5.1 Weaknesses of Markowitz Model

Question 1

• A strict following of Markowitz optimization often results in ___ which are either impossible or at least impracticable
• If the optimizer is run without constraints, it will very often recommend ___ in some assets: BUT–> ___
• If run with a positive constraint, the problem is ___ but does not disappear
• The model will then often result in a portfolio with zero holdings in many assets
  and extreme weights in some assets. Such portfolios are rather counterintuitive

Answer 1

extreme allocations

extreme
negative weights ;
fund managers are often not allowed to take
short positions (at least not in the long run)

moderated

Short-selling –> When stock is believed to be overvalued

Question 2

Large __ of allocations to __ changes in input data
* Small changes in input data of only some asset classes can change allocations of
all asset classes strongly
* Such portfolios will not be used by asset managers because ___

Answer 2

sensitivity; small

their return might be
disastrous with only small changes in the input data (variance, covariance, expected return)

Question 3

It needs too much data
* Depending on the number of assets, the __ becomes too large.
– The number of elements of a covariance matrix is the ___
* It requires the ___ for each of the assets to be optimized.
* These two inputs often lead to ___.

Answer 3

covariance matrix

number of assets
squared

expected returns

estimation errors

Question 4

Estimation error
* Ex-post performance of optimized portfolios depends mainly on the quality of ___, which are more unpredictable than the covariances
* Often, historical data is used to say something about the expected return. What is the issue with this?
* Historical data can contain a lot of noise and by itself does not say anything about
___

Answer 4

prognosis of returns

Might reinforce errors

future returns or future covariances

Question 5

Markowitz does not consider market capitalization

• Markowitz’ model does not account for market capitalization weights of assets
• If assets with a low level of capitalization have high-expected returns and are
  negatively correlated with other assets in the portfolio, the model can suggest a
  ___
• This poses a problem, especially when adding a ___. The model then often suggests ___

Answer 5

high portfolio weight

shorting constraint

very high weights in assets with a low level of capitalization

Question 6

Estimation error
* The theory assumes a ___, which can lead to errors in the
estimation since __ often does not hold in practice.

• In particular, in
  periods of crisis, it may lead to ___ of the portfolio‘s risk (WHY?)
• Classical Markowitz optimization might be an „estimation error maximization “ as
  often most extreme allocations will have the ___ estimation errors:
  – Markowitz’ optimizers __ securities with high expected returns and
  negative correlation and __ those with low expected returns and
  positive correlation.
  – These securities are, according to Michaud (1998), most prone to be subject to
  ___

Answer 6

normal distribution

underestimation

highest

overweight; underweight

large estimation errors

Question 7

The theory ignores the uncertainty and estimation errors of the inputs
* The real value of parameters can only be estimated and not measured exactly
* Thus, input parameter will always have ___
* Also, the resulting portfolio frontier will itself have a variance (____)
* Example:
– The yearly return from S&P 500 from 2003 to 2019 was about 8.79%
– The yearly standard deviation in this period was about 13.40%
– Average return at a 5% significance level will then be in a confidence interval between -17.47% (8.79% - 1.9613.4%) and 35.05% (8.79%+1.9613.4%)

Answer 7

a degree of error

it is not unique

Question 8

Markowitz problems are mainly problems of implementation and input data
* Overall, the theory and logic behind Markowitz portfolio theory is sound

• The problem resulting in practice are mainly implementation problems
• Mean variance optimization ___ statistically estimated data
• The power of the optimization algorithm is far greater than ___
• As we are dealing with statistical data, we have to use statistical methods
  – This is often neglected in the application of …

Answer 8

overfits

the level of investment information in the input data

mean-variance efficiency