficient frontier is average of all the simulated efficient frontier
S4: Do AA base on the average efficient frontier
Key rate Duration (truoc gio bi hieu sai)
+ 1 danh mục có 3 position P1, P2, P3, va P la tong danh muc
+ Mod Du cua tung position la D1, D2, D3
Khi do:
+ KRD1 = D1 x P1/P
+ Danh muc co KRD = KDR1 + KRD2 + KRD3
+ Bien dong gia cua danh muc Delta P = KDR1 x DeltaP1 + KRD2 x DeltaP2 + KRD3 x DeltaP3
tangency portfolio
portfolio tiep tuyen, is corner portfolio
Roy’s Safety first
+ = (Re - Rm)/sigma
+ provides a probability of getting a minimum-required return on a portfolio
Adv & Dis adv of MVO
Adv:
+ widely understood & accepted
+ modeling of EF can be simplified with the use of corner portfolio
Disadv:
+ Estimate errro -> use Resample EF
+ Static -> use MCS
+ Input base on historical bases
Adv & Dis adv of resample EF
Adv:
+ More stable than MVO
-> Able to judge the need for rebalancing
-> less port. turnover & lower transactio cost
+ Better diversification than MVO
Dis Adv:
+ No theoretical basis
+ Static
+ Input base on historical data
Adv & Dis adv of Black litterman
Adv:
+ More stable than MVO
+ Better diversification than MVO
+ Incorporate manager view
Dis adv:
+ Complicated
+ Static
+ Input base on historical data
Adv & Dis adv of MCS
Adv:
+ use to complement to others approach
+ Model path dependency
Dis adv:
+ complicated
+ output is as accurate as input
Adv & dis adv of ALM
Adv:
+ same as MVO but add liabilities
Dis Adv:
+ Sames as MVO
Experiance base
Adv:
+ Incoporate asset allocation experiance
+ Easy to understand
+ Not expensive
Dis adv:
+ too simple
Active accumulator va independence individualist khac nhau ntn
II is:
(1) lower active
(2) some bias is different
When asset classes move in sync, further divergence
from target weights is less likely, which favor …………. rebalancing ranges
wider
When asset classes move in sync, further divergence
from target weights is more likely, which favor …………. rebalancing ranges
narrower
the most comprehensive method:
A. The two portfolio approach
B. Surplus optimization/ Surplus efficient approach
C. Intergrate asset-liability
C. Because it is multiple period
how the funded position of 3 method to use:
A. The two portfolio approach
B. Surplus optimization/ Surplus efficient approach
C. Intergrate asset-liability
All of them can be use for over/under/in funded
but with the two portfolio, only for basic
