**Model**

RD = domestic expected annual arithmetic real total return

SD = domestic volatility

Ri = international expected annual arithmetic real total return calculated in foreign currency

Si = international volatility calculated in foreign currency

RE = expected real exchange rate return

SE = real exchange rate volatility

coviE = expected annual covariance between international return and exchange rate return

corrDI = expected correlation between real domestic and real international returns

Rrf = real risk-free return

First estimate the expected return and volatility of international when expressed in real domestic currency:

RI = international expected annual arithmetic real total return calculated in domestic currency

RI = Ri - RE

SI = international volatility calculated in domestic currency

SI^2 = Si^2 + SE^2 - 2.coviE

Note the minus signs infront of the first RE and 2.coviE. They exist because the domestic value of international investments moves in the opposite direction to the exchange rate.

Now perform mean-variance optimization on RD, SD and RI, SD and compute the tangency portfolio to determine the relative allocations to international and domestic.

**Example**

Here is a rough example of applying the model assuming a world in which the same amount of risk buys the same amount of return when expressed in local currency, and using historical data for future expectations.

RD = Ri = 7% -- Real, arithmetic not geometric; Dimson et al. World returns 1900-2000.

SD = Si = 17% -- Dimson et al. World returns 1900-2000.

RE = 0%

SE = 6% -- Fred: Real trade weighted U.S. dollar index: broad (TWEXBPA) 1974-2016; I am currently uncertain this is the correct data series to use; it would be nice if this was an investment weighted rather than a trade weighted index.

coviE = -0.0055 -- covariance of TWEXBPA against CPI-U adjusted MSCI EAFE total return 1974-2015; corriE = -0.47.

corrDI = 0.92 -- portfoliovisualizer.com: correlation of VTI to VEU 2008-2016.

Rrf = -2% -- Fed: 1 month t-bill rate 0.52% less Survey of Professional Forecasters 2017Q1 CPI-U 2.2% 2017-01-13.

Gives:

RI = 7%

SI = 20.9%

and MVO then gives:

100% domestic, 0% international

**Questions and commentary**

What is wrong with this model? I understand valuations matter, but is it just a case of incorrect inputs, or is this simple model itself seriously flawed. Note that boosting Ri, to say 9%, gives a 57% domestic, 43% international breakdown, so the model doesn't always predict the corner case.

Is there a better model for incorporating the impact of unhedged exchange rate volatility? I'm reluctant to just use MVO on historical returns directly because of the uncertainty regarding the underlying returns. Even with 100 years of data, a 17% standard deviation implies a 6.8% wide 95% confidence interval on the underlying returns.

corrDI is high at 0.92, reflecting the domestic/international equity correlations over just the last 9 years. If I reduce it to 0.69 (the correlation between Shiller U.S. large and MSCI EAFE 1970-2015), I get 81% domestic, 19% international.

I read Vanguard's paper Considerations for investing in non-US equities. They mention exchange rates increase international volatility, but it is not incorporated explicitly into their asset allocation analysis, appearing possibly only indirectly through the data series they employ. They mention "the most likely scenario is one in which correlations remain elevated but in which volatility for non-U.S. markets more closely resembles that of U.S. markets", but it seems to me the volatility of international should always be expected to be higher than domestic due to exchange rate volatility.

If the model is OK, what inputs might you use?