The debate about the falling labor share has brought attention to the income-shares trends, but less attention has been devoted to their variability. We analyze how their fluctuations can be insured between workers and capitalists, and the corresponding implications for financial markets. We study a neoclassical growth model with aggregate shocks that affect income shares and financial frictions that prevent firms from fully insuring idiosyncratic risk. We examine theoretically how aggregate risk sharing is shaped by the combination of idiosyncratic risk and moving shares. In this setting, accumulation of safe assets by capitalists and risky assets by workers emerges naturally as a tool to insure income shares' risk. Then, in a quantitative exploration we show that low interest rates, rising capital shares, and accumulation of safe assets by firms and risky assets by households can be rationalized by persistent shocks to the labor share.