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

Question 1

3 approaches to asset allocation

Answer 1

–Static strategic asset allocation (SAA)

–Dynamic asset allocation (DSAA / strategic tilting)

–Tactical asset allocation (TAA)

Question 2

–Static strategic asset allocation (SAA)

Answer 2

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

Question 3

Dynamic asset allocation

–Tactical asset allocation (TAA)

features

Answer 3

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

Question 4

Dynamic asset allocation

features

Answer 4

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

Question 5

Modern Portfolio Theory

Answer 5

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

Question 6

Theoretical issues with traditional MPT

4. Portfolio optimization across all available assets

In practice, don’t throw thousands of investable assets

Answer 6

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

Question 7

Theoretical issues with traditional MPT

4. Portfolio optimization across all available assets

Answer 7

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

Question 8

Theoretical issues with traditional MPT

3.

Assumes risk aversion is only investor difference that matters

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

Answer 8

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)

Question 9

Theoretical issues with traditional MPT

1. Single Period model

Answer 9

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

Question 10

Theoretical issues with traditional MPT

1. Investment horizon is undefined

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

Answer 10

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

Question 11

Theoretical issues with traditional MPT

1. Investment horizon is undefined

Answer 11

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.

Question 12

How portfolios are built in practice

Analysis tool

computer program does not understand

Answer 12

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.

Question 13

How portfolios are built in practice

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

Answer 13

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

Question 14

How portfolios are built in practice

•Widespread pursuit of active returns (‘alpha’)

Answer 14

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

Question 15

How portfolios are built in practice

•Tiered approach

Answer 15

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

Question 16

How portfolios are built in practice

industry norms

Answer 16

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.

Question 17

How portfolios are built in practice

legacy portfolio

Answer 17

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.

Question 18

Mathetmatical function does not consider

Answer 18

qualitative risk e.g. liquidity risk and investor circustances

Question 19

One way to make mean-variance useful

Answer 19

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

Question 20

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

Answer 20

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.

Question 21

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

Answer 21

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.

Question 22

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

Answer 22

hypersensitivity of mean-variance optimisation

Question 23

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:

Constrain risk relative to benchmark

Answer 23

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.

Question 24

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:

Black litterman assume

Answer 24

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.

Question 25

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:

Black litterman approach

Answer 25

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

Question 26

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:

Answer 26

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

Question 27

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:

Answer 27

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

Question 28

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

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

Answer 28

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

Question 29

M-V as portfolio analysis workhorse

5.Be aware of parameter uncertainty

Answer 29

be aware of parameter uncertainty

Question 30

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

Answer 30

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.

Question 31

M-V as portfolio analysis workhorse

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

Answer 31

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.

Question 32

M-V as portfolio analysis workhorse

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

Data-based

Answer 32

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

Question 33

M-V as portfolio analysis workhorse

2. Represent the distribution of asset returns

Answer 33

forcast E(R), standard deviation and covariance matrix of all the possible asset classes in the portfolio

a)Data-based (‘non-parametric’)

• do not impose distribution assumptions. normal distribution and constant return
• use historical available data

b)Model-based (‘parametric’; E(R)s and covariance matrix)

• to forecast E(r) and covariance matrix
• requires strong assumptions of asset returns. for some assets these assumptions do not hold
• Australian cash are going to be highly correlated

Question 34

M-V as portfolio analysis workhorse

1.Nominate a baseline portfolio

Answer 34

asset allocation of average holding of peers of benchmark.

Question 35

M-V as portfolio analysis workhorse

Answer 35

1. Nominate a baseline portfolio
2. Represent the distribution of asset returns
   a) Data-based (‘non-parametric’)
   b) Model-based (‘parametric’; E(R)s and covariance matrix)
3. Estimate portfolio outcomes: E(Rp), σp, Sharpe ratio, shortfall
   a) Data-based:

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

b)Model-based:

• Directly estimate portfolio statistics (single period only)
• Simulate by drawing from the model (facilitates multiple periods)

4. Investigate impact of changes, e.g. alter the asset allocation, add new assets, different inputs, etc
5. Be aware of parameter uncertainty

Question 36

Applying M-V analysis: Considerations

Missing variables e.g. liquidity, intra-period cash flows

Answer 36

quantifiable measure of risk e.g. probability of lost, STD, we have way to evaluate to finetune.

other risks that are important for investors to achieve their objectives e.g. business risk, own career, property. these should be considered before you make your final decision of asset allocation.

Question 37

M-V framework can provide the basis for a portfolio analysis workhorse:

Answer 37

–Generate basic measures of portfolio risk and return

–Conduct sensitivity analysis, e.g. asset weight changes

–Basis for simulations

Question 38

mean-variance model mechanically allocates

Answer 38

allocates funds to achieve a marginally higher expected return at a given level portfolio variance.

