Economic basis

As Central Banks slowly start to play on the piano of interest rates, interest rate differentials in different currencies become, again, attractive for carry traders.

A carry trade in its basic structure involves a credit in low yielding currency and the investment of this credit amount in a high yielding currency.

A naïve carry trade simply follows the rate differentials. A more sophisticated carry trade looks for reason and shelter. For example a special country has a well-defined exchange-rate-policy, meaning, that the exchange-rate for its domestic money vis a vis another country or a set (basket) of countries shall deviate only xy basispoints from a defined target rate.

For achieving such a goal Centralbanks apply interest rate policy. Historical examples are the European Currency Unit (the predecessor of the EURO) or the long-term peg of the Swedish Krona to a basket of currencies.

A current example are the efforts by the Swiss Centralbank trying to prevent further appreciations of the Swiss Frank, by dictating even negative interest rates.

The trade

Foreign Exchange contracts are a simple way to effect such an “Interest Rate Arbitrage”. Instead of exchanging real flows of money only a fx-position is taken in the relevant cross. The high yielding currency is “longed” and the low yielding currency is “shorted”. Depending on the definition of the exchange -rate (the cross) the underlying contract is shorted or longed.

Lets take EURUSD, that is the defined cross between Euro and USD (this pure convention, USDEUR could be used as well, but the market has chosen EURUSD). If the interest rate in Euro is higher than in USD, we will go long EURUSD, otherwise we will go short EURUSD.

The cost of carry calculator by DUKASCOPY is a very helpful tool, showing all the tradable crosses and the daily cost or income of holding a long or short position in the respective cross. Positive figures imply interest income, negative interest cost.

But that is not the point of my paper. Up till now we have only concentrated on the INCOME SIDE. But as any medallion has a second side and as cited history above has shown, there is always a DOWNSIDE, currency risk – to name it.

According to the cost of carry calculator by DUKASCOPY USDZAR, currently trading at 11,93738, pays to the short position 14,39 bips and demands 18,20 bips from a long position.

On a relativ basis, a short in USDZAR will earn 1,2055 basispoints per day, or 440 basis points (4,40%) a year, ceteris paribus. Even a fully paid position (margin at 100%) would bring a nice yield of 4,40%, even after considering all costs (bid ask spread, slippage, commissions, etc).

At margin rates of 5% (500bp) to 10% (1.000bp) (NEVER go to limits your account is offering, ALWAYS define your personal margin rates , you can live with!) this appears to be the trade of your life.

The risk

But checking the chart for USDZAR shows any position in USDZAR, long or short, is quite a wild ride. As a measure of risk the daily current standard deviation of the rate is +/- 0,15070, (+/- 1,26% on a relative basis). (JForex Charts contain all the necessary information; Standard Deviation, Ranges, Correlation).

USDZAR 11,93738 +/- 0,15070 Correlation -0,3310 EURUSD 1,23666

The wrong move of one day can kill your annual yield expectation by 33%!

To avoid forced liquidation within one day, you should have at least a cash margin of 2,52% in your account. So you run your position on a Return-Risk-Ratio of 4,40% to 2,52% (mixing time periods!).

Now you have to answer the question; is this most return-risk efficient carry trade you can find, or is there a trade with a higher return for the same risk, or another with the same return but at a lower risk?

In this paper I will only introduce one other exchange rate. Given the interest, I will follow up with a more complete view on EFFICIENT CARRY TRADES for the whole Dukascopy universe of currencies.

The cure

Asset prices move together or they do not. The same holds for exchange rates. They might trend to-gether, up or down, they might trend in opposite directions or they might move without any common pattern.

Each of these scenarios is represented by the statistical parameter of CORRELATION. And as all things change in time, this parameter will change in time as well. But the current value is a good starting point to build a position.

Depending on this parameter the most efficient mix of carry positions can be calculated, by hindsight. But as long as I have no chance to predict the most efficent future mix, I will start with the best mix currently available.

EURUSD pays 0,75 pips on short position, in relative terms we get 0,61 bp on a daily basis at a rate of 1,23666. The annual yield is a promising 2,21% (221 bp). About the half of USDZAR.

EURUSD 1,23666 +/- 0,00700 ....... Correlation -0,3310 ....... USDZAR 11,93738

The daily standard deviation is at +/- 0,00700; 0,57% respectively. Our margin requirement is about 1,14%.

Half of the return at less than half the risk of USDZAR shows, our USDZAR position is not efficient. For the risk of USDZAR, we could run 2,21 EURUSD positions, yielding 4,88% annually.
But that is still not the end. According to Nobel laureate Harry Markowitz we can calculate all efficient combinations of the two positions, and moreover we can calculate the specific mix, that has the lowest (historical) risk.

Risk USDZAR (RU): +/- 1,26%.... Risk EURUSD (RE): +/- 0,57%..... Correlation (C): -0,3310....

Risk-minimal weight for USDZAR (WU) = (RE^2 – RU * RE * C) / (RU^2 + RE^2 – 2 * RU * RE * C)

Risk-minimal weight for EURUSD (WE) = 1 – WU

Risk-minimal weight for USDZAR = 0,2356

Risk-minimal weight for EURUSD = 0,7644

The risk-minimal Portfolio of USDZAR and EURUSD promises an annual yield of:
(440bp * 0,2356 + 221bp * 0,7644) = 272,6 bp; 2,726% pa

According to the formula for the Portfolio-risk we get:
Squareroot(WU^2 * RU^2 + WE^2 * RE^2 + 2 * WU * WE * C * RU * RE) = 0,44%


Finally we arrive at an portfolio, that promises an annual yield of 2,73% at minimal margin rate of 0,88%.

Compared to USDZAR we get 62% of the return for taking 34% of the risk. Compared to EURUSD we get 123,5 % of the return for taking 77% of the risk.

That is a promising result. Using all Dukascopy currencies we might not be able to create a ZERO RISK Portfolio, but only practise can show how near we can come to such a goal.
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