C LUSTER A NALYSIS R ESULTS

We now translate the TGARCH parameters into the distance term by using the measure we proposed earlier in Section 2. We use the dendrogram to represent the distance matching for stock pairs. Any stock that has similar volatility characteristics (since we use TGARCH parameters as our input to the model) would be closely matched together in the dendrogram. In addition, the distance shown in certain type of dendrogram cannot use to compare to the distance from other measures because the

distance here has no unit and, as we mentioned earlier, different distance measure yield different distance value for the same pair of stock. Consequently, this tells us how the cluster looks like in term of certain distance measure. Determining the number of groups in a cluster analysis is often the primary goal. Although objective methods have been proposed, their application is somewhat arbitrary and debatable.

The strength of clustering is indicated by the level of similarity at which elements (stocks) join a cluster.

In our analysis, we first used the TGARCH-based distance defined in equation (8). Figure 1 shows the Mahalnobis-like distance dendrogram for Taiwan 50 stock returns, obtained by the complete linkage method in the Matlab program. The dendrogram exhibits a few chaining characteristics; thus, we will separate it into two clusters, for example (one also can divide it into more clusters, but it might be difficult to find some distinct zone for smaller clusters). One is composed of all financial, most technology corporations (semiconductors: MediaTek, Advanced Semiconductor Engineering, United Microelectronics; computers: Wistron, Compal Electronics, Acer, Lite-On Technology; electronic-related: Foxconn Technology, AU Optronics, HonHai Precision Industry, and Synnex Technology International; and communication & internets: HTC), all industrials, and resources (Formosa Petrochemical). The second is mostly composed of technology corporations (communication & internets: Taiwan Mobile; semiconductors: TSMC, Siliconware Precision Industries; computers: Quanta Computer, Asustek Computer;

electronic-related: Delta Electronics), one conglomerate (Pou Chen), and one food corporation (Uni-President). We do not include Epistar, Chunghwa Telecom, President Chain Store, and Far East Tone Telecommunications as a group.

Figure 2 shows the dendrogram for Taiwan 50 stock returns using the Euclidean distance metric. We can divide it into three groups. The first group is composed of some technology corporations (semiconductor; United Microelectronics; and computers: Taiwan Mobile, Acer, Asustek Computer, Quanta Computer, and Lite-On Technology; electronic-related: Delta Electronics, Synnex Technology International), most financial (First Financial Holding, China Development Financial Holding, Mega Financial Holding, Chinatrust Financial Holding, Chang Hwa Bank, Fubon Financial Holding, and Taiwan Cooperative Bank), most industrials (Formosa Chemicals &

Fibre, Taiwan Cement, Cheng Shin Rubber Industry, Nan Ya Plastics, Asia Cement, and Formosa Plastics), and resources (Formosa Petrochemical). The second group is mostly composed of technology corporations and the rest of financial. The last group is composed of Chunghwa Telecom and President Chain Store. Please note that Far East Tone Telecommunications and Epistar are not grouped.

Next, we also examine the dendrogram from the combined distance model as shown in Figure 3. We can see the combined method have a lot of stock pairs that do not stay much far from each other. This looks like a single large cluster; it exhibits a large chaining and the distance between each 2 pairs is very short. Hence, we decide to include it as a single large group with one outlier that is Far East Tone Telecommunications.

Now we introduce the SET 50 stock returns dendrogram. We begin with the Mahalanobis-TGARCH model shown in Figure 4. We decide to make it into two clusters for explanation the cluster characteristics. The first cluster includes all financials, all technology corporations, all property and construction firms, some agro and food corporations (Thai Union Frozen Products, and Charoen Pokphand Foods), most resources (PTT, Glow Energy, IRPC, Electricity Generating, Thaioil, Banpu, and PTT Exploration and Production), and most industrial firms (Siam City Cement, Tata Steel, and The Siam Cement). The second cluster is composed of three companies, which are The Bangchak Petroleum, Ratchaburi Electricity Generating Holding, and Big C Supercenter. We do not classify Minor International as well as Thai Plastic and Chemicals as a cluster.

The Euclidean distance metric dendrogram was shown in Figure 5. From this result, we can divide it into three clusters. The first cluster is composed of all financials, all technology corporations, all property and construction firms, all most services (only except for Big C Supercenter), most resources (except for Ratchaburi Electricity Generating Holding and The Bangchak Petroleum), and most industrial firms (only except for Thai Plastic and Chemicals). The second cluster is composed of three firms, which are Khon Kaen Sugar Industry, Minor International (these two are in agro and food industry), and The Bangchak Petroleum (resources). Also, the third cluster is composed of three firms from different industry. These are Thai Plastic and Chemicals (industrials), Ratchaburi Electricity Generating Holding (resources), and Big C Supercenter (services)

From Figure 6, we can divide the results from the combined method into two clusters: one with a large cluster and another with a smaller cluster. The smaller one is composed of Big C Supercenter and Ratchaburi Electricity Generating Holding. The large one is mainly composed of the rests of the stocks except for Thai Plastic and Chemical.

From the results in Figure 1 to 6 and as mentioned above, we can notice that most stocks tend to form a few large clusters for both stock market proxies no matter which measure we use. However, the dispersions of some certain specific industry stocks have a bit different clustering patterns depending on the method one uses.

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CPN DELTA PSL BBL TTA PTTEP TRUE LH CPF BECL BANPU THAI SCC KBANK QH SCB TOP TUF TSTH EGCO IRPC BGH BH GLOW BAY PTT SCIB TCAP ADVANC TMB AOT MCOT MAKRO HANA KTB SCCC CPALL BEC KSL BCP RATCH BIGC MINT TPC

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Figure 5: Dendrogram for SET 50 stocks using the Euclidean distance.

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Figure 6: Dendrogram for SET 50 stocks using the combined distance.

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