Capital income taxation under full loss offset provisions of a prospect theory investor

In this paper we examine capital income taxation of a reference dependent sufficiently loss averse investor in a two period portfolio choice model under full loss offset provisions. Capital income taxation with loss offset provisions has been found to stimulate risk taking in expected utility models under certain assumptions about attitudes towards risk but would such effect be found under prospect theory type of preferences? We observe that the impact of capital income taxation depends on investors' reference levels relative to their endowment income and thus we explore capital income taxation for different types of loss averse investors in terms of their ambition. We consider the less ambitious investors to be the ones with relatively low reference levels (they avoid relative losses in both periods) and more ambitious investors to be those with relatively high reference levels. We analyze two types of more ambitious investors: investors with higher time preference (who experience relative losses only in the second period under the bad state of nature) and investors with lower time preference (who experience relative losses only in the first period). We observe that capital income taxation stimulates current consumption in most cases which encourages risk taking, although the final outcome would depend on the investors' degree of risk aversion, the rate of time preference and the tax rate in relation to certain thresholds. Current consumption could be discouraged for some ambitious type of investors that have relatively high second period reference levels but not necessary first period reference levels. In summary, to determine the impact of capital income taxation on the decision variables the reference levels in relation to endowment income play the most significant role. Ignoring reference depended preferences can lead to different conclusions for investors reaction to capital income taxation. We also find certain type of investors whose happiness level increases with capital income taxation under full loss offset provisions.