Portfolio Management
Unit – III
Session No. 26
Topic: Optimization
Session Plan
• Recap the previous session
• Optimization
•
•
•
•
•
Mean-Variance Approach
Resampled Efficient Frontier
Black-Litterman Approach
Monte Carlo Simulation
ALM
• Summarizing and Q & A
Optimization
• A critical step in strategic asset allocation is the procedure we use for
converting the inputs to a specific recommended strategic asset allocation.
• Focused on developing and refining a variety of procedures.
• Established procedures have a quantitative flavor.
• Investment advisers, particularly those serving an individual investor clientele,
may use a qualitative approach based on experience.
• All professional investors apply judgment in making recommendations.
Optimization
• Optimization Approaches:
• Mean-Variance Approaches
–
–
•
•
•
The Efficient Frontier
Resampled Efficient Frontier
Black-Litterman Approach
Monte Carlo Simulation
ALM
Optimization
• The Mean–Variance Approach
• Mean–variance analysis provided the first, and still important, quantitative
approach to strategic asset allocation.
• A strategic asset allocation suggested by mean–variance analysis should be
subjected to professional judgment before adoption.
• Return and Risk are the factors used for this analysis
Optimization
• The Efficient Frontier
• According to mean–variance theory, in determining a strategic asset allocation an
investor should choose from among the efficient portfolios consistent with that
investor’s risk tolerance.
• Efficient portfolios make efficient use of risk; they offer the maximum expected
return for their level of variance or standard deviation of return.
• Efficient portfolios plot graphically on the efficient frontier, which is part of the
minimum-variance frontier (MVF).
• Each portfolio on the minimum-variance frontier represents the portfolio with the
smallest variance of return for its level of expected return.
• The graph of a minimum-variance frontier has a turning point (its leftmost point) that
represents the global minimum-variance (GMV) portfolio.
• The GMV portfolio has the smallest variance of all minimum-variance portfolios. The
portion of the minimum-variance frontier beginning with and continuing above the
GMV portfolio is the efficient frontier.
Optimization
Optimization
• The Resampled Efficient Frontier
• By assumption, using sample values of Asset Classes, means, variances and
covariance's, the simulation(reproduction) generates sets of simulated returns
for each sets based on weights is known as simulated efficient portfolios.
– Information in simulated efficient portfolios is integrated into one frontier
called the resampled efficient frontier.
– In simple terms, “ the set of resampled efficient portfolios represents the
resampled efficient frontier”.
Optimization
Optimization
• The Resampled Efficient Frontier
• Resampling provides an improvement over traditional methods
• However, there are issues:
–
–
Average of maximums is not the maximum
Hence, allocation will be suboptimal and we should be able to improve
on this work
• New research on the horizon that provides an alternative.
Optimization
• The Black–Litterman Approach
• Fischer Black and Robert Litterman developed another quantitative approach to
dealing with the problem of estimation error, which we recall is most serious when it
concerns expected returns. Two versions of the Black–Litterman approach exist:
• 1. Unconstrained Black–Litterman (UBL) model .
• Taking the weights of asset classes in a global benchmark such as MSCI World as
a neutral starting point, the asset weights are adjusted to reflect the investor’s views on
the expected returns of asset classes according to a Bayesian procedure that considers
the strength of the investor’s beliefs.
– The procedure does not allow non-negativity constraints on the asset-class weights.
• 2. Black–Litterman (BL) model.
• This approach reverse engineers the expected returns implicit in a diversified market
portfolio (a process known as reverse optimization) and combines them with the
investor’s own views on expected returns in a systematic way that takes into account
the investor’s confidence in his or her views.
– These view-adjusted expected return forecasts are then used in a MVO with a constraint against
short sales and possibly other constraints.
Optimization
Optimization
• Monte Carlo Simulation
• Monte Carlo simulation, a computer-based technique, has become an essential tool
in many areas of investments.
• Monte Carlo simulation involves the calculation and statistical description of the
outcomes resulting in a particular strategic asset allocation under random scenarios
for investment returns, inflation, and other relevant variables.
• The method provides information about the range of possible investment results
from a given asset allocation over the course of the investor’s time horizon, as well as
the likelihood that each result will occur.
• Monte Carlo simulation contrasts to and complements MVO.
• Standard MVO is an analytical methodology based on calculus.
• By contrast, Monte Carlo simulation is a statistical tool.
• Monte Carlo simulation imitates (simulates) an asset allocation’s real-world operation
in an investments laboratory, where the investment adviser incorporates his best
understanding of the set of relevant variables and their statistical properties.
Optimization
• Asset/Liability Management
• Approach for managing risks that arise due to mismatches between the assets and liabilities.
• It is not just about offering solutions to mitigate or hedge the risks arising from the
interaction of assets and liabilities
• It is focused on a long-term perspective.
• Success in the process of maximizing assets to meet complex liabilities may increase
profitability.
• An asset portfolio is meant to fund a specified liability schedule (funding a liability means
being able to pay the liability when it comes due). Such cases call for an ALM approach.
• Using an ALM approach, asset allocation must consider the risk characteristics of the liabilities
in addition to those of the assets, because the focus is on funding the liabilities.
• Earlier we presented the efficient frontier. That efficient frontier is more precisely the ‘‘assetonly’’ efficient frontier, because it fails to consider liabilities.
• Net worth (the difference between the market value of assets and liabilities), also called
surplus, summarizes the interaction of assets and liabilities in a single variable.
• The ALM perspective focuses on the surplus efficient frontier. Mean–variance surplus
optimization extends traditional MVO to incorporate the investor’s liabilities.
Optimization
•
•
•
•
•
•
•
•
•
•
What is the need of Optimization?
What is the use of efficient frontier?
What is MVO?
What is the limitation of the mean-variance approach?
How efficient portfolio helps the investor’s to formulate risk and return?
How resampled efficient portfolio approach is different from MVO?
What is the use of BL model?
What is reverse optimization?
How Monte Carlo is distinct from other models?
Why ALM approach has been used for effective determination of
optimization?