To Hedge or not to Hedge

Get Over It

A foreign stock or bond contains two returns: its return in local currency, and the return of its currency component. What confuses the domestic investor is that when she purchases the security, the two components are intertwined. In order to separate out the local return it is necessary to sell the appropriate currency short, or "hedge." Consider a British stock that over a year's time appreciates 10% in price. This is the return an English investor, who deals in sterling, will receive. However, the American investor also receives the currency return as well. If the dollar appreciates (pound falls) during the holding period, the return will be less. If the dollar falls (pound rises) the return will be greater.

The amount of this currency to "hedge out" is a hotly debated point. On the one hand, there is no doubt that hedging reduces the risk of an individual stock or bond. Contrariwise, the currency component has an approximately zero correlation with almost all assets in local currency, and for this reason may be advantageous.

It is useful for the global investor to consider a foreign stock or bond in these terms. Assume for a moment that your portfolio contains 35% each domestic stocks and domestic bonds, as well as 15% each foreign stocks and foreign bonds. It makes no difference if the foreign stocks are hedged and the bonds are unhedged, or vice versa. Put another way, the portfolio can be considered to contain 35% domestic stocks, 35% domestic bonds, 15% hedged foreign stocks, 15% hedged foreign bonds, and 15% foreign currency. No matter that the total of all this is 115%—it's an extraordinarily useful device to start with foreign stock and bond returns in local currency ("hedged"), and then to add in the currency component as just another class.

In other words, the foreign currency in your portfolio doesn't know whether it is invested in stocks or bonds. Even the savviest investors occasionally fail to realize this.

Couched in these terms, the case for currency exposure (not hedging) seems tenuous. After all, currency is an asset which has a zero expected nominal return, which is not likely to be saved by its lack of correlation with other assets.

The most efficient way to investigate this problem is to consider it in a mean variance framework using reasonable returns assumptions and historical standard deviations and correlations. Unfortunately, because of the peculiarities of MVOs, it is nearly impossible to include an asset which does not "count" as part of the portfolio composition, and when I did so, and erroneously concluded that all portfolio assets should be hedged, reader Dexter Chu pointed out the error of my ways.

So I reverted to a spreadsheet method which allowed me to segregate out the currency components. We proceed as follows:

1. Quarterly returns for multiple global assets were obtained, all in hedged, or "local" returns.
2. Two currency returns series were added: Japanese yen and an amalgam of European currencies (35% Sterling, 15% each French Franc and German Mark, 10% Swiss Franc, Lira, and Guilder, and 5% Peseta).

The correlation grid and SDs are as follows:

	Japan IL	PacxJ IL	Euro IL	S&P	USSM	HEDIB	T Bonds	T BILL	EUROS	YEN
Japan IL	1.00
PacxJ IL	0.35	1.00
Euro IL	0.49	0.66	1.00
S&P	0.58	0.63	0.80	1.00
USSM	0.54	0.59	0.76	0.79	1.00
HEDIB	0.12	0.01	0.06	0.15	0.11	1.00
T BONDS	0.01	-0.24	-0.14	0.05	-0.08	0.68	1.00
T BILL	-0.06	-0.15	-0.08	0.04	-0.17	0.04	0.13	1.00
EUROS	-0.19	-0.34	-0.62	-0.29	-0.53	0.14	0.25	0.15	1.00
YEN	-0.07	-0.15	-0.39	-0.11	-0.26	0.07	0.15	-0.16	0.60	1.00
std (ann)	23.28	24.03	18.13	15.03	21.45	4.30	9.30	0.77	11.14	14.01

(Japan IL = MSCI Japan hedged, PacxJ IL = MSCI Pacific Rim hedged, Euro IL = MSCI-Europe hedged, S&P = S&P 500, USSM = US 9-10 Decile small stocks, HEDIB = Morgan Stanley International Bond Hedged, T BONDS = 20 year US Treasuries, EUROS = European currency return [see above], YEN = Japanese Yen)

Stock returns were assumed to be 10%, except for US small stocks which were assumed to return 11%. T bonds and hedged foreign bonds were assumed to return 6%, and t-bills 4.5%.

