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How lazy trading explains FX market puzzles

Not all market participants respond to changing conditions instantaneously, not even in the FX market. Private investors in particular can take a long while to adapt to changes in global interest rate conditions and even institutional investors may be constrained by rules and lengthy process. A theoretical paper shows that delayed trading goes a long way in explaining many empirical puzzles in foreign exchange markets, i.e. deviations from the rational market equilibrium, such as the delayed overshooting puzzle or the forward discount puzzle. Understanding these delays and their effects offers profit opportunities for flexible information-efficient traders.

Bacchetta, Philippe and Eric van Wincoop (2018), “Puzzling Exchange Rate Dynamics and Delayed Portfolio Adjustment”,  June 3, 2018

The post ties in with SRSV’s summary lecture on information efficiency, particularly the section on why markets are information inefficient.
The below are quotes from the paper. Emphasis and cursive text have been added. Some formulas have been replaced by verbal description.

The plausibility of delayed portfolio adjustment

“Richard Thaler won the 2017 Nobel Prize in Economics for incorporating psychologically realistic assumptions into analyses of economic decision-making…One area in which Thaler has noticed behavior inconsistent with what he refers to as rational efficient markets, is the foreign exchange market…’a rational efficient markets paradigm provides no satisfactory explanation for the observed results…At least some investors are slow in responding to changes in the interest differential…It may be that these investors need some time to think about trades before executing them, or that they simply cannot respond quickly to recent information’.”

“[There is empirical] evidence of delayed adjustment in investors’ portfolios. Investors make changes to their [retirement] allocations very infrequently…The Panel Study of Income Dynamics (PSID) and the Survey of Consumer Finances (SCF) [show] widepread inertia of portfolios in response to stock market fluctuations. [Research] based on PSID data concludes that ‘one of the major drivers of household portfolio allocation seems to be inertia: households rebalance only very slowly following inflows and outflows or capital gains and losses’.”

“Delayed portfolio adjustment can account for a broad set of puzzles about the relationship between interest rates and exchange rates…The equilibrium real exchange rate [under delayed adjustment] depends on the lagged real exchange rate and the present discounted value of expected future real interest rate differentials… Higher portfolio adjustment costs imply that the real exchange rate depends to a greater extent on the value of the real exchange rate during the last period and future expected real interest rates are discounted more heavily in the equilibrium real exchange rate.”

The delayed overshooting puzzle

“Delayed overshooting puzzle [means that] a monetary contraction that raises the interest rate leads to a period of [local currency] appreciation, followed by gradual depreciation… After monetary policy tightening, the currency continues to appreciate for another 25-39 months before it starts to depreciate.”

“Consider an increase in the foreign interest rate. There will be an immediate appreciation of the foreign currency as investors shift to foreign bonds. Subsequent to the shock, there are two opposing forces at work. On the one hand, the foreign interest rate starts to gradually decline again, which leads to a shift away from foreign bonds and therefore a gradual depreciation. On the other hand, to the extent that portfolios are slow to adjust, there will be a continued flow towards foreign bonds, which leads to a continued appreciation. When inertia is sufficiently large, the second force dominates and there will be delayed overshooting….The time to maximum impact rises significantly with inertia.”

The forward discount puzzle

“Forward discount puzzle [means that] high interest rate currencies have higher expected returns over the near future.2

“When there is delayed overshooting, the foreign currency is expected to appreciate for at least one more period after the initial appreciation. The foreign currency will then have a positive expected excess return both due to the higher interest rate and the expected appreciation. Therefore, inertia, which causes a gradual portfolio shift to the foreign currency that leads to continued appreciation, increases…predictability.”

“When inertia is very small, there is not much delayed overshooting, weakening the excess return predictability. If instead inertia is very large, the weak portfolio response causes a very slow response of the exchange rate, which also diminishes excess return predictability. Predictability is therefore largest for an intermediate value of inertia.”

The predictability reversal puzzle

“Predictability reversal puzzle [means that] high interest rate currencies have lower expected returns after some period of time…While the excess return over the next quarter is positive for higher interest rate currencies (forward discount puzzle), after about eight quarters the quarterly excess return is negative for currencies whose current interest rate is relatively high. In other words, there is a reversal in the sign of expected excess returns.”

“When inertia is sufficiently high there will be a predictability reversal. While initially, after the increase in the foreign interest rate, the foreign currency is expected to have a positive expected excess return, after a certain period of time it is expected to have a negative expected excess return…The excess return on the foreign currency is driven both by the higher foreign interest rate and the change in the value of the foreign currency. Under delayed overshooting the foreign currency will at first appreciate for a while and therefore have a positive excess return. But after time it will start to depreciate, which contributes to a negative excess return.”

The forward guidance exchange rate puzzle

“Forward guidance exchange rate puzzle: the exchange rate is more strongly affected by expected interest rates in the near future than the distant future.”

“Under uncovered interest parity the exchange rate is equal to the unweighted sum of all future expected interest rate differentials. This implies that changes in expected interest rates in the near future have the same effect on the exchange rate today as changes in the expected interest differential in the more distant future. However, [empirical research] finds that expectations of interest differentials in the distant future have a much smaller effect on the current exchange rate than expectations of interest differentials in the near future.”

“Under uncovered interest parity the real exchange rate is equal to the interest parity real exchange rate, where there is no discounting.”

“To see the role of inertia…consider an expected one-period increase in the interest rate differential at some time in the future. The only reason the real exchange rate appreciates prior to that future date is an expectation of subsequent appreciation. The response of the real exchange rate prior to the date of the interest differential increase is reduced as a result of a positive inertia as portfolios are less sensitive to expected returns…When going back all the way to the present, the response of the real exchange rate can be very small when time to the future date is large. There are multiple rounds of discounting as each period the real exchange rate response to an expected higher real exchange rate next period is reduced by inertia…[Hence], the [current] real exchange rate gives less weight to expected interest differentials in the distant future than the near future. The higher the inertia, the more future expected interest differentials are discounted in the equilibrium real exchange rate.”

The lack of predictability with long term bonds

“Long-term bond return differentials across countries are not predictable by current interest differentials.”

“The forward discount puzzle has no analogy in long-term bonds. While the international excess return on short- term bonds tends to be positive for currencies with a relatively high interest rate…this is not the case for long-term bonds…The local excess return of long-term bonds over short-term bonds tends to be lower for high interest rate currencies…This offsets the positive expected excess return for short-term bonds…No-arbitrage models in international finance cannot account for this.”

“[Academic research] shows that excess return predictability [of foreign-currency fixed income investments] vanishes when considering monthly returns of long-term bonds.”

“[In a model with long-term bonds] we observe the same delayed overshooting for the real exchange rate…What is new is the response of the relative long-term bond prices…The higher foreign interest rates causes especially foreign investors to reallocate their portfolio from foreign long-term bonds to foreign short-term bonds. This lowers the price of foreign long-term bonds, explaining the increase in the relative price of home long-term bonds…However, the process of reallocating from foreign long-term bonds to foreign short-term bonds continues over time as a result of gradual portfolio adjustment, leading to a continued decline in the relative price of foreign bonds. This generates a negative foreign minus home excess return of long-term bonds over short-term bonds…Even though the foreign currency is appreciating over time, this is offset by the negative foreign local excess return of long-term bonds over short-term bonds.”


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