This thesis consists of one stock return predictability study and two international risk exposure studies. The first study shows that the statistical significance of out-of-sample predictability of market returns given by Kelly and Pruitt (2013), using a partial least squares methodology, constructed from the valuation ratios of portfolios, is overstated for two reasons. Firstly, the analysis is conducted on gross returns rather than excess returns, and this raises the apparent predictability of the equity premium due to the inclusion of predictable movements of interest rates. Secondly, the bootstrap statistics used to assess out-of-sample significance do not account for small-sample bias in the estimated coefficients. This bias is well known to affect in-sample tests of significance and I show that it is also important for out-of-sample tests of significance. Accounting for both these effects can radically change the conclusions; for example, the recursive out-of-sample R2 values for the sample period 1965-2010 are insignificant for the prediction of one-year excess returns, and one-month returns, except in the case of the book-to-market ratios of six size- and value-sorted portfolios which are significant at the 10% level.The second study examines whether U.S. common stocks are exposed to international risks, which I define as shocks to foreign markets that are orthogonal to U.S. market returns. By sorting stocks on past exposure to this risk factor I show that it is possible to create portfolios with an ex-post spread in exposure to international risk. I examine whether the international risk is priced in the cross-section of U.S. stocks, and find that for small stocks an increase in exposure to international risk results in lower returns relative to the Fama-French three-factor model. I conduct similar analysis on a measure of the international value premium and find little evidence of this risk being priced in U.S. stocks. The third study examines whether a portfolios of U.S. stocks can mimic foreign index returns, thereby providing investors with the benefits of international diversification without the need to invest directly in assets that trade abroad. I test this proposition using index data from seven developed markets and eight emerging markets over the period 1975-2013. Portfolios of U.S. stocks are constructed out-of-sample to mimic these international indices using a step-wise procedure that selects from a variety of industry portfolios, stocks of multinational corporations, country funds and American depositary receipts. I also use a partial least squares approach to form mimicking portfolios. I show that investors are able to gain considerable exposure to emerging market indices using domestically traded stocks. However, for developed market indices it is difficult to obtain home-made exposure beyond the simple exposure of foreign indices to the U.S. market factor. Using mean-variance spanning tests I find that, with few exceptions, international indices do not improve over the investment frontier provided by the domestically constructed alternative of investing in the U.S. market index and portfolios of industries and multinational corporations.