Asset Allocation - 2 Flashcards
Optimizer
Most appropriate asset allocation/asset mix
Mean Variance Analysis
-Choose from the efficient portfolios consistent with the investors risk tolerance
-Efficient Frontier
Drawback:
- Highly sensitive to changes in inputs - estimation error.
-The Importance of Quality of Inputs
- Selecting an Efficient Portfolio
Efficient Portfolios
Maximum return for a given level of variance or standard deviation
Minimum Variance Portfolio
“represents the portfolio with the smallest variance of return for its level of expected return”
Global Minimum Variance Portfolio
“has the smallest variance of all minimum-variance portfolios.”
Efficient Frontier
“The portion of the minimum-variance frontier beginning with and continuing above the GMV portfolio is the efficient frontier”
Unconstrained Optimization
Sum of the asset class weights should equal 1 Uses the black two fund theorm
Black two fund theorem
Asset weight of any minimum variance portfolios = linear combination of asset weights of any other two minimum variance portfolios
Sign Constrained Optimization
Asset class weight be non negative and sum be equal to one. No short selling
Corner Portfolio Theorem
- Portfolios hold identical assets 2. the rate of change of asset weight moving from one portfolio to other is constant.
It helps in creating other minium variance portfolios.
The Standard deviation is also the weighted average of the two corner portfolios
Resampled Efficient Portfolio
“Average weights on each asset class
for simulated efficient portfolios with that return rank”
Adv: More diversified and stable
Disadv: Lack of theoretical underpinning for the method and use of historical data
Black Litterman Approach
A. Unconstrained (UBL): Neutral starting point - MSCI World and use Bayensian procedure to determine the weights based on investors preference
Adv: Direct method, well diversified, improved model of MVO (non-unintitutive portfolios)
b. BL: Reverse engineer returns from market portfolio and combines with investor’s views and view adjusted used with MVO and other short selling constraints.
BL model
- Asset allocation is well diversified
- Incorporates investors views and strengthens those views
Steps in BL Model
- Define equilibrium market weights and covariance of the asset classes
- Back solve the equilibrium expected returns
- Express views and confidence of each views - expressed as variance
- Calculate the view adjusted market equilibrium return
- Run mean-variance optimisation
Montecarlo Simulation
Practical issues that are difficult can be grappled using this method
- Terminal wealth path dependent we could use Monte carlo simulation where analytical approach is not feasiable
- Longer time horizon, this method is appropriate
Asset liability management - optimization tools
- Focus on surplus effecient frontier
Surplus - net worth
ALM with simulation - Steps
- Determine the surplus efficient frontier and select a limited set of efficient portfolios ranging from MSV to higher surplus risk portfolios
- Conduct monte carlo simulation for each propsed asset allocation and evaluate satisfies with investor’s return and risk objective
- Choose most appropriate allocation that satisfies those objectives
Experience based approaches
- 60/40 stock/bond allocation is appropriate or at least a starting point for an average investor’s asset allocation
- Allocation to bond should increase with increase in risk aversion
- Investors with long term time horizon should increase their allocation to stock
- A rule of thumb for the percentage allocation to equities is 100 minus the age of the investor
Implementation Choices
- Passive
a. tracking a portfolio of cash market securities
b. derivatives portfolio = cash position plus long position in swap in which return to an index representing that asset class is received - derivatives portfolio = cash position plus long position in index futures for the asset class
- Active
a. portfolio of cash market securities
b. derivatives based positions + market neutrall long-short position - Semi active
a. tracking cash market securities with underweight or overweight of securities
b. derivatives position + controlled active risk in cash position
Currency risk management decision
Hedging the currency risk exposure
Hedging can be passive or active
Outsourced or do it yourself if there are correlations between the security and the currency exposure
Rebalancing to SAA
Refers to rebalancing when the changes in prices has cause the weighted of the asset class to change Methods: Calendar basis or on percentage of portfolio basis
SAA for individual investors
Account for the following:
- part of wealth flowing from current n future labour income and the changing mix as the person ages
- correlation of current and future labour income with financial asset returns
- possibility of outliving one;s resources
Human Capital
PV of future labour income
Young people have larger human capital than financial capital
Human Capital = “Human capital (t) = ∑ I(j)/(1+r)^(j-t)
where
t = current age Ij = expected earnings at age j
T = life expectancy r = discount rate63
Human Capital and asset allocation
- Investors with safe labour capital(human capita) will invest more into equities.
- Investors whose labour income is +vely correlated with stock market should invest in less exposure to stocks
- ability to adjust labour supply tends to increase an investor’s optimal allocation to equities
it is important to consider the riskiness of human capital. if it is risky but not correlated with stock market then treat it risk free, if it related to the stock market, then invest in bonds when the investor is at young age.
