Currency Valuation: A (Basic) Quantitative Analysis of the Foreign Exchange Market

As the world becomes more globalized, currency valuation becomes more important. As the Federal Reserve continues on the slow grind to higher interest rates, currency valuation becomes more important. As inflation increases, currency valuation becomes more important.

Basically, as long as we have fiat currency, we have to pay close attention to the micro and macroeconomic forces.

This is a “learning blog”. It doesn’t have my opinion scattered throughout. This is information from my FIN 436 class at my university, using Jeff Madura’s International Financial Management: 13th Edition Textbook.

So here is a very base-level calculation of currency valuations.

**be on the lookout for my next blog in the coming week**

Exchange Rate Calculations

Let’s say $40 million of cash flows for a company come from the USA and €20 million come from European operations. The exchange rate (S) is EUR/USD $1.30. This means that 1 Euro is worth $1.30 US Dollar.

So how much does the company make, in dollar terms?

To calculate exchange rates, we want to convert Euros into USD. In that case, we would multiply the Euro by the exchange rate. (Euro x S).  So our €20 million Euros are worth  (20m x 1.3) $26 million USD.

But what if we wanted to convert US Dollars into Euros? In that case, we could find the inverse of the above exchange rate

(S = 1/1.30, which would be represented as USD/EUR = 0.78 ) $40m x €0.78

or we could simply divide the USD by the exchange rate (40m / 1.3). Either way, our $40m USD will turn into €30,769,230.

The company makes $40m + $26m = $66m in cash flows in USD. They make €50,769,230 in Euros.

KEY TAKEAWAYS

  • When converting the foreign currency to the base currency, multiply the value by the exchange rate
  • When converting the base currency to the foreign currency, divide the value by the exchange rate

Demand and Supply of Currency

When the value of a currency decreases, the demand for that currency increases. When the value of a currency increases, the supply of a currency increases.

For example, let’s say that a US Parent Company (aka Multinational Corporation or MNC) owns a French Winery, with EU Customers. The US Company wants the Euro to appreciate, because that means that they are getting more dollars per every Euro when the revenues come in.

When expected foreign cash flows increase and the required rate of return decreases (less uncertainty) that improves the value of the US Company.

Conversely, if expected cash flows decrease, the value of the currency decreases (in this case, the Euro), or the required rate of return increases (more uncertainty) then the value of the MNC decreases.

KEY TAKEAWAYS:

MNC Value Increases MNC Value Decreases
Expected Foreign Cash Flows Increase Decrease
Value of the Currency Increase Decrease
Required rate of return Decrease Increase

Balance of Payments

  1. Current Account: summary of flow of funds due to purchases of goods (imports and exports), primary income payments (interest and dividends), secondary income
  2. Financial account: special types of investment, Direct Foreign Investment, and Portfolio Investment
  3. Capital Account: value of financial and non-financial assets across country borders

The Current Account and the Capital Account and the Financial Account should all balance out to equal zero.

Current + Capital + Financial = 0

  • But this normally has to be achieved with a balancing item because this relationship is not always true, for the reasons listed below

Factors Affecting the Balance of Payments:

  1. Cost of Labor: when this increases, the current account decreases
  2. Inflation: current account decrease if inflation increases
    • If inflation increases, prices increase, and exports decrease
    • If there is deflation, prices decrease, and exports increase – but people postpone buying
  3. National Income: imports will increase if a country has more wealth
    • Decreases the current account because imports increase
  4. Credit Conditions: tightens when economic conditions weaken

flow

5. Government Policies

  • Restrictions on imports tariffs and quotas
  • Subsidies to exporters
  • Restrictions to piracy
  • Environmental restrictions
  • Labor laws
  • Business laws

Currency Valuation

If the USD increases in value, demand for the USD decreases. Subsequently, the number of exports would decrease because it is more expensive to purchase those items. The supply would increase because more people are looking to get into a less expensive currency, and it’s a good time to sell.

