# Practical issues in applying modern portfolio theory and mean-variance optimization (mainly Week 3) Flashcards

3 approaches to asset allocation

–Static strategic asset allocation (SAA)

–Dynamic asset allocation (DSAA / strategic tilting)

–Tactical asset allocation (TAA)

–Static strategic asset allocation (SAA)

Assume what we have now is going to last very long term. think of long term investment horizon in average conditions

- unconditional
- don’t assume that australian economy is going to outperform the rest of the world in next 3-5 years. Australia equity market is going to have the same expected return as world equity. Don’t consider dynamic nature of financial market or individual circumstances.
- focus on information i have right now. do not consider investment opportunities The average expectation right now. Given the set of info and what you understand of financial market and economy, we construct a portfolio this way to help client to achieve objectives

Dynamic asset allocation

–Tactical asset allocation (TAA)

features

last few days or months, dynamic and static are long term

conditional; portfolio manager makes positive excess return in short period of time taking adv of temporary market inefficiencies

usually not used alone. it is used together with others to temporarily boost return

Dynamic asset allocation

features

they have target date funds or dynamic funds

- Conditional - e.g. asset risk/return, investor horizon, preferences
- Investors and investment opportunities can evolve through time

Modern Portfolio Theory

Perfect capital market assumptions:

frictionless and efficient

single period. investment horizon is not defined. don’t care about next period

rational and risk averse investors - only care about risk and return trade off. they are price takers. have no influence on market price. objective to maximise utility.

**with homogeneous expectations of assets expected return and variance, covariance metrics**

**all assets are liquid, tradable and accessible by all investors**

same access to market price and information.

•Separation pertains. separate risky and risk free assets

Theoretical issues with traditional MPT

- Portfolio optimization across all available assets

In practice, don’t throw thousands of investable assets

in mean variance optimisation model to let it calculate the market portfolio. we use proxies

fixed income, property, asset classes as a close division of assets available.

if we do run mean variance optimisation problem using MDT, it only returns a very close asset allocation e.g. equity, fixed income and other assets. no instruction on how much you are going to hold in BHP, ANZ etc

Theoretical issues with traditional MPT

- Portfolio optimization across all available assets

Not necessarily feasible (curse of dimensionality); multi-factor models may be more effective

if you consider stock index in today’s financial market, all of the listed australian run mathetical problem of having this optical trade off of return and risk. not a trivial problem.

have to include government bonds, derivatives, properties, gold and other investable assets all into the calculation. will impose great pressure on calculation ability

Theoretical issues with traditional MPT

3.

Assumes risk aversion is only investor difference that matters

(‘separation’ => investors hold combination of M and Rf)

Other investor differences matter, e.g. objectives, liabilities, investment horizon, opportunities, costs, taxes

(=> separation unlikely to hold in practice, i.e. different portfolios may be optimal)

Theoretical issues with traditional MPT

- Single Period model

Real world is multi-period, with stochastically changing investment opportunities. does not address dynamic nature of financial market and investors circumstances

Theoretical issues with traditional MPT

- Investment horizon is undefined

yet in real world it matters. how to mitigate this problem

extending data frequency. instead of using weekly and monthly. use quarterly and yearly data. correlation between quaterly and yearly is very low.

some asset classes is zero; some is high

Theoretical issues with traditional MPT

- Investment horizon is undefined

Yet it matters in the real world, especially if returns are not iid (identically and independently distributed)

identically distributed = following same probability distribution. from same distribution

independent = each return of this period is not correlated with return of previous and future periods

Long term investment horizon. long term view of asset return and std.

How portfolios are built in practice

Analysis tool

computer program does not understand

regret, worry about medical circumstances, worries about retirement, increasing utility.

mathetmical process can provide us a tool. final decision making is made by portfolio manager given his/her understanding of the investor’s circumstances.

How portfolios are built in practice

•Real-world influences matter: liquidity, fees & costs, business risk, resources, decision-making structures

telstra has own super fund management team

call special meeting of board to get things done over few weeks

others have external consultants and limited resources in fund to exploit all investment opportunities.when consultant propose and calls for meeting with board, everywhere in australia. call for special meeting, some cannot come. without vote of directors cannot go ahead with new investment opp. what is directors have questions about risks, portfolio manager speaks to consultant. this process can go on for weeks then investment opportunity is gone

How portfolios are built in practice

•Widespread pursuit of active returns (‘alpha’)

popular way to construct portfolio and to understand performance especially outperformance.

active managers construct a baseline portfolio. e.g. active australian equity has asset allocation in difference sectors banking 25% resource 25%. generate alpha through active return, deviate from industry average. have baseline portfolio similar to asset allocation of peers.

setlight portfolio. small, controlled, underweight positions in market you believe may generate excess return. from small cap start up high tech companies, start up pharamaceutical

How portfolios are built in practice

•Tiered approach

Tiered to portfolio construction (division into buckets: portfolio => asset classes => asset managers => assets)

large superannuation funds. e.g. uni super, retail super funds. just because of size under management, no way to plug in all expected return, standard variation and covariance metrics in the mean variance optmisation model.

asset allocation into equity alone. will have equity managers of australia equity, world quity. geographic division of equity portfolio, e.g. japanese equity, . emerging market equity

How portfolios are built in practice

industry norms

for similar funds australian equity funds hold large proportion of assets in australian banks because within australian market top 100 companies are a few finance companies.

asset allocation will be very similar to your peers. want to beat peers, have to come up with ideas to generate excess return and certain level of tracking error deviating from industry peers.

