Portfolio Optimization with an Envelope-based Multi

Portfolio Optimization with an
Envelope-based Multi-objective Evolutionary Algorithm
J. Branke1 , B. Scheckenbach1,2 , M. Stein1 , K. Deb3 , H. Schmeck1
Institute AIFB, University of Karlsruhe, Germany
SAP AG, Walldorf, Germany
Kanpur Institute of Technology, India
The problem of portfolio selection is a standard problem in financial engineering and has
received a lot of attention in recent decades. Classical mean-variance portfolio selection aims
at simultaneously maximizing the expected return of the portfolio and minimizing portfolio
variance. In the case of linear constraints, the problem can be solved efficiently by parametric
quadratic programming (i.e., variants of Markowitz’ critical line algorithm). However, there
are many real-world constraints that lead to a non-convex search space, e.g. cardinality
constraints which limit the number of different assets in a portfolio, or minimum buy-in
thresholds. As a consequence, the efficient approaches for the convex problem can no longer
be applied, and new solutions are needed.
In this paper, we propose to integrate an active set algorithm optimized for portfolio
selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA
come up with some convex subsets of the set of all feasible portfolios, solve a critical line
algorithm for each subset, and then merge the partial solutions to form the solution of the
original non-convex problem. We show that the resulting envelope-based MOEA significantly
outperforms existing MOEAs.
In finance, a portfolio is a collection of assets held by an institution or a private individual. The
portfolio selection problem seeks an optimal way to distribute a given budget on a set of available
The problem usually has two criteria: Expected return (mean profit) is to be maximized, while
the risk is to be minimized. The optimal solution depends on the user’s risk aversion. As it is
often difficult to weigh the two criteria before the alternatives are known, it is common to search
for the whole set of efficient or Pareto-optimal solutions, i.e. all solutions that can not be improved
upon in both objectives simultaneously. This set of solutions is often called “efficient frontier”,
or “Pareto-optimal front”. Another motivation for searching for the whole efficient frontier stems
from the fact that in many applications, a set of solutions with different trade-offs with respect
to the optimization criteria are desired, e.g. because a bank wants to offer its customers different
choices depending on their risk aversion.
A natural measure for risk is the variance of the portfolio return. Mean-variance optimization
is probably the most popular approach to portfolio selection. It was introduced more than 50
years ago in the pioneering work by Markowitz (1952, 1956). The basic assumptions in his theory
are a rational investor with either multivariate normally distributed asset returns or, in the case of
arbitrary returns, a quadratic utility function (Huang and Litzenberger, 1988). It has been shown
that if these assumptions are valid, the optimal portfolio for the investor lies on the mean-variance
efficient frontier.
The basic mean-variance portfolio selection problem we consider in this paper can be formalized
as follows:
min V (w) = wT Qw
max wT µ = E
(minimize portfolio variance)
(maximize expected return)
(budget constraint)
subject to
wT e = 1
0 ≤ wi ≤ 1
i = 1, . . . , N
where N is the number of assets to choose from, Q denotes the covariance matrix of all
investment alternatives, µi is the expected return of asset i, and e is the unit vector. The decision
variables wi determine what share of the budget should be distributed to asset i, and Eq.1c makes
sure that the sum of all wi is equal to one, i.e. that the whole budget is invested.
Computationally efficient algorithms that calculate a single point or even the whole efficient
frontier of this basic portfolio selection problem have been discussed in a large number of publications. For a basic introduction to portfolio selection see e.g. Elton et al. (2003). The algorithm
to compute the whole efficient frontier (critical line algorithm) is described in detail in Markowitz
(1987). The result of this algorithm is a sequence of so-called corner portfolios. These corner portfolios define the complete efficient frontier as all other points on the frontier are convex
combinations of the two adjacent corner portfolios.
However, these highly efficient algorithms can not take into account more complex constraints
that lead to a non-convex search space, henceforth called non-convex constraints. Examples for
such constraints which are commonly used in mutual fund management include:
1. Cardinality constraints restrict the number of securities which are allowed in the portfolio.
Often, the maximal number of securities in the portfolio is limited to reduce the management
cost e.g. for monitoring the performance of the companies in the portfolio.
2. The 5-10-40 constraint is based on §60(1) of the German investment law (InvG, 2004).
It defines an upper limit for each individual asset and for the sum of all “heavyweights” in
the portfolio. More specifically, securities of the same issuer are allowed to amount to 5% of
the net asset value of the mutual fund. They are allowed to amount to 10%, however, if the
total share of all assets with a share between 5% and 10% is less than 40% of the net asset
3. Buy-in thresholds demand that if an asset is included in the portfolio, at least some
amount l should be bought. The main reason for such a constraint is to reduce transaction
costs. In principle, this constraint could also be handled by our approach in a straightforward
manner, but is not considered further in this paper.
For convex portfolio selection problems, the critical line algorithm is able to generate the complete (continuous) efficient frontier. In the presence of non-convex constraints, most approaches
found in the literature are based on the -constraint method (see e.g. Miettinen (1998)): Instead
of optimizing both criteria simultaneously, they set the expected return to a constant (i.e. Eq. 1b
becomes a constraint), and solve the resulting quadratic optimization problem to minimize the
variance. Of course, this only generates a single solution on the efficient frontier, and the algorithm
has to be applied many times with different expected returns to obtain a reasonable approximation of the true efficient frontier. Furthermore, as the solution of each quadratic sub-problem is
computationally complex in the presence of non-convex constraints1 , usually heuristics are used
to solve the individual sub-problems, which means that the generated solutions don’t necessarily
lie on the true efficient frontier. Some heuristic approaches like evolutionary algorithms allow to
consider multiple objectives simultaneously, generating a set of solutions approximating the efficient frontier in one run. However, they are still point-based, generating a finite set of alternative
In this paper, we propose to combine multi-objective evolutionary algorithms with an embedded critical line algorithm to solve complex portfolio selection problems with non-convex constraints. The basic idea is to let the EA handle the non-convex constraints and to basically divide
the problem into a set of problems with convex constraints, which can be solved optimally with a
critical line algorithm. The overall solution to the problem is then the combination of the solutions
to the individual convex problems. As we will demonstrate, the approach significantly outperforms other state-of-the-art evolutionary algorithms. Furthermore, to our knowledge, this is the
first approach to non-convex portfolio selection yielding a continuous solution set, as opposed to
the discrete solution set generated by the point based approaches.
Our paper is structured as follows. First, we provide a brief overview on approaches to portfolio
selection subject to non-convex constraints. A short introduction to multi-objective evolutionary
algorithms is provided in Section 3, followed in Section 4 by a short description of a state-of-the-art
