Mean-variance portfolio theory can apply to the streams of payoffs such as dividends following an initial investment … an indexed perpetuity - the risk-free payoff - and a long-run mean-variance efficient payoff. "Long-run" moments sum over …

consumption based model, and models based on interest rates plus a constant risk premium …

risk sharing is better than you think. Conversely, if risks really are not shared internationally, exchange rates should … vary more than they do -- exchange rates are much too smooth. We calculate an index of international risk sharing that … formalizes this intuition in the context of both complete and incomplete capital markets. Our results suggest that risk sharing …