It doesn’t understand diversification across asset classes, let alone fundamental risk factors.

It doesn’t consider investors’ specific circumstances, for instance accessibility to financial products/market sectors.

Question 39

mean-variance model

hypersensitivity

If your estimation of expected return of one asset class is biased,

Answer 39

If your estimation of expected return of one asset class is biased, that one “trivial” error, optimization model can amplify that one parameter error and change asset allocation completely.

Mean-variance optimization tend to overweight securities of large estimated returns, negative correlations and small standard deviations.

Question 40

How much of portfolio return variations can be explained by asset allocation decisions ON AVERAGE?

Answer 40

90%

Question 41

CFS Freedom Fund (hyperthetical) has an asset allocation target of 80-20 mix of growth assets and fixed income. The manager is allowed a 5% band either way around the target asset allocation. Occasionally the actual asset allocation may deviate from the defined band of asset allocation. If appproved by the board, the manager may take on long or short positions in some assets over a short period of time to generate excess returns. Which one of the following best describe the asset allocation apporach of the fund?

Answer 41

static strategic asset allocation overlayed with tactical asset allocation

Question 42

An optimizer is used to generate mean-variance optimal portfolios. Some of the portfolios contain weightings of over 100% in international fixed income, the majority of which is offset by large short positions in local fixed income. What is the most likely source of this result?

Answer 42

international fixed income has been given a higher expected return, while both asset classes make a similar contribution to total portfolio risk.

Question 43

How portfolios are built in practice? Choose all correct statements.

Answer 43

Tiered approach to portfolio construction along the dimensions of: asset classes, sub-classes, asset managers, asset selection

Industry “norms”, eg. average asset allocation target of all similar funds

Legacy portfolio as starting point with marginal changes to improve performance or other particular objectives

Considerations of liquidity need, tax, cost, asset availablity, fund governance may all play important role in the asset allocation decision.

Question 44

Possible measures to mitigate the hyper-sensitivity problem of Optimizer may include

Answer 44

weighting constraint, constraint risk relative to a benchmark (so that the portfolio weights don’t wander away too much from the peers), or approach that incorporates investor’s expectations.

Question 45

Problems with MPT

Answer 45

Single Period Model

Does not incorporate investor’s objectives. does not incorporate dynamics of investment opportunities

Question 46

CFS Freedom Fund (hyperthetical) has an asset allocation target of 80-20 mix of growth assets and fixed income. The manager is allowed a 5% band either way around the target asset allocation. Occasionally the actual asset allocation may deviate from the defined band of asset allocation. If appproved by the board, the manager may take on long or short positions in some assets over a short period of time to generate excess returns. Which one of the following best describe the asset allocation apporach of the fund

Answer 46

band: deviate from this band to take advantage of temporary market inefficiences

static strategic asset allocation overlayed with tactical asset allocation.

static strategi asset allocation is for long term investment horizon. tactical is for short period.

Question 47

An optimizer is used to generate mean-variance optimal portfolios. Some of the portfolios contain weightings of over 100% in international fixed income, the majority of which is offset by large short positions in local fixed income. What is the most likely source of this result?

Answer 47

International fixed income has been given a higher expected return, while both asset classes make a similar contribution to total portfolio risk.

optimisier is a mathematical process chases highest level of portfolio return given level of risk.

Question 48

How portfolios are built in practice?

Answer 48

B

Tiered approach to portfolio construction along the dimensions of: asset classes, sub-classes, asset managers, asset selection. “Fill the bucket”

C

Industry “norms”, eg. average asset allocation target of all similar funds. esp for managers given a benchmark or performance evaluated against a performance

D

Legacy portfolio as starting point with marginal changes to improve performance or other particular objectives. take over portfolio, mandate already there. certain assets you can invest in, band.

E

Considerations of liquidity need, tax, cost, asset availablity, fund governance may all play important role in the asset allocation decision.

Question 49

How to use mean-variance optimisation?

Answer 49

input historical returns of all asset classes and run “solver” in Excel so that the optimal portfoio weights are generated to produce the highest portfolio return or minimum portfolio variance.

Question 50

Given historial returns….

Answer 50

run mean-variance optimisatoin to generate aset weights

Question 51

How does shifting the time horizon to 5 years under the bootstrap influence the risk measures?

Answer 51

Use of bootstrap methods can be inappropriate when returns are NOT independent through time.