point-based MOEA which will be used as a reference later on. Our approach, called envelope-based
multi-objective evolutionary algorithm (E-MOEA) is presented in Section 5. Section 6 reports on
the empirical evaluation of our approach. The paper concludes in Section 7 with a summary and
some ideas for future work.
In fact, some variants are NP-complete, e.g. the cardinality constrained portfolios if the maximum cardinality
is a fraction of the total number of assets (Bienstock, 1996)
Related work
The work on non-convex portfolio selection problems can be roughly divided into mixed integer
approaches and metaheuristics which will be discussed in turn.
Mixed Integer Approaches
By adding integer variables, the convex problem presented in the previous section can be extended
to take non-convex constraints into account. For example, buy-in thresholds and cardinality
constraints can be modeled as follows:
min V (w) = wT Qw
subject to
wT µ = E
wT e = 1
ρi ≤ N
lρi ≤ wi ≤ uρi
ρi ∈{0, 1}
i = 1, . . . , N
i = 1...N
where ρi is the binary variable that specifies whether asset i should be included in the portfolio,
and l and u are the lower and upper bounds for the weights if the corresponding asset is included.
The modelling of the 5-10-40 constraint as MIQP is not as straightforward, and requires to
triple the number of variables:
min V (w) = wT Qw
subject to
wT µ = E
wT e = 1
w − 0.05ρ ≤ 0.05e
t − 0.1ρ ≤ 0
t−w ≤0
w + 0.1ρ − t ≤ 0.1e
tT e ≤ 0.4
w, t ≥ 0
ρi ∈{0, 1}
i = 1, . . . , N
Thereby, ρi = 1 implies that asset i is allowed up to 10%, while ρi = 0 restricts asset i to
5%. If ρi = 0, Inequality 3e requires ti = 0, otherwise ti = wi by Inequalities 3e, 3f, and 3g.
Inequalities 3h and 3i restrict the “heavyweights” to 10% and their sum to 40%.
Once formulated appropriately, any of the available mixed integer quadratic programming
(MIQP) solvers can be used to solve the model. Software packages that contain such a solver
can be found at NEOS Guide (2006), although – compared to the number of available QPsolvers – there are by far fewer programs with the required capability. In any case, there is
no guarantee for getting the optimal portfolio quickly. If there is not enough time to allow the
algorithm to terminate regularly, the best valid portfolio calculated so far can be used instead — a
normal practice when working with mixed integer solvers. Of course, this abandons the optimality
For further information about the mixed integer approach to the cardinality constrained problem without using an external MIQP-solver, the reader is referred to Bienstock (1996). Bienstock
examined the computational complexity of the problem, tested a self-developed branch-and-cut
algorithm using disjunctive cuts, and discussed some of the implementation problems that occurred.
Jobst et al. (2001) use a branch-and-bound algorithm to solve the cardinality constrained
problem with buy-in thresholds as well as an index tracking problem, where a portfolio subject
to cardinality constraints should perform as closely as possible to an index in terms of mean and
variance. As they calculate many points on the efficient frontier, the available time is too short
for individually solving each MIQP to optimality. Therefore, they limit the number of nodes in
the search tree of the branch-and-bound algorithm for each given expected return E. To speed
up the algorithm further, a previously calculated solution for an adjacent point is used as a warm
start solution for the new value of expected return.
Advantages of the mixed integer approaches are certainly that optimality is guaranteed if the
algorithm terminates. On the other hand, running time is difficult to predict, and modelling
complex constraints is not always straightforward. Finally, the efficient frontier can only be
calculated pointwise, a mixed integer version of the critical line algorithm is not known.
Because of the potentially extensive running times of the mixed integer approaches and their
complex implementation, many researchers have turned to metaheuristics. The term metaheuristic
usually describes a generic optimization principle that is widely applicable to many different
problem domains. Very often, the basic idea behind a metaheuristic is inspired by nature, be it a
physical process like simulated annealing (SA) or biologically inspired algorithms like ant colony
optimization (ACO) or evolutionary algorithms (EAs). Such metaheuristics do not guarantee
optimality, but it is hoped that they find reasonable solutions quickly.
There are several publications discussing the use of metaheuristics to solve non-convex portfolio
selection problems. Most of them apply the metaheuristic just to solve the MIQP with a given
desired expected return, i.e. to generate a single point of the efficient frontier in mean-variance
objective space.
Chang et al. (2000) compare an EA, tabu search, and SA to solve portfolio selection problems
where each solution has to contain a predetermined number of assets. Because none of the approaches turned out to be a clear winner, they suggest to run all three and combine the results.
Schaerf (2002) improves on the work of Chang et al. by testing several neighborhood relations for
tabu search. Crama and Schyns (2003) apply simulated annealing to a portfolio selection problem
with cardinality constraints as well as turnover and trading restrictions. They particularly focused
on ways to handle constraints, partially by enforcing feasibility, partially by introducing penalties.
A hybrid between SA and EA is proposed in Maringer and Kellerer (2003). In Maringer (2002),
ACO is used only to determine the relevant assets for a cardinality-constrained portfolio selection
problem, while the weights are determined with a conventional QP solver. The only authors who,
to our knowledge, address the 5-10-40 constraint are Derigs and Nickel (2001). They use SA for
optimization, but do not provide details on how they ensure feasibility of solutions. In Derigs
and Nickel (2003), they expand their previous work, but the focus is put on developing a decision
support system for portfolio selection. In Ehrgott et al. (2004), a problem with five objectives and
non-convex constraints is considered, but the five objectives are accumulated into one based on
multiattribute utility theory. Then local search, SA, tabu search and an EA are used to solve the
resulting single-objective mixed-integer problem.
Eddelbüttel (1996) uses a QP solver within a genetic algorithm to solve the index-tracking
problem. Here, the GA determines which assets should be included in the portfolio, while the
optimal weights are calculated by the QP solver.
Instead of setting the expected return E as constant and then solving a separate single-objective
optimization problem for several E as do all of the above methods, Streichert et al. (2003, 2004a,b),
apply a multi-objective evolutionary algorithm (MOEA). MOEAs are variants of EAs that exploit
the fact that EAs work with a population of solutions, and simultaneously search for a set of
efficient alternatives in a multi-objective setting, see also the following section. Note that while
this approach generates several solutions along the efficient frontier in one run, it is still pointbased (i.e. it only generates a discrete set of solutions). Since we will use this algorithm for
empirical comparison with our approach, it will be discussed in more depth below.
Other publications reporting on the use of MOEAs for portfolio selection include Lin and Wang
(2002) who consider roundlots2 , and Fieldsend et al. (2004), who address the cardinality issue but
consider the number of allowed assets, K, as a third objective to be minimized. Armananzas and
Lozano (2005) apply multi-objective variants of greedy search, SA and ACO to the cardinalityconstrained portfolio selection problem. Schlottmann and Seese (2005) consider credit portfolio
optimization and use a gradient-based local search within their MOEA.
General advantages of metaheuristic approaches are certainly their flexibility. It would be
In a portfolio selection problem with roundlots, an asset can only be bought in multiples of a minimum lot.