**This is at the individual level. For businesses, they look to invest in countries where the currency is expected to strengthen**

If the USD decreases in value, demand for the USD increases. For the same reason above, the number of exports would increase because it is less expensive to purchase those items. The supply would decrease because the currency is cheap to hold onto.

Foreign Exchange Market

The bank makes money through the difference between the bid (buy) and ask (sell) quote. The bid ask spread can be represented by dividing (Ask Rate – Bid Rate) by the Bid Rate **this is confusing sometimes: for individuals, the ask is the buy quote and the bid is the sell quote**

Changes in Exchange Rate 

E = f(∆INF, ∆INT, ∆INC, ∆GC, ∆EXP)

  • Inflation
    • Increase in inflation: increase in demand for foreign goods, decrease in demand for US goods. This puts upward pressure on the foreign currency
  • Interest Rates
    • Increase in rates leads to an increase in demand for USD, which puts upward pressure on the dollar
  • Income Levels
    • Increase in US income leads to an increase in US demand for foreign goods, putting upward pressure on the foreign currency
  • Government Controls
    • Imposing foreign exchange rules and trade barriers reduces the demand for the USD
Increase Decrease
Inflation Demand for Foreign Goods ⇑ Demand for US Goods ⇑
Interest Rates Demand for USD ⇑ Demand for Foreign Currency ⇑
Income Levels Demand for Foreign Goods ⇑ Demand for US Goods ⇑
Government Controls Demand for Foreign Goods ⇑ Demand for US Goods ⇑

Foreign Exchange Example

Chicago Co. expects the exchange rate of the New Zealand dollar (NZ$) to appreciate from its present level of $.50 to $.52 in 30 days. Chicago Co. is able to borrow $20 million on a short-term basis from other banks. Present short-term interest rates (annualized) in the interbank market are as given in the table. What steps Chicago should take?

 Currency Lending Rate Borrowing Rate
USD 6.72% 7.2%
NZD 6.48% 6.96%

First of all, the currency is expected to appreciate. For that reason, we would borrow in USD, because we don’t want to pay more at the end of the term because of currency valuation changes.

  1. We would borrow $20m in the US @ 7.2%
    • We have to adjust this interest rate for 30 days, which involves using the bank lending rate equation:
      • 1+(.072*30360) = 1.006
      • We would then multiply that by $20m to get $20,120,000m
  2. We would then lend the $20m into $NZ markets
    • NZ/USD = $0.50 –> $20m / 0.5 = $NZ 40m (converting from USD)
    • The interest rate in this market is 1+(.0648*30360) = 1.0054
    • The number of $NZ received is $40,216,000m
    • This equates to $40,216,000 x 0.52 = $20,912,320 USD
  3. The profit recieved is $20,912,320 – $20,120,000 = $792,320

What if the currency is expected to depreciate, falling from $0.50 to $0.48?

If the currency is expected to depreciate, then we would want to borrow in the foreign currency so we don’t have to pay back as much in the end.

  1. We would borrow $20m in New Zealand @ 6.96%
    • $20,000,000 / $0.50 = $NZ 40m
    • We have to adjust this interest rate for 30 days, which involves using the bank lending rate equation:
      • 1+(.0696*30360) = 1.0058
      • We would then multiply that by $NZD 40m to get $40,232,000m
      • Convert to USD = $40,232,000m x 0.48 = $19,311,360
  2. We would then lend the $20m into USD markets @ 6.72%
    • $20m x 1+(.0672*30360) = $20,112,000m
  3. The profit recieved is $20,112,000 – $19,311,360 = $800,640

KEY TAKEAWAYS:

When a currency is expected to appreciate, you borrow the domestic currency, and lend the foreign currency. When a currency is expected to depreciate, you borrow in the foreign currency, and lend the domestic currency.

Carry Trade

Let’s say that you have $100,000 that you want to invest. You notice that British interest rates are expected to increase soon. You decide to take your $100k and borrow 600,000 Euros to invest the British Pound (GBP).

