Currency Appreciation vs Depreciation: One Move, Two Numbers

Appreciation is a currency buying more of another than it did before. Depreciation is the same currency buying less. Appreciation and depreciation are not mirror images in arithmetic: a rate is a ratio, so a rise of a given per cent in one currency is always a smaller per cent fall in the other. And neither direction is good or bad on its own. Each helps one set of people and hurts another.

All of it comes out of one sentence established under the exchange rate and the market that sets it. The number 80.00 says that one Marut unit costs eighty Sankhya rupees, and it says at the same moment that one rupee buys one eightieth of a Marut unit. Two readings, one number. Move the number and both readings move together. Each reading is the other turned upside down, so they cannot move by the same proportion.

What is currency appreciation?

A currency appreciates when it buys more of another currency than it did before. The definition is complete as it stands, and notice what is not in it. There is no mention of growth, of confidence, of strength, of anything at all happening inside the country whose currency it is. Appreciation is a statement about what one currency fetches in terms of another, and nothing more.

Work it on Sankhya. Suppose the rate moves from 80.00 to 76.00 Sankhya rupees per Marut unit. Read it the first way: one Marut unit now costs Rs 76/- instead of Rs 80/-, so a Marut unit is cheaper in rupees. Read it the second way: one rupee used to buy 0.012500 Marut units and now buys 0.013158 of them, so the rupee fetches more. Both readings describe the same event. The rupee has appreciated against the Marut unit.

Nothing inside Sankhya needs to have changed for its currency to appreciate. The rate is a price between two currencies, and either side of it can move. If more Marut units come looking for rupees this week than last, the rupee buys more, and a Sankhya factory that never traded abroad in its life has done nothing differently. The move happened on the other side of the price.

Feel it at household scale. A household in Sankhya sends a daughter to study in Marut. The fee is written in Marut units and the college has not changed it by a single unit. But each rupee now covers more of the fee, so the rupee amount the household has to transfer falls. Nobody negotiated. Nobody earned more. The price of the currency moved and the rupee bill followed. Appreciation arrives in a kitchen as a smaller transfer for an unchanged fee.

One more thing belongs inside the definition. Appreciation is always a statement about a pair. The rupee can buy more Marut units this month and fewer units of some third currency in the same month, and both sentences are true at once. So the question is never whether the rupee appreciated, but what it appreciated against.

What is currency depreciation?

A currency depreciates when it buys less of another currency than it did before. Same shape, opposite direction, and it deserves exactly the same room. Depreciation is the word readers get wrong far more often than the other one.

Take the same starting point and move it the other way. The rate goes from 80.00 to 84.00 Sankhya rupees per Marut unit. First reading: one Marut unit now costs Rs 84/- instead of Rs 80/-, so a Marut unit is dearer in rupees. Second reading: one rupee used to buy 0.012500 Marut units and now buys 0.011905 of them, so the rupee fetches less. The rupee has depreciated against the Marut unit, and a basket priced at Rs 8,000/- before the move takes Rs 8,400/- after it.

A fall does not by itself mean anything has gone wrong inside Sankhya. That sentence is the mirror of the one in the block above, and it is the harder of the two to accept. A currency can depreciate because the country on the other side of the price has become a place more people want to hold money in, for reasons that have nothing to do with Sankhya at all. The rupee number moved. Sankhya may have had an entirely ordinary week.

Back to the same kitchen. The fee written in Marut units has not changed, the college has not raised anything, and the household now has to transfer a larger rupee amount for the identical bill. The daughter is studying the same course. Depreciation is not a judgement that has been passed on Sankhya. Depreciation is a larger number on a transfer slip, and the two are constantly confused.

Note also that these are words about direction, never about level. A rate of 84.00 is not a weak rate and 76.00 is not a strong one. Both numbers take their size from which currency is written on top, and a currency that moves in both directions across a hundred trading days has appreciated and depreciated many times over without either word describing where it stands.

Why is one currency's rise not the other's fall in equal measure?

Now put the two definitions beside each other and something awkward falls out. Take the depreciation above, from 80.00 to 84.00, and ask how large the move was. There are two honest answers and they are different numbers.