This problem has been proven to be NP-complete.
straightforward e.g. to use alternative, risk measures. Also, the multi-objective versions allow to
generate a whole set of solutions, approximating the efficient frontier with a single run.
Multi-objective evolutionary algorithms
Although a detailed introduction into multi-objective evolutionary algorithms (MOEAs) would
exceed the scope of this paper, in this section we will briefly introduce the main ideas which are
needed as foundation for the subsequent sections. For a more detailed introduction to MOEAs,
the reader is referred to Deb (2001) or Coello et al. (2002). A survey on MOEA applications in
finance can be found in Schlottmann and Seese (2004).
Evolutionary algorithms are stochastic iterative optimization heuristics inspired by natural
evolution. Starting with a set of candidate solutions (population), in each iteration (generation),
promising solutions are selected as potential parents (mating selection), and new solutions (individuals) are created by mixing information from the parents (crossover) and slightly modifying
them (mutation). The resulting offspring are then inserted into the population, replacing some
old or less fit solutions (environmental selection). By continually selecting good solutions for reproduction and then creating new solutions based on the knowledge represented in the selected
individuals, the solutions “evolve” and become better and better adapted to the problem to be
solved, just like in nature, where the individuals become better and better adapted to their environment through the means of evolution.
The basic operations of an evolutionary algorithm can be described as follows:
t := 0
initialize P (0)
evaluate P (0)
WHILE (termination criterion not fulfilled) DO
copy selected individuals into mating pool: M (t) := s(P (t))
crossover: M 0 (t) := c(M (t))
mutation: M 00 (t) := m(M 0 (t))
evaluate M 00 (t)
update population: P (t + 1) := u(P (t) ∪ M 00 (t))
t := t + 1
with t denoting the generation counter, P (t) the population at generation t, and s, c, m, and
u representing the different genetic operators. Evolutionary algorithms have proven successful in
a wide variety of applications. For a more detailed introduction to EAs, the reader is referred to
Eiben and Smith (2003).
Because EAs maintain a population of solutions throughout the run, they can also be used to
simultaneously search for a set of solutions approximating the efficient frontier of a multi-objective
The main difference between single objective EAs and MOEAs is the way they rank their
solutions for selection. While in single objective EAs the ranking is unambiguously defined by the
solution quality, this is not so straightforward in the case of multiple objectives. MOEAs have
two goals: they want to drive the population towards the efficient frontier, while at the same
time maintaining a diverse set of alternative solutions. To achieve the first goal, most MOEA
implementations rely on the concept of dominance. Solution A dominates solution B if A is at
least as good as B in all objectives, and better in at least one objective. A solution is called
non-dominated with respect to a set of solutions if and only if it is not dominated by any other
solution in that set.
One particularly popular MOEA variant is the non-dominated sorting genetic algorithm (NSGAII), see Deb (2001). It ranks individuals according to two criteria. First, individuals are ranked
according to non-dominancy: All non-dominated individuals are assigned to Front 1, then they are
removed from the population, again all non-dominated solutions are determined and are assigned
Front 2, etc. until the population is empty. The result of this process is illustrated in Figure 1(a).
Within a front, solutions are ranked according to the crowding distance, which is defined as the
circumference of the rectangle defined by their left and right neighbors, and infinity if there is
no neighbor. This concept is illustrated in Figure 1(b). Individuals with high crowding distance
are preferred, as they are in more isolated regions of the objective space. In the example in Figure 1(b), individuals a and d have the highest priority within the front, followed by individual b
and then c because the rectangle defined by the respective left and right neighbor is larger for
individual b.
front 3
front 2
front 1
(a) Non-dominance sorting to determine fronts
(b) Crowding distance calculation within a
Figure 1: NSGA-II first ranks individuals according to non-dominance sorting (a) and within a
front according to crowding distance (b).
In every iteration, NSGA-II generates p offspring solutions, where p is the population size.
The old and offspring population are then combined, ranked according to the above two criteria,
and the better half forms the new population. For mating selection, tournament selection is used
which randomly draws two solutions from the population and chooses the one on the better front
or, if they are from the same front, the one with the larger crowding distance.
A point-based multi-objective EA
Although there is, to our knowledge, no definite comparison of the different approaches discussed
in Section 2, we consider the approach by Streichert et al. (2003, 2004a,b) as state-of-the-art
metaheuristic. Not only is it one of the few papers applying MOEAs, but they have also tested
and compared a number of variations regarding encoding and operators. We re-implemented
their algorithm, and will use it as reference for empirical comparison with our newly developed
envelope-based MOEA. The algorithm is described below. Note that some adaptations to the
5-10-40 constraint were necessary, as this constraint has not been considered in Streichert et al.
(2003, 2004a,b).
As already mentioned in the introduction, the approach uses a MOEA for optimization. In
particular, it is based on the standard non-dominated sorting genetic algorithm (NSGA-II and its
predecessor NSGA) as described above.
As genetic representation, Streichert et al. (2003, 2004a,b) recommend to use a hybrid binary/realvalued encoding, which is also used by several other successful approaches like Chang et al. (2000).
With this encoding, a solution is defined by a vector of continuous variables c = (c1 , . . . , cN )T
representing the weights of the individual assets. An additional vector of binary variables k =
(k1 , . . . , kN )T is used to indicate if the asset is included in the portfolio at all. The latter vector
allows the EA to easily add or remove an asset by simply flipping the corresponding bit, and thus
facilitates the handling of cardinality constraints.
For a portfolio selection problem that contains a cardinality constraint and buy-in thresholds,
the decoding of the two vectors to get the actual portfolio works as follows (see e.g. Chang et al.
(2000); Streichert et al. (2004a)):
1. All ci are set to zero if ki = 0.
2. If
sign(ki ci ) is more or less than the required cardinality, the solution is repaired by
changing some elements of c. For the maximum cardinality problem, elements are set to 0
in the order of increasing ci (i.e. the assets with the smallest share are set to zero).
3. The vector c is normalized:
c0i = P
4. The final weight wi is calculated:
 l + c0 (1 − |Υ|l)
wi =
 0
if i ∈ Υ
where l is the minimum buy-in threshold and |Υ| denotes the number of elements in Υ.
The 5-10-40 constraint has not yet been considered by Streichert et al., and thus we had to
adapt the decoding and repair mechanism. It works in 7 steps as follows.
2. The vector c is normalized:
wi = P
3. The surplus amount exceeding the 10% threshold is calculated, Ω =
(wi − 0.1). All
wi >0.1
wi > 0.1 are set to 0.1.
4. the surplus Ω has to be redistributed to the weights below 10%. Each weight below 10% is
(0.1 − wi ). If Ψ < Ω, no weight will
raised by the amount (0.1 − wi ) · Ψ
, where Ψ =
0<wi <0.1
have a value above 10% after the first step.
5. In the group with more than 5%, we only accept the assets with the largest weights such
that the sum is still less than or equal to 40%. All others are capped to 5% and the excess
