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CPS1863 La Gubu et al.
0 are the risk aversion parameters, namely the relative measure of risk
avoidance.
The optimum solution to equation (1) with constraint of equation (2) is
1
′ −1
−1 ′ −1
−1
′ −1
(, Σ) = (Σ −1 − Σ −1 ( Σ ) Σ ) + Σ −1 ( Σ ) (3)

Equation (3) shows that the optimal portfolio (w) depends on inputs and Σ.

2.2 Clustering stocks
Because the number of stocks available in the capital market is quite large,
it is very difficult to determine the proportion of investment for each stock.
Therefore, it is necessary to use data mining techniques to deal with this. One
of the data mining techniques that can be used is cluster analysis. Cluster
analysis is a statistical analysis that aims to separate objects into several
groups that have the same/different characteristics from one group to another
group. In this analysis each group is homogeneous between members in
groups or variations of objects in groups that are formed as small as possible.
Cluster analysis, also called segmentation, has various purposes. Everything is
related to grouping or segmenting several objects into subsets or clusters.
Objects in a cluster will have a closer relationship compared to objects in other
clusters.
There are many cluster techniques in the literature. In this study, the
hierarchy complete lingkage clustering technique will be applied. Hierarchical
complete lingkage clustering technique is a clustering method based on the
farthest distance between objects. If two objects are separated by long
distances, then the two objects will be in one cluster, and so on.

2.3 Sharpe ratio
After the clusters are formed, then the performance of each stock will be
assessed in each cluster using the Sharpe ratio. Sharpe ratio or Sharpe index
is a measure of excess return (or risk premium) perunit risk in an asset. Sharpe
ratio is used to characterize how well asset returns compensate investors for
the risks taken. Sharpe ratio () is calculated by comparing the difference
between stock returns () and risk return free rate ( ) with a standard

deviation of stock return () or can be written as follows:
−
= (4)

In general, it can be said that the greater the value of the Sharpe ratio of a
stock, the better the performance of the stock.

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