Count it on the Marut unit. The Marut unit cost Rs 80/- and now costs Rs 84/-, a rise of Rs 4/- on Rs 80/-, or 5.00 per cent. Count it on the rupee. The rupee bought 0.012500 Marut units and now buys 0.011905, a fall of 0.000595 on 0.012500, or 4.76 per cent. One event. Five per cent up on one side, four point seven six per cent down on the other, and neither figure is a mistake.

The difference is not rounding: a ratio and its reciprocal cannot move by the same proportion, and the gap between the two readings widens as the move gets larger. The cleanest way to see why is to say it without any algebra at all. The hundred the Marut unit started from was its own old rupee price, so the Marut unit rose by five parts in that hundred. The rupee fell by those same five parts, but the base the fall is divided by is the new, larger number, so the rupee fell against a hundred and five. Five in a hundred is 5.00 per cent. Five in a hundred and five is 4.76 per cent. Those two bases are the entire asymmetry.

Watch the gap grow

Take a much larger move on the same pair, from 80.00 to 100.00. The Marut unit rises by twenty parts on eighty, or 25.00 per cent. The rupee falls by twenty five parts on a hundred and twenty five, or 20.00 per cent. The gap is no longer a quarter of a point. The gap is five whole points, more than twenty times as wide as before, on a move only five times as large.

Draw the gap against the size of the move and it stops looking like a curiosity. The line bends upward. For small moves the gap is nearly invisible, and nobody argues about a rate that shifts by a tenth of a per cent. For large moves the gap becomes the difference between two headlines that both claim to describe the same week.

Two useful habits fall out of this. The first is a rule that carries anywhere. Whichever currency rose is the one divided by the smaller starting number, so that currency always shows the bigger percentage. The second is a warning. A report that says the rate moved by five per cent has given half a ratio, and which half cannot be told without asking which currency was written on top.

The shape is familiar for a reason. The treatment of terms of tradeThe ratio of the prices a country gets for what it sells abroad to the prices it pays for what it brings in. Covered in the international trade sequence. ran into the identical arithmetic, because that too is an index built as one price divided by another, and dividing is what produces the asymmetry. The asymmetry is not a currency quirk. It is what ratios do.

Who is helped and who is hurt in each direction?

Here is where the two words stop being arithmetic and start landing on people. And the most useful thing to notice first is structural: every group that gains from a move has a counterpart group that loses from the same move, usually sitting in the same country and sometimes in the same street.

Think about a wedding. The caterer raises the rate per plate. The caterer is better off by exactly what the household paying for the wedding is worse off by, and no wealth has been created or destroyed by the change in the rate per plate. The wealth has been moved. A currency move works the same way, except that the two sides are usually strangers to each other and neither can see the transfer happening.

Run both directions across the same rows. Read the middle column for a rupee that falls from 80.00 to 84.00 and the right column for a rupee that rises from 80.00 to 76.00.

Every row that gains has a counterpart row that loses, so a currency move is a transfer between groups inside a country rather than a gain or a loss for the country. Read the table as four pairs rather than eight rows. The seller abroad is paired with the buyer abroad. The maker competing against goods from Marut is paired with the household buying those goods. The household receiving money from Marut is paired with the borrower owing money in Marut units. The guest house is paired with the traveller. Each pair sits on opposite ends of the same move.

Two terms help here, and both are defined elsewhere. Anything bought from Marut arrives with a landed costWhat a brought in good actually costs by the time it reaches the buyer: the price abroad, converted, plus freight, insurance and any duty. that is settled partly by the rate on the day. And a borrower with instalments written in Marut units carries an exposureAn amount whose value in the holder's own currency depends on a rate the holder does not control. Instruments for managing one are covered under derivatives. whose rupee size moves without anyone at the borrower doing anything. Managing such an exposure is a derivatives subject, covered separately.

Why can a country not simply prefer one direction?

If a fall helps everyone selling abroad, the obvious next thought is that a country selling a great deal abroad should simply want its currency lower. The two effects run through the same books, so the thought does not survive contact with a single firm.

Take Vaneri Looms, an invented Sankhya exporter. The firm sells 5,000 Marut units worth of cloth a year, and the price in Marut units does not change when the rate does. Its input bill is Rs 3,00,000/- a year at a rate of 80.00, and 60 per cent of that bill, Rs 1,80,000/-, buys yarn and dye from Marut. The yarn and dye come to 2,250 Marut units of inputs. The other Rs 1,20,000/- is spent at home and is untouched by any rate.