On your Euros, you pay 0.5% interest. The exchange rate is EUR/USD = $1.20. On the GBP, you receive interest of 1%. GBP/USD = $1.80.

The first thing that you have to do is calculate the carry rate. This is a little bit confusing, but the general structure behind exchange rates is that the currency in the numerator is the one that you are “calculating” for. So, the exchange rate above – EUR/USD = $1.20 – means that 1 Euro is equal to $1.20 dollars.

  1. So when we calculate the carry rate in this situation, we want to find how many Euros equals one pound, because we are converting our Euros into pounds. To do this, we would calculate GBP/EUR, which is:
    • $1.8 / $1.2 = 1.5. So this means that 1 pound is equal to 1.5 Euros.
  2. The next step would be converting our USD $100,000 into pounds. In this scenario, we would divide the USD by the exchange rate, because we are converting from USD. If we were converting pounds into dollars, then we would multiply:
    • $100,000 / 1.8 = 55,555 pounds.
  3. Then, we need to convert our Euros into GBP. This involves taking the exchange rate we already calculated (GBP/EUR = 1.5):
    • 600,000 / 1.5 = 400,000 pounds
  4. The next step would be to add those together, to get a total investment of 455,555. We receive a 1% return on that investment, which calculates to:
    • 455,555 x 1.01 = 460,110 pounds- So we received a total of 460,110 pounds on our investment in the GBP.
  5. However, we still have to repay our 600,000 Euro loan. There was an interest rate of 0.5% on this loan.
    • 600,000 x 1.005 = 603,000 Euros
  6. We would then divide these 603,000 Euros by the GBP/EUR exchange rate of 1.5 to convert it into pounds.
    • 603,000 / 1.5 = 402,000 pounds
  7. So we received 460,110 pounds in our investment, but have to repay 402,000 pounds as a result of the leverage used to invest.
    • 460,110 – 402,000 = 58,110 pounds – this is the profit that we made on our investment.
  8. To convert that back to dollars, we would multiply by the GBP/USD exchange rate
    • 58,110 x 1.80 = $104,598
  9. We initially invested $100,000 of our own money, which means that we made $4,598 on that investment
    • $104,598 – $100,000 = $4,598

But what if the Euro appreciated by 3% during that time period?

That would mean the EUR/USD exchange rate would increase to $1.236 (1.2 x 1.003). The GBP/EUR exchange rate would then be 1.8 / 1.236 = 1.456.

We would need to start again at Step 5 in the above process. We wouldn’t start at step 3 because the appreciation happened over time. The GBP/EUR rate was 1.5 in the beginning of the transaction, but declined to 1.456 by the end of the period.

  1. We now have to pay back 414,148.35 pounds, versus the 402,000 without appreciation.
  • 603,000 / 1.456 = 414,148.35 pounds.
  1. The profit on our investment has changed. We now make:
  • 460,110 – 414,148.35 = $45,961.65 pounds
  1. Converting that back to dollars results in
  • 45,961.65 x 1.8 = $82,730.97
  1. We initially invested $100,000 of our own money, which means that we made $4,598 on that investment
  • $82,730.97 – $100,000 = $17,269.03 LOSS

Conclusion

It is important to know the intricacies behind the calculations above. But honestly, this is a really basic look at valuations. Also, macroeconomic forces have a tendency to wreck things, so this is definitely in a vacuum.

Currencies are really interesting, and I plan to spend more time analyzing them in the future – but from a Kyla perspective. A good friend is currently writing his thesis on how cryptos move compared to fiat currency.

I will eventually find a way to link my outside work somewhere on the blog, but for now, enjoy my whitepapers about various subjects. Because that’s what this blog really is.

Also, this blog is probably my favorite thing I do. It’s mine, and it enables me to process things in a unique way and share it with others.

What more can you ask for?

– KS

Disclaimer: These views are not investment advice, and should not be interpreted as such. These views are my own, and do not represent my employer. Trading has risk. Big risk. Make sure that you can balance your risk/reward, and trade small, and trade often.

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