CAIA L2 - 3.4 - Asset Allocation Processes and the Mean-Variance Model Flashcards
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Strategic asset allocation
x
Tactical asset allocation
3.4 - Asset Allocation Processes and the Mean-Variance Model
- Strategic asset allocation decisions are long term in nature, and they focus on long-term goals and risk preferences. For a passive investor, these are the only decisions that matter.
- Tactical asset allocation decisions are short term and opportunistic. These are attempts to earn alpha through short-term allocation changes.
3.4 - Asset Allocation Processes and the Mean-Variance Model
Formula
Utility Functions
in Terms of:
- Expected Returns and Variance
- Value at Risk
3.4 - Asset Allocation Processes and the Mean-Variance Model
Utility Functions in Terms of Expected Returns and Variance:
E[u(w)] = μ − [ (λ/2) × σ^2]
µ= mean return on an investment
λ= constant for the level of risk aversion
λ = [ E(R’p’)−R’f’ ] / (σ’p’^2)
σ^2= variance of an investment
Utility Functions With Value at Risk
E[u(w)] = μ − [ (λ’VaR’/2) × VaRα]
3.4 - Asset Allocation Processes and the Mean-Variance Model
Formula
risky asset’s weight “w” of
Mean-Variance Optimization With Risky and Riskless Assets
and
with growing liabilities
3.4 - Asset Allocation Processes and the Mean-Variance Model
w = (1/λ) * [E(R−R’0’)] / (σ^2)
λ= constant for the level of risk aversion
λ = [ E(R’p’)−R’f’ ] / (σ’p’^2)
σ^2= variance of an investment
__–__–__
with growing liabilities:
w = { (1/λ) * [E(R−R’0’)] / (σ^2) } + L [δ/(σ^2]
δ= covariance between the growth rates in the liabilities and assets
L = size of the liabilities relative to the assets (e.g., if the value of the liabilities is 30% higher than the value of the assets, then L =1.3)
3.4 - Asset Allocation Processes and the Mean-Variance Model
Formula
Hurdle Rates
3.4 - Asset Allocation Processes and the Mean-Variance Model
E[R’New’] – Rf > [E(R’p’) – R’f’] × β’New’
E[R’New’] = new asset’s expected return
E[R’p’] = optimal portfolio’s expected return
R’f’ = riskless rate
β’New’ = new asset’s beta in relation to the optimal portfolio
A new asset “New” is included to a portfolio “p” if the expression above is true
3.4 - Asset Allocation Processes and the Mean-Variance Model
List
3 Ways
to address
Skewness and Kurtosis
(in a MVO)
3.4 - Asset Allocation Processes and the Mean-Variance Model
1. Change the optimization process to account for skewness and kurtosis.
2. Add constraints for skewness and kurtosis. However, this can be difficult to achieve, as predicting higher moments is difficult.
3. Limit the weights applied to assets with higher moments (e.g., set a maximum weight that can be given to investments with high tail risks/negative skew).
3.4 - Asset Allocation Processes and the Mean-Variance Model
Formula
Return adjustment for illiquidity
(Mean-variance optimization Framework with
Liquidity Penalty Function)
3.4 - Asset Allocation Processes and the Mean-Variance Model
max R’p’−[(λ/2) × σ’p’^2] − ϕL’p’
L’p’ = ∑w’i’ × L’i’
ϕ = a positive number that represents investor preference for liquidity
Most illiquid assets have a penalty of 1 (i.e., L’i’ = 1), which reduces expected returns by ϕ.
3.4 - Asset Allocation Processes and the Mean-Variance Model
Describe
resampling
to reduce the effect of estimation error
3.4 - Asset Allocation Processes and the Mean-Variance Model
resampling returns is executed by repeated analysis of
(1) hypothetical returns simulated from the original sample or
(2) new samples drawn from the original sample with replacement
3.4 - Asset Allocation Processes and the Mean-Variance Model
Describe
shrinkage
to reduce the effect of estimation error
3.4 - Asset Allocation Processes and the Mean-Variance Model
process of establishing constraints to reduce the effects of sample variation
it could be applied by narrowing confidence intervals or by establishing constraints
3.4 - Asset Allocation Processes and the Mean-Variance Model
Describe
Black-Litterman Approach
3.4 - Asset Allocation Processes and the Mean-Variance Model
Black-Litterman approach
- gives investors the ability to combine their own opinions on asset returns with the market equilibrium model weights
- was created to curtail the unreasonable weights given by MVO
- asset prices should be in equilibrium based on the risk-return profile of the investment and market demand
- Common tactic - limiting:
1. correlation related to the optimal portfolio’s return and a benchmark return
2. deviations between the portfolio and benchmark weights
3. the range of portfolio weights
3.4 - Asset Allocation Processes and the Mean-Variance Model
List
4 Common conditions
as alternatives to the usage of
resampling, shrinkage, or the Black-Litterman
in an asset allocation process
3.4 - Asset Allocation Processes and the Mean-Variance Model
Mean-Variance Optimization and the Use of Constraints
Rather than deploying a formal approach like resampling, shrinkage, or the Black-Litterman approach, some investors choose to instead impose conditions. Common conditions include limiting
- weights to non-negative values (i.e., no short selling);
- the maximum allocation to any given assets or asset class;
- correlations; and
- active share (i.e., deviation from market weightings).
3.4 - Asset Allocation Processes and the Mean-Variance Model