weight is distributed to the the other assets analogously to the above step.
6. If there is not enough room for all the excess weight to be redistributed among the assets
with less than 5%, the remaining is used to fill up the assets between 5% and 10% up to
10% in order of decreasing weight.
7. The previous step may again lead to a violation of the 5-10-40 constraint. In this case, assets
are removed from the 5-10% group in order of increasing weights, and the weight in excess
of 5% is distributed to the other assets in the 5-10% group similar to the previous step.
Note that any valid portfolio for the problem with 5-10-40 constraint contains at least 16
different assets (4 times 10% plus 12 times 5%). If this is the case, the above decoding will result
in a feasible portfolio. By appropriate mutation and crossover operators (see below) we make sure
that the binary string has always at least 16 bits set to “1”.
For both cardinality constraints and the 5-10-40 constraint, the weights after the above repair
steps are written back into the weight-vector of the genotype and overwrite the original values.
This allows the information gained by the repair mechanism to be inherited to the offspring
(Lamarckism) and has been recommended in Streichert et al. (2004b).
For mutation, simple bit flip is used on the binary vector, and Gaussian mutation on the
real-valued vector. For crossover, we use N-point crossover independently on both real-valued and
binary vector. In Streichert et al. (2004a), this crossover operator was reported to be competitive to
other, more complex crossover operators. We follow this suggestion for the cardinality constrained
problem. For the 5-10-40 constraint, as explained above, we need at least 16 assets with ki = 1
for a feasible solution. Therefore, for this constraint we modify the operators on the bit string as
follows. The crossover operator first transfers all bits to the child where both parents are equal.
The remaining bits are traversed in random order and randomly taken from either parent until
the maximum number of zeros has been reached (i.e. N − 16 if N is the number of assets). Any
remaining bits are set to 1. If after mutation the resulting bit string contains less than 16 ones,
some of the performed 1 to 0 bit flips are reversed to make the string valid.
In the remainder of this paper, we will denote this point-based MOEA as P-MOEA.
Envelope-based multi-objective evolutionary algorithm
In this section, we will present our new envelope-based multi-objective evolutionary algorithm (EMOEA) for portfolio selection problems. It combines the efficiency of the critical line algorithm for
calculating the whole continuous front with the ability of multi-objective evolutionary algorithms
to take complex constraints into account and to generate multiple solutions within a single run.
The main idea of our paper is to use the MOEA to define suitable convex subsets of the original
search space, run the critical line algorithm on every subset, and then recombine the partial
solutions to form the complete front.
A single solution (individual of the MOEA) defines a convex subset by specifying how the
non-convex constraints are to be handled. In case of a cardinality constraint, a solution defines
which assets are allowed a weight greater than zero. The corresponding convex problem is just the
standard problem which contains only those variables not forced to zero. Note that, in particular
if the allowed cardinality is much smaller than the total number of available assets, this means
that the generated sub-problem is much smaller than the original problem, which results in a
tremendous reduction of the running time of the critical line algorithm.
For the case of the 5-10-40 constraint, a solution defines which assets are allowed up to 10%
and hence have to be included in the 40% constraint. All other assets are restricted to at most
For each subset, the critical line algorithm can be used to efficiently calculate the whole efficient
frontier of the corresponding standard mean-variance portfolio selection problem. For more details
to the critical line algorithm, the reader is referred to Markowitz (1987). Because we apply the
critical line algorithm to every individual generated by the EA, an efficient implementation is
crucial. We use a modified variant of the algorithm described by Best, M. J. and Kale, J. K.
(2000). For an in-depth discussion of implementation intricacies see Stein et al. (2006).
The result of the critical line algorithm is a front in the mean-variance space which is efficient
for the sub-problem, but not necessarily for the overall problem with non-convex constraints. We
call such a partial front an envelope. The EA is now used to find a collection of such envelopes
which together form a solution to the overall problem.
For this purpose, we use a multi-objective EA based also on the general framework of NSGA-II
(Deb, 2001). But instead of a solution being represented by a single point in the mean-variance
space, now every solution is represented by an envelope in the mean-variance space. An exemplary
population is depicted in Figure 2(a). The example shows that situations where envelopes entirely
dominate other envelopes occur very rarely. Instead, at many points, envelopes intersect with
other envelopes. Even without intersections, many envelopes have dominated and non-dominated
parts. Thus, we had to adapt the non-dominated sorting and crowding distance calculation to
work with envelopes. The basic idea can be described as follows.
We are interested in the non-dominated part of the set union of all envelopes. Let us denote
the non-dominated part of the unit set of all envelopes as (first) aggregated front. Following the
idea of non-dominated sorting, we assign Rank 1 to all individuals contributing at least partially
to the first aggregated front. Then, we iteratively remove these individuals/envelopes from the
population, and determine the aggregated front of the remaining individuals, assigning them the
next higher rank, etc. The resulting ranking and the generated aggregated fronts are depicted in
Figure 2(b).
It is clear that different individuals contribute differently to an aggregated front. Some may
contribute only a small segment of the front, some may contribute large segments. Also, some
parts of the aggregated front may be represented by several individuals. We use this information
to rank the individuals within a front (substituting the crowding distance sorting in NSGA-II).
For this purpose, we determine for each individual the length of the contributed segment of the
aggregated front3 . Parts common to several individuals are shared among those individuals. For
example, if the part contributed solely by an individual i has length 5, and a part with length 4 is
shared with another individual j, the overall contribution of individual i is 5 + 4/2 = 7. Within a
Although in principle it would be possible to calculate the true length of a segment, for reasons of simplicity
we approximated the length by the Euclidean distance between the end points. Another possible criterion would
have been the reduction in hypervolume if the individual is removed.
(a) A population of envelopes.
(b) Corresponding aggregated fronts and assigned ranks.
Figure 2: Ten randomly initialized envelopes and the five corresponding aggregated fronts for the
max-card problem with k = 4 for the Nikkei dataset.
front, individuals contributing more are considered more important. Parts of the efficient frontier
not belonging to the aggregated front are not taken into account. The actual implementation of the
above envelope-based non-dominated sorting is rather tricky, the reader is referred to Scheckenbach
Representation and genetic operators
As discussed above, the EA is only responsible for handling the non-convex constraints, the appropriate weights are then determined by a critical line algorithm. Thus, in principle, a simple
binary encoding would be sufficient. However, we wanted to feed back some information from the
critical line algorithm to the evolutionary algorithm. For this reason, we are using a permutation