Serial correlation of 0.3 for the investor’s portfolio suggests this is indeed the case. Implication is that the bootstrap in particular may under-estimate the risk of the investor’s portfolio over multiple years, i.e. the 5 year portfolio risk may be greater than the bootstrap implie

Below are the historical means. Current AC yields are around 1%-2%, so how can 7% returns on these assets be expected going forward? Also, it is probably unreasonable to expect WE to earn 1- 2% less than AE and only slightly more than WFI going forward

Question 52

Historical mean returns can be questionable as measures for expected returns looking forward b/c

Answer 52

Risk associated with events not captured in the data history

About other forms of risk: illiquidity, business risk, governance failures, etc

How the portfolio meets the needs of the end-investor, e.g. is it utility maximizing? what if the investor has other assets? where is the investor in their life cycle?

Question 53

Should investors attempt to eliminate risk, at least as far as possible?

Answer 53

Investor circumstances may matter. Does the investor have some comparative advantage (disadvantage) that makes places them in a better (worse) position to accept certain types of risk with a view to increasing return?

For instance, long-term investors are better placed to buy illiquid assets, and capture ‘illiquidity premiums’

Question 54

Scrutinize the unconstrained weightings. What is the optimizer doing?

Answer 54

Optimizer willingly goes short

. − Starts with relatively balanced minimum variance portfolio of mainly defensive asset classes.

− To secure higher returns, the optimizer increasingly goes long AE and WFI, funded by shorting all other assets classes (especially AFI).

− This captures differential returns for asset classes with similar risk profiles. For instance, it favors AE as the highest returning ‘risk’ asset; and goes long WFI/short AFI. Weightings are very impractical.

Question 55

Scrutinize the long-only weightings. What is the optimizer doing?

Answer 55

Again starts with relatively balanced minimum variance portfolio of mainly defensive asset classes.

− Optimizer captures additional returns by moving towards WFI and then AE. These are the defensive and growth assets with the highest (historic) returns.

• Also, WFI is favored over AFI due to a lower correlation with AE plus lower standard deviation. − Other assets such as WE and LP barely get a look in. Portfolio is imbalanced.

− Solver can’t satisfy highest return requirements once return > highest asset class return (AE) as unable to go short. Stays at 100% equity investment from return = minimum variance return + 0.25% onwards.

Question 56

The inputs to mean variance optimization are

Answer 56

the expected returns, variances and covariances of each asset class.

Question 57

Optimization using adjusted returns suggested weightings now make sense for most part.

except

Answer 57

Direct property is the key exception. This is due to the fact that its contribution to portfolio risk is understated given smoothed and lagged (appraisal-based) returns. The 10% constraint is imposed to avoid DP emerging as a dominant asset, which is clearly counter-factual.

Without the 10% constraint, direct property is 32.7% of the minimum variance portfolio

Question 58

Optimization using adjusted returns

Answer 58

suggested weightings now make sense for most part. This arises because the expected returns are in better alignment with the contribution of assets to portfolio risk

NB: WFI is still being favored over AFI, at least at lower levels of returns. Standard deviation gives the clue why: WFI 3.44%, AFI 4.30% pa

Question 59

Usefulness of analysis

The aim is to use the ‘Solver’ add-in in Excel to estimate the mean-variance efficient frontier of portfolios under the three conditions listed below.

(a) Unconstrained portfolios i.e. (short positions are permitted), with inputs based on historic data without adjustment.
(b) Long-only portfolios, with inputs based on historic data without adjustment.
(c) Unconstrained portfolios, with expected returns imposed, i,e. the mean return for each asset class is to be adjusted towards certain target compound expected returns. The target returns and associated monthly means for ln(1+R) can be found in the worksheet named ‘E(R) adjust’.

Answer 59

Generated weightings are sensitive to assumptions – assumed returns and the overall set-up (e.g. constraints) – and hence need to be used with caution.

Sample means give highly unreliable results. The output based on adjusted returns makes more sense, and might be (cautiously) used as a reference point when building portfolios.

Question 60

Problems with using traditional mean-variance optimization to set asset allocation in practice

4. Investment is typically a multi-period, dynamic process, not a one-shot event

Answer 60

A single period approach is simplistic. Investment typically continues beyond any assumed holding period. Further, setting a defined holding period ignores any opportunities to respond to changes in the interim.

Question 61

Problems with using traditional mean-variance optimization to set asset allocation in practice

Answer 61

1. Hyper-sensitivity to uncertain inputs
2. Objectives
3. Key risks may be missing from the analysis
4. Investment is typically a multi-period, dynamic process, not a one-shot event

Question 62

things that don’t invalidate use of optimizers, but lead to difficulties in doing so

asset forecasting

Answer 62

Generating forecasts is a non-trivial exercise. Only limited guidance or distorted data may be available for some assets. Costs like taxes and transaction costs matter, but are tricky to incorporate. The output relies heavily on the inputs (see point 1), but good inputs are hard to generate.