Now let the rupee fall from 80.00 to 84.00 and hold the Marut prices and the quantities where they are.

Both lines rose. Every Marut unit earned now converts into more rupees, so the receipts rose by 5.00 per cent. The imported part of the input bill rose by exactly the same 5.00 per cent for exactly the same reason, and that drags the whole bill up by 3.00 per cent. Two fifths of the bill never left Sankhya.

The two effects run through the same firm, so whether the move helps Vaneri Looms is an empirical question about how much of what it sells was bought abroad first. The two lines are not subtracted from one another, for a reason. Getting a difference out of this table requires holding four things still at once: the Marut price of the cloth, the number of units sold, the Marut price of the yarn, and the domestic part of the bill. A real move rarely leaves all four alone. So the subtraction would not measure the firm. The subtraction would restate the four assumptions in rupees and return them looking like a finding.

Change the imported content and the picture changes with it. A firm that buys nothing abroad keeps the whole rise in receipts and sees no rise in costs. A firm that buys everything abroad sees both lines rise by the identical 5.00 per cent. Which is why a sentence beginning with the name of a country cannot end with an answer about a firm.

What does the direction of a move leave unsaid?

Both words are now in place, along with the arithmetic that makes them unequal and the groups they land on. One thing is still missing, and it is the thing readers most often assume they were given.

The direction does not say why. Two entirely different events can produce the identical fall from 80.00 to 84.00. In the first, Sankhya households and firms want more goods from Marut this quarter than last, so more rupees are offered for Marut units to pay for them. In the second, portfolio moneyForeign money placed in shares and bonds, able to leave at short notice, unlike money sunk into a factory. The two kinds are covered separately. that had been parked in Sankhya assets is sold and taken home, so more rupees are offered for Marut units to carry it out. Same pressure, same direction, same closing number on the screen.

A fall driven by rising demand for goods brought in and a fall driven by money leaving are the same direction and different events, so a number that gives only the direction says almost nothing about what follows. They differ in speed, in what else moves alongside them, in which part of the external account records them, and in how long they last. The reading on the screen carries none of that.

Whether one of them shows up in the current accountOne half of the external account, holding trade in goods and services, income and money sent home, while the other half holds claims and assets. Set out under the balance of payments. or against the money side of the external account matters a great deal for what comes next, and that split is set out under the balance of payments. Nor does the direction say anything about the policy rateThe rate at which the central bank lends to banks, the anchor for short term rates in the economy. Set separately, in the monetary policy sequence., or about prices at home, or about whether goods bought from Marut will get dearer at the shop and by how much. The causes of a fall, and who each cause reaches first, are the whole subject of rupee depreciation and who it hurts.

How does an analyst read a currency move on one firm?

Watch what somebody covering firms actually does when a move lands. The order of their steps is the practical form of the arithmetic above.

An analyst does not start with the direction. They start with the firm, and the first number they go looking for is what share of its costs was bought abroad, along with the currency each of its bills is written in. The currency on the bill is the detail people skip. The bill from a supplier can arrive with an invoice currencyThe currency a bill is actually written in, which decides who carries the rate risk on it. A sale abroad billed in the seller's own currency carries none for the seller. that is not the rupee, so a firm can sell entirely at home and still carry a rate exposure.

Then they run the same move across the whole of that firm rather than one line of it. Receipts, the imported part of the cost base, any instalment written in another currency, and the price of the competing goods on the shelf next to its own. A move that lifts one of those lifts others, and the useful output is a list of the lines it touched rather than a single word about whether it helped.

A lender does the same work for a different reason. When a borrower carries instalments written in Marut units and earns in rupees, the rupee size of the obligation moves without the borrower selling one item less, so the lender wants to know whether earnings move alongside it or not at all. And a household does a small version of it every time it plans a fee abroad, a trip, or a purchase with a long delivery date.

The direction of the move is national and the answer is firm by firm. The practitioner therefore reaches for imported content before reaching for an opinion. Nobody who does this work reads the rate and concludes anything about a company. They read the rate, then go and look at the company.