encoding. Then, for the maximum cardinality constraint, simply the first K assets are used in
the portfolio. For the 5-10-40 constraint, the first K assets are considered potential heavyweights,
with a share of at most 10%4 and inclusion in the 40% constraint, while all others are restricted
to less than 5%. The parameter K here is variable and also part of the solution encoding.
After the critical line algorithm has been applied, the permutation is sorted with respect to the
average weight an asset had in all corner portfolios that are part of the aggregated front. Thus, an
Note that the weight of these assets can be set below 5% by the critical line algorithm, although they are still
included in the 40% constraint. This helps in the sorting, as such an asset is then moved behind more important
assets that are set to 5%, leading to a smaller chance to be included again after mutation.
asset which received a high weight will appear early on the permutation, and subsequently have
a higher probability to be among the first K after crossover and mutation.
As genetic operators, we use the uniform order based crossover and swap mutation. For the
latter, an asset that belongs to the first K is swapped with an arbitrary other asset. For the
5-10-40 constraint, the parameter K is modified by adding a Gaussian number with mean 0 and
standard deviation Pm . The size is then rounded and capped if necessary.
To further improve the efficiency of our algorithm, we introduced two additional concepts:
duplicate elimination and a variable population size. In duplicate elimination, we remove individuals that share a part of an aggregated front with another individual, but which are nowhere
better than the other individual. The variable population size allows us to increase the number
of individuals in the population if the current first aggregated front consists of more individuals
than would fit into the population. Keeping a fixed population size would then mean to delete
a valuable part of the solution. Note that because our approach is envelope-based, it requires a
much smaller population size than point-based approaches anyway. The alternative to an adaptive
population size, namely to work with an equally large population as the point-based approaches
from the beginning, would have slowed down convergence unnecessarily. Independent of the population size, the number of offspring generated in every iteration remains constant and equal to
the original population size.
Empirical evaluation
Benchmark problems and performance measure
Many authors test their approaches on the publicly available benchmarks provided in the ORlibrary (Beasley, 2006). We will also use some of these benchmarks, namely
P1 The smallest problem, the Hang Seng benchmark consisting of 31 assets.
P2 The S&P benchmark consisting of 98 assets
P3 The largest problem in the OR-library, the Nikkei benchmark consisting of 225 assets.
Because we want to show that our algorithm also scales well, we additionally tested it on
share with
highest variance
variance of
ideal front
share with
lowest yield
ideal front
max. delta-area
ideal delta-area
lowest yield of
ideal front
Figure 3: Ideal and maximum ∆-area.
P4 a benchmark with 500 assets, generated according to a method described in Hirschberger
et al. (ming) and generously provided by Ralph Steuer.
For the cardinality constrained problems, we set the maximum cardinality to K = 4 for P1 and
P2, and to K = 8 for P3 and P4.
Measuring performance in a multi-objective setting is difficult, because it requires the comparison of frontiers (not only solutions). A number of possible performance measures are discussed
e.g. in Zitzler et al. (2003). In the following, we will judge a generated front by its deviation
from the ideal front, which is defined as the efficient frontier of the problem without non-convex
constraints5 . This ideal front is an upper bound on the performance and can be computed efficiently with the critical line algorithm. To measure the deviation, we calculate the area between
the resulting front and the ideal front. One difficulty with area-based methods is to define the
maximum variance and minimum return boundaries to calculate the area, see Figure 3. If these
values are set far apart, extreme portfolios have a very large impact on solution quality. If they
are set too close, some parts of the front may be cut off. Since the appropriate borders are not
clear, we report on two values here: The area using the maximum variance and minimum yield
portfolios from the ideal front (ideal delta-area), and the maximum variance and minimum yield
from any asset in the available universe.
For the problem with 5-10-40 constraint, all assets are restricted by 10%.
Parameter settings
For P-MOEA, we use the same parameter settings as in Streichert et al. (2004a), i.e. a population
size of 250 and tournament size of 8. For the bit string, bit flip mutation with mutation probability
for each bit 2/(number of assets) and N-point crossover with probability 1.0 are applied. For the
real-valued string, mutation is done by adding a value from a Normal distribution with σ = 0.05
to each weight, crossover is again N-point crossover with probability 1.0.
For E-MOEA, the following parameter settings have been chosen without much testing. The
initial population size is set to 30, and 30 individuals are generated in every iteration.
The mutation and crossover operators have been described above. Probability to swap each
of the first K assets for the cardinality problem is 1/K, for the 5-10-40 constrained problem,
probability to swap any of the heavyweights is 1/7.
As discussed before, P-MOEA requires a significantly larger population size, as each individual
only represents a single point, as opposed to a whole envelope as in E-MOEA.
All reported results are averages over 30 runs. Experiments were conducted on a PC with AMD
Sempron 1.6 GHz processor and 1 GB RAM. Maximum allowed running time for the problem with
5-10-40 constraint was set to 500, 1000, 2000, and 4000 CPU seconds for P1, P2, P3, and P4,
respectively. Since the cardinality constrained problem seemed easier, we allowed only half the
running time for each problem.
Test results
The results on all 4 benchmark problems are summarized in Tables 1 to 4. Table 1 reports on
the max-delta-area, i.e. the area between obtained efficient frontier and ideal front with wide
margins, for the cardinality constrained problem at the end of the run. The same information,
but with respect to ideal-delta-area, is provided in Table 2. As can be seen, E-MOEA significantly
outperforms P-MOEA on all benchmark problems. In terms of the ideal-delta-area, the relative
performance of P-MOEA is somewhat better, indicating that it particularly has a problem in
finding the portfolios with high expected return or low variance.
The results for the problem with 5-10-40 constraint look similar (see Tables 3 and 4), although
the differences between P-MOEA and E-MOEA are generally smaller.
Typically obtained efficient frontiers for P1 and P3 with cardinality constraint are depicted in
Table 1: Max-delta-area at the end of the run for E-MOEA and P-MOEA for all four test problems
with cardinality constraint, average ± std. error, all values in terms of 10−6 .
P1 (K = 4)
P-MOEA 1.1613 ± 0.0159
0.2275 ± 0
P2 (K = 4)
P3 (K = 8)
P4 (K = 8)
2.7787 ± 0.0521
9.3292 ± 0.2287
4124.1363 ± 123.6716
0.8048 ± 0.00003 0.0561 ± 0.0052
5.9063 ± 0.2939
Table 2: Ideal-delta-area at the end of the run for E-MOEA and P-MOEA for all four test problems
P1 (K = 4)
P-MOEA 1.0605 ± 0.0160
0.1371 ± 0
P2 (K = 4)
P3 (K = 8)
P4 (K = 8)
1.6981 ± 0.0175
2.1250 ± 0.0189
125.1611 ± 1.1580
0.5222 ± 0.00003 0.0123 ± 0.0003
2.4398 ± 0.09637
with 5-10-40 constraint, average ± std. error, all values in terms of 10−6 .
P-MOEA 1.3274 ± 0.0002
1.5107 ± 0.0197
1.7339 ± 0.0138
446.7284 ± 11.4963
E-MOEA 1.3019 ± 0.0007
1.2416 ± 0.0001
1.6511 ± 0.0047
344.7926 ± 3.8489
0.2188± 0.00002
0.1028 ± 0.0009
0.0807 ± 0.0003
7.6607 ± 0.1116
E-MOEA 0.2023 ± 0.00001 0.0631 ± 0.0001
0.0700 ± 0.00006 4.9756 ± 0.0290
ideal front
ideal front
expected return
expected return
