This is a group of small to medium, brightly coloured Sphecid wasps. The species found in Singapore and also in Hong Kong is probably Ampulex compressa, a species which has been introduced all over the world along with its usual host, the pestiferous American cockroach (actually not from America; both this cockroach and Ampulex compressa supposedly originated from Madagascar). There are other species variously distributed throughout Southeast Asia, South China and elsewhere; all are quite similar in appearance.
Ampulex compressa is a small to medium-sized wasp, between 10 and 19mm long. It has comparatively short wings (compared to its body) and is a brilliant metallic blue-green.
As previously mentioned, these wasps prey on cockroaches, and Ampulex compressa, preying on such a pest species as the American cockroach, is certainly beneficial. Although the wasps are never in such abundance as to have a significant effect on the cockroach population, they cause no harm and should be left alone. They can sting if accidentally touched, but are normally good at avoiding people.
Due to their choice of prey, these wasps can sometimes be found in urban areas. However, the misuse of pesticides appears to have some adverse effects on populations of these wasps. Many people I have spoken to in Singapore, for example, remember that these insects used to be very common, and it was not unusual to see one dragging a cockroach, even across the common corridors of public apartments! However, regular fumigation intended to counter disease-carrying mosquitoes was implemented some years ago, along with the constant use of household pesticides. In the end, the intended victims, such as flies, mosquitoes and cockroaches, seem to have developed partial immunity to such chemicals, while most of the beneficial insects were not so tolerant; those in areas exposed to the chemicals died and populations seemed depleted. This beautiful wasp is one such example; it is still not uncommon to seeAmpulex compressa in Singapore, but they tend to occur only in more unpolluted outdoor areas these days. The American cockroach, however, is just as common in urban areas.
These wasps do not generally prepare nests, although some species are said to burrow. Ampulex compressa generally drags its prey into crevices in walls.