The expected return of both the yen and Euro is assumed to be zero, of course.

These inputs were fed into the spreadsheet optimizer, and after several system crashes, including one hair-raising DOS message reading "hard drive general failure," the following efficient frontier output was obtained (For the hard-core portfolio theorists among you, spreadsheet optimizations do not produce corner portfolios per se, just portfolios at given SDs or returns. They are considered to be rebalanced quarterly):

Japan	PacXJ	Euro	S&P	USSM	HedIB	T Bond	T Bill	Euros	Yen	Ret	SD
0.0%	16.7%	0.0%	0.0%	83.3%	0.0%	0.0%	0.0%	152.4%	0.0%	12.80%	18.44%
2.9%	18.1%	0.0%	0.0%	79.1%	0.0%	0.0%	0.0%	142.8%	0.0%	12.80%	18.00%
5.6%	13.8%	22.8%	0.0%	57.9%	0.0%	0.0%	0.0%	125.8%	0.0%	12.63%	16.00%
6.2%	7.9%	46.6%	0.0%	35.2%	0.0%	4.1%	0.0%	106.6%	0.0%	12.12%	14.00%
5.2%	8.1%	40.9%	0.0%	27.6%	0.0%	18.2%	0.0%	86.1%	0.0%	11.34%	12.00%
4.2%	7.3%	34.2%	0.0%	20.9%	14.0%	19.5%	0.0%	67.4%	0.0%	10.42%	10.00%
3.2%	5.6%	26.7%	0.0%	15.0%	38.3%	11.2%	0.0%	50.3%	0.0%	9.40%	8.00%
2.3%	3.6%	19.3%	0.0%	10.1%	54.2%	0.0%	10.4%	35.2%	0.0%	8.24%	6.00%
1.5%	2.8%	12.3%	0.0%	6.9%	32.5%	2.9%	41.0%	22.6%	0.0%	7.03%	4.00%
1.1%	2.2%	8.9%	0.0%	5.3%	25.2%	1.8%	55.5%	16.5%	0.0%	6.40%	3.00%
0.7%	1.5%	5.3%	0.0%	3.6%	18.7%	0.0%	70.2%	10.3%	0.0%	5.74%	2.00%
0.3%	0.9%	1.3%	0.0%	1.8%	8.4%	0.0%	87.4%	3.1%	0.0%	5.00%	1.00%
0.0%	0.3%	0.0%	0.0%	0.5%	2.1%	0.0%	97.2%	0.0%	0.0%	4.60%	0.74%

 

Like all optimizer outputs, these need to be taken with a bucket of salt, but our suspicions about currency are not confirmed. Clearly, European currency exposure seems to have great value, with ample representation in the high and medium risk portfolios—in fact, in amounts greater than that demanded by European stock and bond contributions. Not until the minimum variance portfolio (almost all t-bills) does the need for it disappear entirely. Not until the Euro annualized return is reduced below -2.8% does it disappear from the 10% SD portfolio. The reason why the Yen is less desirable is uncertain.

So hedging, at least for European stocks and bonds, is unnecessary. It also has real tax disadvantages—these are short-term contracts, which generate lots of unwanted income taxable at the marginal rate from time to time.

Until recently, passively managed international portfolios are available only in unhedged form. For the faint of heart, hedged portfolios (with expense ratios of about 1.3%) are now available from World Wide Index Funds. However, I still think that unhedged foreign exposure is the way to go. So when it comes to worrying about currency-induced portfolio volatility, get over it. If your foreign stock fund goes down the toilet with a fall in the Euro, take solace in the fact that:

1. In the long run, currency exposure reduces overall portfolio risk, and probably increases return, and
2. Your next visit to Tuscany just got a whole lot cheaper.

copyright (c) 1999, William J. Bernstein