We recently wrote a piece titled "Does the U.S. Need a Strong Dollar?" in which we argued that the fall of the dollar was 1) not unprecedented and 2) would only help the U.S. economy through export relief.

A number of readers commented that, even though a falling dollar may help the broad economy, a weak currency will harm asset prices and stunt future growth.

Further, as the drop in currency persists, bond returns will also depreciate.

Statistical analyses of stock and bond returns yield the opposite result. A weak currency helps boost returns of U.S. assets.

The common conclusion was that firms had used the options market to successfully hedge against exchange-rate risk and, as a result, investors did not worry about firms losing profit due to changes in the dollar's value.

In a paper titled "The Exchange-Rate Risk Exposure of Asset Returns," Chow et al. evaluated the exchange-rate risk problem a little differently.

Exchange-rate risk is a temporal problem, i.e., firms hedge against the risk but the quality of the hedge depends on the time duration between the firm's cash-flow and its options call. Short-term hedging results are a much better forecast of exchange-rate risk than long-term.

Chow et al. looked at how investors handled the exchange-rate risk by evaluating stock market returns at different lengths of time.

What they found was that exchange rates played no statistical role in determining stock market returns at 1-, 3-, or 6-month intervals. However, as exposure to exchange-rate risk became greater over time, stock market returns showed stronger statistical correlations at 12-, 24-, 36-, and 48-months.

Chow et al. offered statistical proof that short-term investors should not worry about exchange-rate risk.

While it is interesting to know who should worry about exchange-rate risk, it is also important to know what exchange-rate risk can do to stock market returns.

The statistical results showed that increases in the dollar's value negatively impact stock market returns in the long-run but produce no effect in the short-term.

The reason is a little complicated. Exchange-rate risk can be broken down into two components: interest-rate effects and cash-flow effects.

The interest-rate effect looks at how changes in the exchange rate affect current and future interest rates. While it may seem odd considering many of the financial pundits have been calling for the Fed to raise rates to stop the current currency depreciation, historically a depreciating currency is accompanied by decreases in interest rates.

If this relationship holds, when firms invested their current cash in the short-term they would not only reap the benefits of the current interest rate, but if the currency depreciates they will also receive a higher rate than what they would receive in the future.

The cash-flow effect looks at how changes in the exchange rate affect future cash-flow receipts.

Let us assume the dollar's value unexpectedly depreciates. In the near term, the firm's revenue would decrease due to the drop in the value of the dollar. However, in the long-run the firm is able to adjust for the price depreciation by selling more goods. Revenues should rebound over time until a new equilibrium point is reached.

Chow et al. was able to determine that a 1% depreciation in the dollar would lower earnings per share between $0.39 and $0.49 during the first year, but the increase in sales would push up earnings between $4.18 and $4.51 in the second year and another $0.75 to $1.87 in the third year. By the fourth year, sales would stabilize.

In the end, short-term returns do not show any gains from changes in the dollar's value as the interest-rate and cash-flow effects cancel each other out. However, in the long-run both the interest-rate and cash-flow move in the same direction, which pushes returns higher when the dollar depreciates.

Bonds do not have a cash-flow component as the payments are all made in U.S. currency. The only way exchange-rates affect bonds is through interest-rate effects.

Given that interest rates, historically, have fallen when the dollar has depreciated, lower future interest rates shrink yields and increase prices.

Bond prices would then increase, not only in the short-run, but also in the long-run.

So bond investors need not worry about exchange-rate risk, regardless if they are short-term or long-term buyers, so long as the dollar is depreciating. They would need to worry, however, whether they are short-term or long-term buyers, in the event the dollar appreciates.

While the media continues to plug away that the depreciation of the dollar is bad for the market, statistical evidence shows otherwise.

Stock market returns have no relationship with exchange-rate risk in the near term, and in the long-term, equities rally when the dollar depreciates.

Bond returns increase in both the short-term and long-term when the dollar depreciates.

--Jeffrey Rosen, Ph.D., Economist