How portfolios are built in practice

legacy portfolio

super funds have a mandate determined by board. they all agree date. have certain asset allocation in this way. do not invest in coal mining or tobacco companies. social responsibilities in investment

have context of existing porfolio and mandate in place.

Mathetmatical function does not consider

qualitative risk e.g. liquidity risk and investor circustances

One way to make mean-variance useful

add constraints e.g. if illiquidity is risk, put illquid assets as a constraint

A) M-V optimization - in practice

If M-V optimization is going to be used, a method will be needed to ensure sensible portfolio weightings:

modified Black litterman approach second type

imposing probability function on market equilibrium and investor’s views are hard to apply so practitioners come up with two methods

First: extracts spirits from market equilibrium model. assume that what we observe the average asset allocation of all my peers is the efficient portfolio and that is the most efficient asset allocation of risky portfolio. from there i work backwards of mean variation optimisation process and let model decide itself the expected return, covaraince, STD of all assets within the portfolio so that the portfolio i observe in the market is the most efficient one. model decides what set of ER, STD so this asset allocation is optimal.

A) M-V optimization - in practice

If M-V optimization is going to be used, a method will be needed to ensure sensible portfolio weightings:

modified Black litterman approach one type

Use the spirit CAPM model of the single market factor.

Impose on investors own view in the E(R) of each asset class e.g. i believe Australian equity should have a spread over Australian cash of 5% and i have expected return and all other classes this is based on investor’s views. Not probability function.

A) M-V optimization - in practice

If M-V optimization is going to be used, a method will be needed to ensure sensible portfolio weightings:

modified Black litterman approach gets over

hypersensitivity of mean-variance optimisation

A) M-V optimization - in practice

Constrain risk relative to benchmark

many managers are given a capitalization-weighted index as performance benchmark, it is relevant to optimize the portfolio construction by constraining the tracking error, or standard deviation of the portfolio excess returns.

A) M-V optimization - in practice

Black litterman assume

asset returns do deviate from its equilibrium level and imbalances in market will push them back.

Two distinct sources of information about future excess returns – investor views and market equilibrium; both sources of information are uncertain and are best expressed as probability distributions.

A) M-V optimization - in practice

Black litterman approach

asset allocation should not be solved in CAPM is single market equilibrium.

expected asset returns reflects combination of market equilibrium model like CAPM and investor’s expectations. both are represented by probability function.

Implied views’ in text: Black-Litterman without investor expectations

A) M-V optimization - in practice

Sensitivity analysis is another tool to make mean-variance model useful

What if i change some key inputs into mean-variance optimisation problem. e.g. small change and observe dramatic change in portfolio performance, be careful in allocating assets into these assets because they wil have significant impact on the performance

A) M-V optimization - in practice

- Impose weighting constraints
- Constrain risk relative to benchmark, i.e. TE (tracking error)
- Use approach of Black & Litterman (1989)
- Use re-sampling to generate the distribution of optimal portfolios

- Use re-sampling to generate the distribution of optimal portfolios

run mean-variance optimisation given constraints, tracking error so i can produce reasonable asset allocation thousands of times.

Generate distribution of asset weights. each asset is going to have a distribution. better ideas how that asset allocation in Australian equity can change in this distribution

M-V as portfolio analysis workhorse

5.Be aware of parameter uncertainty

be aware of parameter uncertainty

M-V as portfolio analysis workhorse

4.Investigate impact of changes, e.g. alter the asset allocation, add new assets, different inputs, etc

Consider other implementation issues

requires client to sell all their properties including their home. do they agree?

all of this practical implementation issues should be considered before you make final decision of asset allocation.

M-V as portfolio analysis workhorse

4.Investigate impact of changes, e.g. alter the asset allocation, add new assets, different inputs, etc

having assset allocation and portfolio outcome is not enough.

run sensitive analysis. key inputs into model. E(r), STD or covariance assumptions in key assets. if beating market index or benchmark portfolio, introduce an overweight, a strategic tilting into your own portfolio to generate excess return.

M-V as portfolio analysis workhorse

- Estimate portfolio outcomes: E(Rp), σp, Sharpe ratio, shortfall

Data-based

run mean-variance optimisation and given you have weighting constrained and tracking error in place to generate set of asset weights, portfolio outcome, STD and other measures of risk.

- Examine hypothetical historical performance
- Simulate by ‘bootstrapping’ from the data