Portfolio construction

Modern portfolio theory: Why investing overseas may be better than you think

By: Eric Legunn | August 29, 2017

Investors familiar with modern portfolio theory may have seen the Markowitz efficient frontier as shown in Figure 1. The efficient frontier represents portfolios of risky assets that have the highest expected return (Y-axis) for a given level of risk (X-axis). Portfolios on the efficient frontier dominate all other portfolios (represented by individual points in Figure 1) on a risk versus expected return basis. In other words, any portfolios that fall below the efficient frontier are sub-optimal because they do not provide as much expected return per unit of risk as do portfolios on the efficient frontier.

If investors can invest in a hypothetically risk-free T-bill (represented by Rf in Figure 1), they can combine it with optimal portfolios on the efficient frontier to create various Capital Allocation Lines (CAL). The CAL with the steepest slope (i.e. Sharpe Ratio) will be the CAL that combines the risk-free asset with the tangency portfolio labeled M in Figure 1. This portfolio is optimal because it has the highest Sharpe Ratio. Modern portfolio theory suggests that for a passive investment strategy that does not devote resources to picking individual stocks, the tangency portfolio will be a capitalization-weighted market portfolio, which is why we choose a label of “M”. Relatedly, the optimal CAL that passes through M is known as the Capital Market Line (CML). Combining Rf and M in various weights creates portfolios that plot along the CML. This line dominates the efficient frontier because it represents portfolios that have a higher level of return per unit of risk than any portfolios on the efficient frontier. In essence, the CML becomes the new efficient frontier in an environment where investors can borrow and lend at a hypothetical risk-free rate.

For illustrative purposes only. Not representative of any particular product or portfolio.

This framework suggests that it is optimal for investors to hold the market portfolio M (keep in mind that this construct assumes that investors cannot generate alpha by deviating from a market portfolio), which could be represented by the S&P 500 for instance. But, what if we were to tell you that the scatter of individual portfolios in Figure 1 only represents a specific market, namely the U.S. market, and that it is not inclusive of all possible risky assets that an investor can buy? What if we added portfolios of foreign stocks to the mix?

To answer these questions we examined historical data for U.S. and foreign stock market indices. The data show that U.S. stocks and foreign stocks are not perfectly correlated with each other and that foreign stock markets have different Sharpe Ratios than the US stock market. This implies that a portfolio that combines U.S. and foreign stock market indices can achieve a Sharpe Ratio that is higher than the Sharpe Ratio of the U.S. market portfolio alone. The mathematics of the efficient frontier explain this implication. The efficient frontier is bow shaped because of the uncorrelated nature of assets that make up optimal portfolios (those that maximize return per unit of risk) along the frontier. As assets become more uncorrelated the risk of a portfolio that combines them declines, and the bow shape of the efficient frontier becomes more exaggerated. The opposite is also true, if assets were perfectly correlated the efficient frontier would resemble a straight line.

The benefits of diversification are made clear by the efficient frontier, and the effect becomes more pronounced as more uncorrelated assets are introduced. Since foreign asset returns are not perfectly correlated with U.S. asset returns, by combining the blue points (foreign assets) with the orange points (domestic assets) in Figure 2, investors could achieve better diversification and risk reduction than they could have otherwise achieved with domestic assets alone. This would cause the efficient frontier of optimal portfolios to improve to become Efficient Frontier* in Figure 2. The improved frontier would result in a more optimal global market portfolio (M*) and a new CML (CML*), that has a higher Sharpe Ratio than the original CML.

For illustrative purposes only. Not representative of any particular product or portfolio.

The overall conclusion is that investors who are passively investing in a U.S. market index can benefit by broadening their horizons and investing in international equity markets. In theory, buying the global market portfolio M* should provide investors with the highest attainable Sharpe Ratio. Low-cost foreign equity ETFs are a great way to access foreign markets efficiently. The benefits of international diversification were also discussed in one of our previous white papers.

Diversification may not necessarily ensure a profit or protect against a loss.

Eric Legunn
ETF Strategist
 
For general inquiries:
(844) 851-4255

 

Investors who are passively investing in a U.S. market index can benefit from broadening their horizons and
investing in international equity markets.

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