Figure 4: Typical fronts obtained on test problem P1 (left) and test problem P3 (right) with
cardinality constraint.
Figure 4. As can be seen, for the small problem (P1), both algorithms perform quite well. In fact,
the figure zooms in on only a part on the front, as on a plot of the whole front, the differences
would be hard to see. Still, E-MOEA clearly outperforms P-MOEA and is indistinguishable from
the ideal front over large parts. For the larger problem, P-MOEA does not seem to be able to
come close to the performance of E-MOEA. In particular in the area of higher returns, there are
clear deficiencies. It seems that P-MOEA does not scale very well to larger problem sizes6 . One
reason may be that there are usually only few assets with a high return, and exactly those have to
be combined in the portfolio to obtain an overall high return. Identifying the high-return assets
out of a large set may prove difficult for the P-MOEA. E-MOEA on the other hand finds solutions
hardly distinguishable from the ideal front also for the larger problems.
For the 5-10-40 constraint, the fronts obtained by P-MOEA and E-MOEA are much closer
to each other, and further away from the ideal front. Still, the front obtained by E-MOEA
dominates P-MOEA’s front basically everywhere. Note that again for visibility, the plot for the
larger problem only shows a segment of the overall front.
When looking at the obtained solution quality in terms of max-delta-area over running time,
it is clear that the advantage of E-MOEA over P-MOEA is significant throughout the run. Figure 6(a) looks at P3 with cardinality constraint. Clearly, E-MOEA starts out much better, and
converges much faster than P-MOEA (for the small problem, E-MOEA even found the best so6
In Streichert et al. (2004a,b, 2003), the algorithm was only tested on small problems with up to 81 assets.
ideal front
ideal front
expected return
0.0016 0.0018 0.002 0.0022 0.0024
expected return
Figure 5: Typical fronts obtained on test problem P1 (left) and test problem P3 (right) with
5-10-40 constraint.
lution within 5 out of the allowed 250 seconds in every single run). Note that we plot against
running time. Because E-MOEA has to run a critical line algorithm for every individual, it can
only evaluate about 13500 individuals during the 1000 seconds allowed, while P-MOEA generates
and evaluates approx. 1,945,000 individuals in the same time frame.
For the problem P3 with 5-10-40 constraint, E-MOEA also starts better than P-MOEA, then
P-MOEA quickly catches up only to fall behind again (see Figure 6(b)). The difference in the
number of individuals evaluated is even more striking here than for P3 with cardinality constraint,
because the 5-10-40 constraint does not allow to remove a large fraction of the assets for the
critical line algorithm. While E-MOEA can generate only about 3000 individuals in the given
2000 seconds, P-MOEA generates approx. 3,475,000.
One explanation for the superiority of E-MOEA, besides being envelope-based, is certainly
its in-built weight optimization by the critical line algorithm. This effect is visible in Figure 7,
which compares the solution quality or randomly generated solutions with both, the P-MOEA and
the E-MOEA. Clearly, E-MOEA has a much better start, as the majority of randomly generated
envelopes is clearly better than the majority of randomly generated portfolios.
max. delta-area
max. delta-area
Figure 6: Convergence curves for P3 with cardinality constraint (left) and 5-10-40 constraint
ideal front
500 random envelopes
200,000 random portfolios
Figure 7: Randomly initialized populations of envelopes and portfolios for the 5-10-40 problem
and the Hang Seng Dataset.
The critical line algorithm is a very efficient algorithm to calculate the whole efficient frontier for a
standard mean-variance portfolio selection problem. However, this method is no longer applicable
if practical real-world constraints such as maximum cardinality constraint, buy-in thresholds, or
the 5-10-40 rule from the German investment law have to be considered, because such constraints
render the search space non-convex. Researchers have therefore resorted to solving these problems
point-based, approximating the efficient frontier by iteratively solving a sub-problem with a fixed
expected return, for many different settings of the expected return. Because even the sub-problems
are rather complex, often meta-heuristics are used.
In this paper, we have proposed a new envelope-based multi-objective evolutionary algorithm
(E-MOEA), which is a combination of a multi-objective algorithm with an embedded algorithm
for parametric quadratic programming. The task of the MOEA is to define a set of convex subsets
of the search space. Then, for each subsets the critical line algorithm can efficiently generate an
efficient frontier which we call envelope. The combination of all generated envelopes then forms
the overall solution to the problem.
To our knowledge, our approach is the first metaheuristic approach which is not point-based,
but which is capable of generating a continuous front of alternatives for portfolio selection problems
with non-convex constraints. Compared with a state-of-the-art point-based MOEA, E-MOEA was
shown to find significantly better frontiers in a shorter time.
As future work, we are planning to integrate a more intelligent mutation operator that uses
shadow prices to influence mutation probabilities. Also, the ideas of envelope-based MOEAs
should be transferred to other applications. In particular, we are planning to consider portfolio
re-balancing problems that include consideration of fixed and variable transaction costs.
Acknowledgements: We would like to thank Ralph Steuer for providing us the large benchmark test cases.
Armananzas, R. and Lozano, J. A. (2005). A multiobjective approach to the portfolio optimization problem. In
Congress on Evolutionary Computation, pages 1388–1395. IEEE.
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optimisation. Computers & Operations Research, 27:1271–1302.
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problems. Kluwer.
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investment guideleines. In Metaheuristics International Conference.
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John Wiley and Sons, 6th edition.
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LNCS, pages 788–793. Springer.
Hirschberger, M., Qi, Y., and E., S. R. (forthcoming). Randomly generating portfolio-selection covariance matrices
with specified distributional characteristics. European Journal of Operational Research.
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Co., Inc.
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selection models in the presence of discrete asset choice constraints. Quantitative Finance, 1:489–501.
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Optimization, 4(1):13–27.
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algorithm. OR Spectrum, 25:481–495.
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AIFB, University of Karlsruhe, Germany.
Schlottmann, F. and Seese, D. (2004). Financial applications of multi-objective evolutionary algorithms: recent
development and future research directions. In Coello-Coello, C. and Lamont, G., editors, Applications of
Multi-Objective Evolutionary Algorithms, pages 627 – 652. World Scientific.
Schlottmann, F. and Seese, D. (2005). A hybrid heuristic approach to discrete multi-objective optimization of
credit portfolios. Computational Statistics Data Analysis, 47(2):373 – 399.
Stein, M., Branke, J., and Schmeck, H. (2006). Efficient implementation of an active set algorithm for large scale
portfolio selection. Technical report, Institute AIFB, University of Karlsruhe.
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Streichert, F., Ulmer, H., and Zell, A. (2004b). Evaluating a hybrid encoding and three crossover operators on the
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Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M., and da Fonseca, V. G. (2003). Performance assessment of
multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117–


