###### Pricing Fixed-Income Forward and Futures

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The uncovered interest rate parity suggests that with time, high-yielding currencies will depreciate while the low-yielding ones will appreciate. That is, if the uncovered interest rate parity holds consistently, an investor will earn a profit by taking a long position in high-yielding currencies and short positions in those with low returns.

Research has, however, shown that uncovered interest rate parity does not hold in short to medium investment horizons. Moreover, high-yielding currencies do not tend to depreciate, and the low-yielding currencies do not seem to appreciate, on average. Consequently, this goes against the uncovered interest rate parity, which creates a suitable environment for the **carry trade strategy**. This strategy involves taking a long position in high yield (high returns) currencies and a short position in those with low yield (low returns).

For instance, a trader borrows the US dollars at a rate of 5% and gains 10% from an investment in Canadian dollars for one year, making a profit of 10% − 5% = 5%. To achieve this, the investor does the following:

- Borrows the US dollars at time 0 (at the beginning of the year).
- Sells the US dollars and buys Canadian dollars at time 0.
- Invests in Canadian dollars at time 0.
- Liquidates the Canadian dollar investment at the end of the year (time 1).
- Sells Canadian dollars and buys US dollars at a spot rate in time 1.
- Pays the borrowing cost (paying the US dollar loan).

The investor is entitled to a profit of more than 5% if the Canadian dollar appreciates and vice versa. The worst-case scenario is when the Canadian dollar depreciates by more than 5%. The trader would then suffer a loss.

The returns from a carry trade are affected by the volatility of the FX markets. That is, during the low volatility periods, carry trade gives positive yields. The strategy can, nevertheless, miserably fail during turbulent periods. It is to this characteristic that carry trade’s non-normal distribution is attributed.

Consider the following information in an interbank market.

$$ \begin{array}{c|c|c|c|c} \textbf{Currency} & \textbf{Annual} & \textbf{Currency}& \textbf{Spot rate} & \textbf{Forward rate} \\ & \textbf{Libor} & \textbf{Combination} & & \textbf{(Spot rate after} \\ & & & & \textbf{One year)} \\ \hline EUR & 3.50\% & EUR/USD & 1.2025 & 1.2023 \\ \hline AUD & 6\% & USD/AUD & 1.4802 & 1.4810 \\ \end{array} $$

A European investor employs a carry trade strategy in this market by borrowing in EUR terms and investing in AUD Libor. Calculate the all-in return of the investor after one year.

A carry trade involves borrowing in a lower-yielding currency (in this case, EUR) and investing in a high-yielding currency (AUD). An investor makes a profit after financing the borrowing costs and exchange rate fluctuations.

To find the all-in return for a European investor, we need to compute the EUR/AUD cross-rate now and after one year. That is:

$$ \frac{EUR}{AUD}=\frac{EUR}{USD}\times\frac{USD}{AUD} $$

The current cross-rate

$$ \left(\frac{EUR}{AUD}\right)_{\text{Now}}=1.2025\times1.4802=1.7799405\approx1.7710 $$

After one year, the cross rate is:

$$ \left(\frac{EUR}{AUD}\right)_{\text{After one year}}=1.2023\times1.4810=1.7806063\approx1.7806 $$

The investor borrows in EUR, buys AUD at a spot rate at time t=0, invests this amount at the AUD Libor, and finally reconverts the amount back to EUR. Intuitively, the return of this investment at the end of the year will be:

$$ \frac{1}{1.7710}\left(1+0.06\right)1.7806-1=0.06575 $$

Therefore, the gross profit is 6.575%. You must remember that the investor had borrowed using the EUR Libor. Logically, therefore, the net profit is 6.575% − 3.50% = 3.075%.

## Question

Consider the following information in an interbank market, containing spot rates and interest rate for a proposed Carry Trade.

$$ \begin{array}{c|c|c|c|c} \textbf{Currency} & \textbf{Annual} & \textbf{Currency}& \textbf{Current} & \textbf{Estimated} \\ & \textbf{Libor} & \textbf{Combination} & \textbf{Spot} & \textbf{Spot rate} \\ & & & \textbf{rate} & \textbf{after One} \\ & & & & \textbf{year} \\ \hline USD & 0.70\% & CAD/USD & 1.2025 & 1.2023 \\ \hline CAD & 1.91\% & EUR/CAD & 0.8802 & 0.8810 \\ \hline EUR & 2.50\% \end{array} $$

An investor decides to make a carry trade involving the USD and EUR. The potential all-in USD profit on the carry trade is closest to:

- 1.72%.
- 2.5%.
- 0%.

Solution

The correct answer is A.A carry trade, in this case, involves borrowing in a lower-yielding currency (USD) and investing in a high yielding currency (EUR). Profit is calculated after financing the borrowing costs and exchange rate fluctuations. In this case, carry trade involves borrowing USD and investing in EUR.

To compute the all-in USD return from a one-year EUR Libor deposit, evaluate the current and one-year USD/EUR exchange rate. Using the cross-rate formula:

$$ \frac{EUR}{USD}=\frac{EUR}{CAD}\times\frac{CAD}{USD} $$

So,

$$ {\left(\frac{EUR}{USD}\right)}_{\text{Present}}=1.2025\times 0.8802=1.0584 $$

And

$$ \left(\frac{EUR}{USD}\right)_{\text{After one year}}=1.2023\times0.8810=1.0592 $$

Therefore, the return in dollars of an investment profit for a risky EUR Libor deposit is:

$$ \left(1.0584\right)\times\left(1+0.025\right)\left[\frac{1}{1.2023\times0.8810}\right]-1=2.42\% $$

But we have to subtract the borrowing costs (USD Libor), so the net return is:

$$ 2.42\% – 0.70\%=1.72\%. $$

*Reading 6: Currency Exchange Rates: Understanding Equilibrium Value*

*LOS 6 (i) Describe the carry trade and its relation to uncovered interest rate parity and calculate the profit from the carry trade.*