Britain was the first country in the world to industrialise - to move from primary industries to secondary and tertiary industries with the raw material being imported. With industrialisation became also a phenomenon called maturation where the economy stopped developing so quickly as the competitor economies, because they could copy the findings of Britain (i.e. building of railways was 4 times cheaper in Argentina and USA than in UK) and invent themselves, whereas UK could only use the latter option. Thus the same kind of investment was very often more productive in abroad. UK had developed a large pool of capital and other countries needed capital to realise their growth potential (there was so much to be copied). Also there was very little competition in abroad for the public utilities, railways and such. This eliminated the fear of price wars and trade cycles and secured the high returns for extended periods. This is the macroeconomic reasoning for the investment.
Many people in England had idle resources that they wanted to invest securely into securities. Opportunity existed in England, but the returns were comparatively lower. With the appearance of investment banks and the overall developing of financial system it became much easier to invest abroad. Added the government guarantee that some countries (India's railways) the foreign investment was the option to choose. This is the microeconomic reasoning for foreign investment.
In boom years foreign investment was even higher than British exports or investment locally. This yielded extra income and thus provided even more possibilities to invest abroad. British capital became increasingly dominant with the total amounting over 4000 million pounds and returning 200 million each year. There were two main ways a person could profit from an investment abroad - a gain on capital because the increase in bond prices (speculative investment) and the dividends foreign firms could pay (rentier type of investment).
Initially the speculative investment dominated. It had started when the Baring Brothers and the Rothschilds started lending to Europe, so that defeated Quadruple Alliance countries could finance their PSBR and later on public utilities and railways. Overseas markets were not necessarily more profitable, but they were more risky and exciting. Speculators were making short-term investments in booms and left as soon as prices started to stagnate causing large investment cycles. This speculative investment, especially remarkable in mining industries remained through to 1914 and was market by several booms. With the rose of business confidence, investment started to less responsible governments in Mexico, Greece and in 1820s also to the newly - established South-American countries, mainly to help mining. Only 5-10% of the actual nominal capital was needed to make an investment, so speculation rose enormously. In December 1825, when prices stopped rising, the bubble burst. All the republics were defaulting in South-America and the British banking system could not finance the lending, so until 1850s not much investment was made to the South-America. The 1830s saw a similar boom in the investment to North-America to finance the building of railways. Often the loans were underwritten by state governments guaranteeing a return on investment payable from the tax receipts, so main types of loans were state bonds, instead of direct investment used in the previous decade. Speculation with cotton in 1839 lead to a fall in its prices, which caused panic and collapse of the whole system again. In 1840s the flow of funds was actually reversed as US securities were repatriated. Old British colonies, specially India, were also in need of new investment. By 1868 a huge amount of railways was built in India, its return was guaranteed by the government, but it proved to be unprofitable. In 1865 there was again a speculative flow to Argentina, because it had formed a stable government. After 1870 yields on investment started to fall. Insurance funds and other investors needed became increasingly adventurous to maintain the yield on investment. Loans stopped abruptly in 1890, because inflation had risen to worrying levels and 1889 had a bad harvest. Around the same time South-African gold - findings became important speculative investment target.
Australia received much investment during 1877-86 to railways and to the expansion of the pastoral economy. But investment to other colonies did not surprisingly increase during 1870s. After 1900 investment to Canada and United Stated started to rise again. Money went mostly to metal mining. The investment continued to rise for an extraordinary long period, reaching a peak called the "Edwardian climax". This period has received relatively little attention from the historians, but this boom was definitely greater than the previous ones, collapsing in the First World War.
The character of investment after 1860s was mainly to securities in the unpopulated lands. 47% of the total went to colonies, 20% to US, 20% to Latin America and 6% to Europe.
From 1830 however rentier type of investment started to grow in importance and by 1880 it had become predominant. The character of the loans consisted mostly of first class bonds (accepted by merchant banks) and securities. Much was invested to government bond (3/5) mainly to finance military expenditure and PSBR. All these forms existed in England as well, but their return was lower. Scottish savings were also playing a large role in British investment. There were stock exchanges in Liverpool and they amounted to a quarter of total investments in the second half of 19th century. Investors were looking for targets that were secure, albeit not so profitable, and relevant to their home country well-being. Investment to food resulted in cheap food prices in England (after trade barriers were abolished), so it profited England macroeconomically more than just the dividend the investors received. Investment was done mainly in "packages" - when UK invested in Indian railways it meant that all the equipment was bought from UK and transported there by UK's ships. Similarly railways were built to parts of the USA where cotton could be transported easily to Britain, investors themselves being large manufacturing firms that directly benefited from lower raw material prices.
Rentier type of investment was much more stable, little falls in profits did not initiate a major collapse as the money surpluses had to be invested somewhere, when people would have pulled out their money immediately after returns fell from 7% to 6% say, they would have earned nothing at all. Rentier investment did fall in 1890 when one of the major investment house, the Barings, nearly went into liquidation and US railways defaulted. This caused the returns in England to fall and thus "pushed" the investment out again. As few people were willing to invest abroad the securities were priced low and had higher PI ratio, so they "pulled" the investment out, both resulting in capital leaving Britain again.
Of course there were movements from one country to other in rentier investment as well, but they were much more gradual than with speculative investment. Capital was moved either because the relative risks and returns in another country became more favourable, for example with the change of government or some discovery or when a particular product emerged that Britain wanted to support. Emigration was also a possible factor affecting investment as investment appeared to be done, but not exclusively, to countries that received most immigrants from Britain.