How to build a currency basket? I

Imagine our main currency is euros. We are paid in euros and we live in a euro country. But we don´t trust our currency that much, or we are not sure where we will live in a few years, or simply to diversify our portfolio, we want to create a currency basket. Problem: which currencies and in which percentage?

First of all, we don´t want to talk about the different tools to invest in a specific currency (funds, Forex account, foreign stocks...). Here we will only show an algorithm to build a reasonable currency exposure.

Second, we have picked the currencies based on fundamental reasons and volume, with no emergency countries involved. The result is CHF, AUD, CAD, USD, and GBP. We will return to this selection in another article. (Note: no yen due to awfully bearish perspective.)

To calculate their weights in our basket we will deal with 4 aspects: PPP (Purchase Power Parity), market, inflation, and interest rates:
  1. Using the Big Mac Index, we will display the "fair value" of each currency against the euro: EURCHF=1.929, EURAUD=1.288, EURCAD=1.228, EURUSD=1.062, and EURGBP=0.68.
  2. Now, we will consider that the market knows the fair price for these pairs and we will write down the 130-simple-monthly average of each one. With the same order as in the previous point: 1.5143, 1.663, 1.4884, 1.2287, and 0.7218.
  3. We will average the data from 1 and 2, and we will get what we call Simple Big Market Value (SBM): 1.7217 (CHF), 1.4755 (AUD), 1.3582 (CAD), 1.1454 (USD), and 0.7009 (GBP).
  4. Next, we will write their interest rates, using Global Rates, for instance. Libor 12 month of each currency will serve: 0.54%, 6.5%, 1.87%, 0.73%, and 1.58% for the pound.
  5. Then, we will extrapolate next-year inflation with the help of Index Mundi. How? We add last year differential to the present inflation. Step by step. We will search "inflation Switzerland" within Index Mundi, and we will get this page. We can see that in 2010 inflation was -0.5% and in 2011: 0.7%. Then we will estimate that in 2012, inflation is going to be 0.7+(0.7-(-0.5))=1.9%. We do the same thing with each currency and get: 1.9%, 4%, 2.9%, 2.7%, and 4.4%.
  6. We calculate the difference between the figures in point 4 and point 5 (RIR, real interest rates) and obtain: -1.36% (CHF), 2.5% (AUD), -1.03% (CAD), -1.97% (USD), and -2.82% (GBP).
  7. Somehow, investors prefer to earn money through interest rates avoiding inflation. We take it into account by calculating (1+RIR)^10: 87.19%, 128.01%, 90.19%, 81.93%, and 75.09%, respectively. We call it CORRECTION.
  8. We are close, now. Under no other circumstances, the usual weight should be 20% each currency (100%/5). However, we have seen some other factors. Let´s take them into account with the following formula: 20%*(ACTUAL PRICE/SBM)*CORRECTION, and we get: 12.19% (CHF), 23.33% (AUD), 18.5% (CAD), 20.24% (USD), and 18.82% (GBP). (Note: we have used EURCHF= 1.2036, EURAUD=1.3445, EURCAD=1.3928, EURUSD=1.415, and EURGBP=0.8784.)
  9. The problem is that the corrected weights don´t correspond with 100% but 93.08% in this case. Instead of 93.08% we want to show the weights for 100%, so linearly we just have to divide each weight by 93.08% and we finally get: CHF>13.1%, AUD>25.06%, CAD>19.87%, USD>21.75%, and GBP>20.22%.
The above follows a very practical approach. We just have to check out the portfolio every 2, 3, or 4 months.