This paper measures the mean, standard deviation, alpha and beta of venture capital investments, using a maximum likelihood estimate that corrects for selection bias. Since Þrms go public when they have achieved a good return, estimates that do not correct for selection bias are optimistic. The selection bias correction neatly accounts for log returns. Without a selection bias correction, I Þnd a mean log return of about 100% and a log CAPM intercept of about 90%. With the selection bias correction, I Þnd a mean log return of about 5% with a -2% intercept. However, returns are very volatile, with standard deviation near 100%. Therefore, arithmetic average returns and intercepts are much higher than geometric averages. The selection bias correction attenuates but does not eliminate high arithmetic average returns. Without a selection bias correction, I Þnd an arith- metic average return of around 700% and a CAPM alpha of nearly 500%. With the selection bias correction, I Þnd arithmetic average returns of about 57% and CAPM alpha of about 45%. Second, third, and fourth rounds of Þnancing are less risky. They have progres- sively lower volatility, and therefore lower arithmetic average returns. The betas of successive rounds also decline dramatically from near 1 for the Þrst round to near zero for fourth rounds. The maximum likelihood estimate matches many features of the data, in particular the pattern of IPO and exit as a function of project age, and the fact that return distributions are stable across horizons.

Exchange rates depreciate by the difference between the domestic and foreign marginal utility growths. Exchange rates vary a lot, st of the variation of average stock risk through time and it is idiosyncratic risk that drives the forecastability of the stock market.” as much as 10% per year. However, equity premia imply that marginal utility growths vary much more, by at least 50% per year. This means that marginal utility growths must be highly correlated across countries - international 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 is indeed very high across several pairs of countries.”

We solve a model with two “Lucas trees.” Each tree has i.i.d. dividend growth. The investor has log utility and consumes the sum of the two trees’ dividends. This model produces interesting asset-pricing dynamics, despite its simple ingredients. Investors want to rebalance their portfolios after any change in value. Since the size of the trees is fixed, however, prices must adjust to offset this desire. As a result, expected returns, excess returns, and return volatility all vary through time. Returns display serial correlation, and are predictable from price-dividend ratios in the time series and in the cross section. Return volatility can be greater than the volatility of cash flows, giving the appearance of “excess volatility.” Returns can be cross-correlated even when the cash flows are independent, giving the appearance of “contagion” or “spurious comovement.”