The monetary approach starts from two assumptions and follows them to the end. Prices are flexible, and purchasing power parity holds. Then the price level in each country is set by its own money market, and the exchange rate is just the ratio of the two price levels:
S = P_domestic / P_foreign, with P = M / (k Y) in each country
so a permanent 10% rise in the domestic money supply raises the domestic price level 10% and depreciates the currency 10%. Clean, and empirically hopeless at horizons under a few years, because exchange rates move far more than money supplies and price levels do.
How does Dornbusch overshooting work?
Rudiger Dornbusch's 1976 paper in the Journal of Political Economy fixed the model by weakening exactly one assumption. Goods prices are sticky in the short run; asset prices are not. That single change produces a result nobody had derived from a rational model before: the exchange rate overshoots its long-run level on impact, then walks back.
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Follow the mechanism in words and let Worked Example 5 do the arithmetic. Spot is ₹84.5000 and a permanent 10% money-supply increase means the long-run rate must be ₹92.9500, because purchasing power parity holds eventually. In the short run prices have not moved, so the real money supply has risen and the domestic rate must fall to clear the money market, say from 6.75% to 3.35% against an unchanged 4.35% abroad.
Uncovered interest parity still has to hold as an equilibrium condition on asset returns. With the domestic rate 100 basis points below the foreign rate, investors hold rupee assets only if they expect the rupee to appreciate, by exactly (1.0335)/(1.0435) − 1 = −0.958313% over the year. But the long-run level is 10% weaker than today. The only way to expect an appreciation of 0.958313% and still arrive at 92.9500 is to jump past 92.9500 first:
S_impact = 92.9500 / (1 − 0.00958313) = ₹93.849371
That is an 11.064344% depreciation on impact against a long-run move of 10.00%, an overshoot of 1.064344 percentage points. The real exchange rate depreciates by the same 11.064344% on impact, drifts back as prices adjust, and returns exactly to where it started. Every long-run effect of the shock is nominal and every short-run effect is real, which is why a monetary devaluation buys trade competitiveness for a year or two and then stops.
Is overshooting rational, and what drives its size?
The overshoot is not irrationality and not a bubble. It is the unique path consistent with rational expectations when one price in the system moves instantly and another does not. That result explains a great deal of observed exchange-rate volatility without appealing to anybody behaving badly, and it is why "the currency moved more than the fundamentals justify" is a sentence that needs more work before it means anything.
The model is fragile in one place, which is the interest-rate response it does not itself observe. Halve the shock to 5% and let the domestic rate fall only to 3.95%, and the impact rate is ₹89.066414, a move of 5.404040% against a long-run 5.00%, so the overshoot shrinks to 0.404040 percentage points. A central bank that lets rates fall further overshoots more, and one that does not let them fall at all does not overshoot.