Tags Ezra Zuckerman Sivan

Tag: Ezra Zuckerman Sivan

Three in One: Creation, Exodus, and Equality

Ezra Sivan presents a new analysis of Shabbat and how it throws light on so much more in the Torah.

Between Shabbat and Lynch Mobs

Ezra Sivan asks what light the narratives of Shabbat and the scouts shed on some critical social questions.


Commonplace book I

But what have been thy answers, what but dark
Ambiguous and with double sense deluding
Which they who asked have seldom understood.

If one had studied the human spirit a little, one knows what power the marvelous has over it.

Since inquiry is the beginning of philosophy, and wonder and uncertainty the beginning of inquiry, it seems only natural that the greater part of what concerns the gods should be concealed in riddles.


In some cases, couples are not able to reach agreements about some or all of the issues presented in their family law matter. The family law court is available to make orders on most such disputed issues, but the litigation process can vary significantly based on the issues, location, and personalities involved, among other factors.

In general terms, it is necessary to file certain forms with the court whether or not the parties have an agreed-upon settlement. A Petition and Summons must be filed with the court and served on one party so that the court has jurisdiction to make binding orders. The parties must generally exchange certain information, then an agreement can be negotiated. If the parties are not able to come to an agreement on some or all issues, they can ask the court to make orders on those issues. The court can make orders for support or parenting, or other issues, while the case is pending, and can make orders as to the final disposition of issues as well. Sometimes matters can be resolved in a short hearing, and in other cases a more extensive hearing is conducted to allow the parties and their attorneys to present evidence on the issues and the judge to make findings based on the evidence. In some matters, evidence can be presented by declaration and in other matters, live testimony or other kinds of evidence is used. This kind of court involvement in generally referred to as “litigation.”

Litigation can be useful in cases in which parties are not able to reach agreements on immediate issues, such as temporary support and parenting time. In many cases, parties attend one or more hearings on temporary issues but are able to negotiate a final resolution of their case. In other cases, one party does not participate in the case at all, making it necessary for the other party to ask the court to make orders on all issues in order to complete the case. There can be other factors that make litigation appropriate in specific cases, whether to resolve all issues between a couple or only certain issues. It is important to be aware that litigation is not the only approach available to resolve a family law matter, and in many cases it is not necessary or beneficial. People should carefully consider all of the dispute resolution options and evaluate the option or combination of options that is most appropriate for their situation.

Even in matters in which litigation is necessary, the approach the parties and their attorneys take to the process can make a significant different in the long-term relationship between the parties. This can be especially important if the parties have children together or other reasons to have an ongoing relationship after the divorce is over. We believe that family law litigation should be conducted respectfully and courteously, in a manner designed to reduce acrimony between the parties whenever possible. When appropriate, we also help parties locate resources, such as communication or parenting classes, that can help them develop a more constructive parenting relationship in the future.


Home > Current Affairs GK> GK & Current Affairs- December 2016

21 . What was the theme of the 2016 International Day of Persons with Disabilities?
A. Arts, Culture and Independent Living
B. Decent Work for Persons with Disabilities
C. Achieving 17 Goals for the Future We Want
D. Inclusion matters: access and empowerment for people of all abilities

A. South Africa B. Japan
C. Iran D. North Korea

23 . Twelve eminent personalities were recently awarded with the Yash Bharti Award 2016. It is the highest honour of which of the following states?
A. Uttar Pradesh
B. Rajasthan
C. Hiamchal Pradesh D. Tamil Nadu

A. Cuba B. Haiti
C. Honduras D. Mexico

25 . Which of the following domestic space technology start-ups recently signed a contract with the Indian Space Research Organisation to send a robot to the Moon?
A. TeamIndus
B. Web Engage
C. Cucumber town D. Druva Software


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Conveyancing In Woore Q & A's

Can I agree a sale price without involving an estate agent or solicitor?

This depends on whether you have signed up with an estate agent and what agreement is already in place. While it might seem unfair if you’ve found a buyer outside of the estate agency process and you’re expected to still pay the agent their fees on sale, you should be very careful about stepping outside the agreed terms and conditions since this is legally binding and you may face penalties as a result. Therefore, if you want to follow this course, it’s worth checking the details with a solicitor to ensure you’re following the letter of the law.

If you’re not with an agent, you can publicise your house details with a number of publications and online sites (some are free, others require a fee), but you’ll need to do all the legwork and administration. For a legal standpoint, you don’t need to appoint a solicitor to perform the conveyancing, but it would be an unwise option to pursue as you will probably have neither the training or experience in some its complexities, and you won’t have the protective indemnity insurance in the event of a problem arising with your work.

Is gazumping accepted in Woore?

This happens when a lower offer is, following agreement, later rejected by the owner, in preference to a greater offer. The will be a risk of gazumping in any transaction, because offers are not binding until exchange of contracts. You should instruct your conveyancing solicitor as soon as possible to reduce the chance of your transaction being gazumped.

What are property searches in reference to?

Conveyancing searches are a pack of queries undertaken on your behalf, which may include a drainage search. Purchasers need to be aware that, searches only relate to issues with the property's title.

Should we get a chancel search? We are buying near a priory built in the 1400s in Woore.

Chancel liability repair costs can run into £100,000s, which owners of affected property will be compelled to pay on demand to the Woore Church council. Insurance may be available to protect a buyer should a Woore Parochial Church Council enforce liability. Church of England properties in the local area include S.Leonard.

What’s the difference between exchange of contracts and completion?

How can we determine more data about the conservation areas in Woore?

Local Woore conservation area matters e.g. trees or rundown streets are governed by the local authority (Newcastle-under-Lyme).

English Heritage have created a list of the condition of conservation areas along with the risk of a decline in standards.

When is it appropriate to instruct a solicitor to handle our purchase?

Whether you are buying or selling in Woore, instructing as soon as possible is wise. Some authors recommend postponing instruction until a chain is completed, but delays can risk the other side pulling out, particularly in uncertain market conditions.


Senior Data Scientist

Washington, DC Metro Area

Current Clearance Level

Active Public Trust Clearance

Company Description

HVH Precision Analytics applies AI/machine learning techniques to a broad range of data resources, both structured and unstructured, to provide actionable insights to our government and commercial clients.  Our ability to collect, aggregate, and analyze disparate data sets combined with our deep expertise in AI and machine learning has led to significant growth at HVH over the past 3 years.

We are seeking highly motivated individuals who are passionate about AI/machine learning and its application across disparate data resources to help our clients gain insights not previously possible.

Job Description

Data science professional to design, implement, and deploy advanced machine learning / artificial intelligence algorithms and solutions across multiple domains including, but not limited to government healthcare and media.  Responsibilities will involve developing solutions to support HVH’s existing platform and to provide solutions to support client needs and other business needs.  The professional will be a member of HVH’s analytics team.

This Senior Data Scientist position will involve developing and applying machine learning algorithms to data provided by a Government Customer.  This position is located in the DC Metro area and will involve regular travel to Government Customer facilities located in the region.

Job Requirements

  • Proven ability to develop, implement, and deploy advanced machine learning / artificial intelligence algorithms applicable across multiple domains processing multi-terabytes of data.
  • Active Public Trust Clearance

Required Skills

The skills required for this position are listed below:

  • BS/MS Degree in any of the following majors: Engineering, Computer Science, Mathematics, Bioinformatics, Physics
  • Subject Matter Expert in machine learning / artificial intelligence
  • Client interface and presentation skills
  • Proficiency in one or more of the following programming languages:
    • Python (pandas, scikit-learn, Numpy, Scipy)
    • R (machine learning packages)
    • Java
  • Proficiency in one or more of the following machine learning frameworks:
    • MXNet
    • Tensor Flow
    • AWS Sagemaker
    • Microsoft CNTK
    • AWS (Redshift)
  • Consideration will be given to publications, independent software projects completed, and non-proprietary code authored by the candidate


Seven Ukrainian civilians and five government soldiers have been killed in the past day of clashes with pro-Russian insurgents despite a truce between the two sides.