Question 63

things that don’t invalidate use of optimizers, but lead to difficulties in doing so

Deciding which portfolio you want on the efficient frontier

Answer 63

The trade-off risk and return is often difficult to characterize, i.e. determining risk tolerance, and optimizing ‘utility’. The MPT notion that all investors will hold the ‘tangent portfolio’ with maximum Sharpe ratio assume the existence of a risk-free asset and the ability to borrow (i.e. leverage the portfolio). This assumption is tenuous in practice.

Question 64

things that don’t invalidate use of optimizers, but lead to difficulties in doing so

investment horizon

Answer 64

Need to settle on a specific investment horizon. As an essentially single-period model, a choice of specific investment horizon needs to be made to do the analysis, e.g. quarterly, yearly, multiple years, etc. This choice is not straightforward, and can often be arbitrary.

Further, the choice matters to the results if returns are not iid1

Question 65

Measurement of risk and diversification potential using historically-based statistics like standard deviation and correlation has a whole range of shortcomings.

Correlation and standard deviations can be distorted downwards

Answer 65

Correlation and standard deviations can be distorted downwards when prices adjust with a lag due to aspects like thin trading, appraisal valuations.

In all these cases, diversification benefits can be over-stated and risk potentially under-stated.

Question 66

Measurement of risk and diversification potential using historically-based statistics like standard deviation and correlation has a whole range of shortcomings.

measurement period

Answer 66

Historically-based statistics represent what happened on average over a particular measurement period. Both standard deviation and correlation can be unstable over time

Question 67

Measurement of risk and diversification potential using historically-based statistics like standard deviation and correlation has a whole range of shortcomings.

normal distribution

Answer 67

Asset returns are not well described by a single normal distribution. It is well known that returns have fat tails, and are sometimes skewed.

Question 68

portfolio optimisation based on historical measures is not reliable because T

Answer 68

They don’t reveal the full story.

Supplementing with an alternative approach can be very useful, if not essential.

Question 69

strategic asset allocation

fixed

Answer 69

fixed strategic asset allocation would be consistent with the constant investment opportunities and risk rolerances

Question 70

strategic asset allocation

Answer 70

based on long-term goals. e.g. need asset allocation today for the next 30 years.

Question 71

tactical asset allocation respnds to

Answer 71

short-term changes in investment opportunites

Question 72

how do some active allocation managers use tactical asset allocation?

Answer 72

they may define a band around strategic weights within which weights my be set in the short term but never deviate by so much so that tactical bets overwhelm the strategic allocation

e.g. long-term average target weight of 50% stocks with a plus minus 10 percent band yielding a 40-60% range would incorporate both strategic and tactical allocations

Question 73

when will allocations be set tactically

Answer 73

investors who frequently adjust their exposure to stocks, bonds and cash i.e. market timer

they seek to profit from short-term market movements in the market, expect to change their asset weights in the near future and may not worry much about the long-term implications of their average weights

Question 74

dynamic asset allocation is driven by

Answer 74

changes in risk tolerance typically inducated by cumulative performance relative to investment goals or an approaching investment horizon

Question 75

Why are the results from the optimiser so sensitive

Answer 75

Small changes in ER , optimiser will switch from one combination to another

weights on assets in the portfolio may be unstable or take extreme values

go long in one and short in the other

optimiser does not see this as a problem because it does not attach any significance to wehther a particular asset is held long, sold short or omitted.

Question 76

real problem with optimiser

Answer 76

optimiser’s sensitivity to the inputs

we do not know the true values of the necessary model inputs: ER, variances and covariances

if we knew, then we would be confident that optimiser is giving accurate advice

Question 77

classic MV optimisatoin assumes that

Answer 77

investor prefers a portfolio of securities that offers maximum ER for a given level of risk

Question 78

Potential benefits of MV optimisers

Answer 78

1. Convenient framework to integrate simple but important client constraints and objectives within portfolio
2. Efficient use of investment info: designed to use info optimically while ad hoc weighting can be counterproductive
3. Portfolio optimisers can process large amounts of info quickly, good for large institutional that needs to determine impact of new info on its portfolios quickly

Question 79

MV optimisers overweight?

Answer 79

optimisers significantly overweight (underweight) securities that have large (small) ER, negative (positive) correlation) and small (high) variances

Question 80

MV optimisers are

because

Answer 80

estimation error maximisions because risk and return are subject to estimation error

Question 81

MV optimisation ignores fundamental factors including

Answer 81

liquidity i.e. percentage of company’s market capitalisation represented by portfolio holding

Question 82

Asset Allocation With Respect to a Benchmark

How can this enhance MV optimisation

Answer 82

benchmark can significantly alter the characteristics of MV-optimal asset allocations. In general, benchmark asset allocation is strongly dependent on the economic characteristics of the liabilities.

It is consequently far less time-period dependent or unstable and appears to have substantially more practical investment value.