Superviser professor mois alt r msc student george popescu
Download
1 / 39

Superviser: Professor Moisă Altăr MSc Student: George Popescu - PowerPoint PPT Presentation


  • 91 Views
  • Uploaded on

ACADEMY OF ECONOMIC STUDIES DOCTORAL SCHOOL OF FINANCE-BANKING ORDERED MEAN DIFFERENCE AND STOCHASTIC DOMINANCE AS PORTFOLIO PERFORMANCE MEASURES with an approach to cointegration. Superviser: Professor Moisă Altăr MSc Student: George Popescu. Scheme. • THE EQUIVALENT MARGIN

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Superviser: Professor Moisă Altăr MSc Student: George Popescu' - kendall


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Superviser professor mois alt r msc student george popescu

ACADEMY OF ECONOMIC STUDIESDOCTORAL SCHOOL OF FINANCE-BANKINGORDERED MEAN DIFFERENCE AND STOCHASTIC DOMINANCE AS PORTFOLIO PERFORMANCE MEASURESwith an approach to cointegration

Superviser: Professor Moisă Altăr

MSc Student: George Popescu


Scheme

Scheme

• THE EQUIVALENT MARGIN

• THE OMD. UTILITY FUNCTION AND POVERTY GAP FUNCTION.

• STOCHASTIC DOMINANCE

• THE ECONOMETRIC MODEL

• EMPIRICAL APPLICATION


The equivalent margin
THE EQUIVALENT MARGIN

  • r: fund return

    R: benchmark return

    t: penalty levied on the fund return

    x: investment in fund

  • investor’s decision problem:



The omd bowden 2000

P

The OMD(Bowden, 2000)

= the special case when, in the equivalent margin formula, the utility function has the form of a put pay-off


Motivation for this kind of utility function
Motivation for this kind of utility function

  • Investor is interested in obtaining a target return P, being indifferent to values of R in excess of P and negatively exposed if the return falls below the target

  • P- established according to his appetite for risk

  • exactly the converse of the poverty gap function (Davidson and Duclos, 2000)

  • idea from Merton (1981) and Henriksson and Merton (1981)


A and B: two random variablesA second order stochastically dominates (SSD) B up to a poverty line z if:


Davidson and duclos 2000 demonstrate that the ssd condition can be written as

Davidson and Duclos (2000) demonstrate that the SSD condition can be written as:

The Poverty gap function:


Interpretation of ssd condition in terms of poverty gap function

Interpretation of SSD condition in terms of poverty gap function:

The average poverty gap in B (the dominated distribution) is greater than in A (the dominant distribution) for all poverty lines less than or equal to z. There is a longer way from the actual level of income B to the poverty threshold than from the actual level of A to the same poverty threshold.


The put payoff like utility function

The put payoff - like utility function: function:

The poverty gap function:

So: this kind of utility function shows how far we are from the poverty threshold, after we surpassed the threshold


The omd

The OMD function:

Introducing the utility function in the equivalent margin formula gives:

OMD = the average area between the regression curve of the fund return on the benchmark return and the benchmark return itself, taken on the Ox axis

If t(P)>0 for all P, then the fund was superior to the benchmark



Interpretation

Interpretation: of OMD’s

- each investor can be seen as a spectrum of elementary investors (“gnomes” as named by Bowden), each having a put option profile utility function, but differing by the “strike price” (P), which represents the degree of aversion to risk (P moves to the right as the aversion to risk decreases)

tU: independent of the degree of aversion to risk


Testing for ssd

Testing for SSD of OMD’s

or, in terms of the poverty gap function:


Omd for r with r as benchmark

OMD for of OMD’sr with R as benchmark:

OMD for R with r as benchmark:


The econometric model
THE ECONOMETRIC MODEL of OMD’s

  • Using the Forsyhte polynomials, transform the initial regression of the fund return on the benchmark return into a regression of the fund return on a set of regressors whose matrix is orthogonal

  • the benchmark: divided into several indexes

  • insures of non-multicollinearity between independent variables



The estimated equation

The estimated equation: of OMD’s

The estimated values for OMD [t(P)]


Empirical application
EMPIRICAL APPLICATION of OMD’s

  • Data:

    • r: Capital Plus return (VUAN series)

    • R:mutual fund index return (IFM series)

  • Period:

    • 3 January 2000 - 1 April 2002

  • Frequency:

    • weekly

  • Number of observations:

    • 118


Initial gross regression equation 34 regressors

Initial (gross) regression equation (34 regressors): of OMD’s

Only the significant regressors maintained in terms of t-Statistic (p-values <0.05):





Computation of omd

COMPUTATION OF OMD of OMD’s

- series sorted in ascending order after the IFM values


Interpretation1
Interpretation: of OMD’s

  • OMD positive for every realisation of the benchamark the fund was superior (OMD dominant) to the benchmark and preferred by every risk averse investor, no matter his degree of aversion to risk (because if OMD is positive, then the equivalent margin, which is a weighted average of OMD’s, is also positive)


  • Preferred by both less and more risk averse investors of OMD’s

  • a downward trend the more risk averse investors prefer more than the less risk averse investors the fund

  • the fund added utility to both less and more risk averse investors, but the more risk averse ones appreciate more the utility given by the fund than the less risk averse investors.



  • The area is always positive the fund was OMD dominant over the market, though there were points where the fund return was less than the benchmark return

  • Inconvenient: the first values for OMD are computed using few values

  • Remedy: Baysian approach; I tried implement the exponentially weighted OMD (EWOMD), which gives less weighting to the first values


Did the fund ssd the benchmark inverting the benchmark

Did the fund SSD the benchmark? over the market, though there were points where the fund return was less than the benchmark returnInverting the benchmark:

The regression to be estimated:


Verifying the ols presumptions1
Verifying the OLS presumptions: over the market, though there were points where the fund return was less than the benchmark return


The omd for ifm
The OMD for IFM over the market, though there were points where the fund return was less than the benchmark return


Interpretation2
Interpretation: over the market, though there were points where the fund return was less than the benchmark return

  • OMD is not negative for all the fund return values the fund did not SSD the market (represented by the benchmark)

  • not always the poverty gap was less for the fund than for the benchmark

  • the fund SSD the benchmark only for the greater values of the fund returns the fund was preferred especially by the more risk averse investors (who fix lower levels they wish the fund to attain)


An approach to cointegration
AN APPROACH TO COINTEGRATION over the market, though there were points where the fund return was less than the benchmark return

  • both the OMD measure and the cointegration theory describe long run behaviour

  • the fund is allowed to have temporary fall below the benchmark, but these falls do not affect the overall conclusion if the long run behaviour indicates the superiority of the fund

  • Does exist a cointegration relation between VUAN and IFM that verifies the superiority of the fund?


Vuan and ifm series non stationary

VUAN and IFM series: non-stationary over the market, though there were points where the fund return was less than the benchmark return

VAR(3) system


Var 3 and not var 2 because of
VAR(3) and not VAR(2) because of: over the market, though there were points where the fund return was less than the benchmark return

  • LR test

  • Akaike and Schwartz

  • lack of autocorrelation of residuals


Apply the johansen test to find a cointegrating relation
Apply the Johansen test to find a cointegrating relation: over the market, though there were points where the fund return was less than the benchmark return

  • The dominance of the fund in terms of OMD verified by the cointegrating relation


Remained to be developed
Remained to be developed: over the market, though there were points where the fund return was less than the benchmark return

  • Computation of OMD (the first values: computed using few values) - Baysian approach, EWOMD

  • equivalent margin - martingale measures


ad