The toll was one of the highest reported since the signing of the truce agreement on 5 September.

It brings the number of civilians killed in sporadic mortar and rocket attacks to 14 since the weekend.

The civilians were killed in both the eastern rebel-run territories of Lugansk and Donetsk, local officials said.

The Ukrainian military said its soldiers were also killed across the industrial Russian-border region.

"As a result of shelling and clashes in various areas where the anti-terrorist operation is being waged, five Ukrainian servicemen died," National Security and Defence Council spokesman Andriy Lysenko told reporters.

Ukraine launched an "anti-terror" operation in mid-April, several days after separatist gunmen seized government buildings across nearly a dozen towns and cities in the Russian-speaking east.

The rebels do not report their own losses and Ukraine's daily claims of heavy casualties in their ranks have been impossible to confirm.

The latest casualties bring to 100 the number of Ukrainian soldiers and civilians reported killed since the truce agreement, which was backed by Russia and European envoys.

Insurgency leaders signed up to the peace pact but soon accused Ukraine of breaking the ceasefire.

Some have since vowed to keep fighting until all Ukrainian forces pull out of their self-proclaimed states.

The heaviest daily clashes are being waged around the northern outskirts of the main rebel-held city of Donetsk, where outnumbered government forces have been holding on to a besieged airport since the end of May.


108.13 0.5%

as of Jan 16 '20

52 Week Range:

20,184.85 24,115.95

Market Condition

Index is in a bull stage

Latest index price 24,041.26 is above long term (200 days) moving average (MA200 is 21,959.49). 50 day moving average is 23,496.44 and above 200 days moving average.

60.44 50 Relative Strength Index (RSI) is 60.44.

Current value is above 50 levels, which means that index's recent performance is relatively good.

The stock charts below are:

Price Chart
Moving Averages
Price Chart includes short term (10 and 30 day), middle term (50 day) and long term (150 and 200 day) moving averages as well as volume and average volume bar charts. Read more »
Bol. Bands
Bollinger Bands® is an indicator designed to provide traders with information regarding price volatility. Many traders believe the closer the prices move to the upper band, the more overbought the market, and the closer the prices move to the lower band, the more oversold the market. Read more »
Weekly Price Chart
Weekly Price Chart includes weekly price chart and 30 weeks moving average.
Relative Strength Index (RSI) intended to chart the current and historical strength or weakness of a stock. Read more »
Relative Strength (RS) is a measure of price trend that indicates how a stock is performing relative to other stocks in its industry. It is calculated dividing the price performance of a stock by the price performance of an appropriate index for the same time period. Read more »

One Year Statistics

Beta: 0.8673

Beta of 0.8673 suggests that the asset is less volatile than the rest of the market.

Alpha: -0.0005

Alpha of -0.0005 suggests that the asset is underperforms the market.

Sharpe Ratio: 0.9135

Sharpe Ratio of 0.9135 suggests that asset's reward/risk ratio is fair.

Last Year Returns & Risk / Reward Ratios

1 year6 month1 month
Total Return 17.36% 13.45% 0.48%
Average Daily Return 0.07% 0.11% 0.04%
Average Daily Volatility ± 0.91% ± 0.94% ± 1.21%
Risk / Reward Ratios
Beta (Volatility) 0.8673 0.8779 2.3643
Alpha (Surplus) -0.000482 0.000328 -0.006103
Sharpe Ratio (Risk-Reward) 0.913485 1.550346 0.207969


Mavla (Mallow) Plants

    The genus Malva contains about thirty species of annuals, biennials, and perennials.  These species are found in dry, open habitats, waste ground, and roadsides, throughout Europe, North Africa, and temperate Asia.  The rounded kidney-like leaves are either toothed, shallowly lobed, or pinnasect (opposite lobes that are deeply cut, almost to midrib).  Grown for ease of culture and unique flower forms and colors.  Our malva offerings are perennial plants that offer large blooms, long blooming seasons, and durability to the garden border.


“What? You didn’t know?” How I’ve solved a lot of communication, knowledge, and performance problems with one simple solution

Question: How many people waste time looking for information that they need to do their jobs?

Answer: Pretty much everyone!

This time wasted adds up. In fact, some estimates say that employees wasting time looking for information costs the average company with 100 employees up to $500,000. That’s half a million dollars!

I have solved a lot of communication, knowledge, quality and performance problems with a very simple solution: an information hub.

The idea of a communication or information hub is not revolutionary. In fact, some people think things like an intranet site is old school. But my work with almost every client has proven that building an information hub can be a game changer. And I am not alone in understanding the value of an information hub. Oracle, IBM, and Cisco have measured the benefit of their intranet sites at $1 billion each. The trick is to provide the content that people want and need,  and to organize the information so it is easy to find and even easier to understand.

In one recent project, we were providing information related to financial procedures. Boring –  right? But making sure employees understood the procedures and followed them was extremely important. We created an online communication hub with all of the information that employees needed and it was designed around how they worked. The traffic to the hub was off the charts. But the best result was that calls and emails to the people who would normally get questions dropped dramatically and when they did get questions, it was easy to point employees to the online resource.

In another project I worked on with crime scene investigators at the RCMP, we created a knowledge hub to share best practices and procedures so that these forensic experts could easily access the information they needed to do their jobs. Visits to the site increased 700% and the feedback from the field was fantastic.

Follow these steps to create a great information hub

Set clear goals: be strategic about what you want to achieve. This helps zero in on the information that is really essential because the last thing you want to do is overwhelm your busy employees with unnecessary details.

Identify your audience: understanding who will be using the hub is critical. Create employee personas and map the employee journey so you have a clear picture of your audience.

Use design thinking: Map out the functionality and content organization based on the needs of the users (see above!). This is an extremely important exercise because, at the end of the day, the information hub needs to address the specific pain points and information needs of your audience.

Layer your content: The great thing about online information is that you don’t need to drown people in details. Instead, provide the detailed information in linked documents for the employees that really need performance support or in-depth information.

A few more tips

Once you have built your hub, you need to let people know about it. All of your communications tactics should drive people to the hub. And the beauty of a hub is that your emails, town halls or other tactics can be light on details because all of the information is found in the hub. If people ignore your email, miss the town hall or simply forget (it happens), they know where to find the information they need.

It’s relatively easy to measure the effectiveness of an online information hub. Use web analytics to understand who your visitors are and their behaviour, including a comment form or a pop-up survey to help gather feedback about the hub or organize a focus group. This information will help you plan updates or new content so that your hub stays useful and relevant.

Internal communication is NOT company news.

Internal communication is NOT company news.