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Unsustainable? If a current account deficit is financed through borrowing it is said to be more unsustainable. This is because borrowing is unsustainable in the long term and countries will be burdened with high-interest payments. E.g. Russia was unable to pay its foreign debt back in 1998. Other developing countries such as Brazil, African countries have experienced similar repayment problems. Countries with large interest payments have little left over to spend on investment.
Risk of capital flight - A very high balance of payments deficit may, at some point, cause a loss of confidence by foreign investors. Therefore, there is always a risk, that investors will remove their investments causing a big fall in the value of your currency (devaluation). This can lead to a decline in living standards and lower confidence for investment.A factor behind the Asian crisis of 1997 was that countries had run up large current account deficits by attracting capital flows (hot money) to finance the deficit. But, when confidence fell, these hot money flows dried up, leading to a rapid devaluation and crisis of confidence. When confidence fell and the exchange rate fell, there was a degree of capital flight as foreign investors sought to return assets.
Foreign ownership of assets. If you run a current account deficit, it means you need to run a surplus on the financial/capital account. This means foreigners have an increasing claim on your assets through FDI, which they could desire to be returned at any time. For example, if you run a current account deficit, it could be financed by foreign multinationals investing in your country or the purchase of assets. There is a risk that your best assets could be bought by foreigners, reducing long-term income.
Problem for countries who cannot manage their XR - a current account deficit can be a real problem for countries in the Euro - who cannot devalue to restore competitiveness. For example, 2000-2007, a divergence in inflation rates caused very large current account deficits in southern Eurozone economies. This lack of competitiveness and low level of export demand was a factor behind the weak domestic demand 2008-13 of Greece, Portugal, Spain during the Eurozone recession of 2008-13.