Suppose you own and rent out a condominium in Europe. A property manager recruited by you can vary the rent, making sure that someone always rents and occupies the property.

Now, assume you receive € 1,800, € 2,000, or € 2,200 per month in cash for rent, as shown in Table 1. Let’s say each rent is a state, and as is obvious, any of the rents have a 1/3 probability. The forecasted exchange rate for each state, which is S has also been estimated. We can now calculate the asset’s price, P, in U.S. dollars by multiplying that state’s rent by the exchange rate.

__Table 1 – Renting out your Condo for Case 1__

State | Probability | Rent (Euro) | Exchange Rate (S) | Rent (P) |

1 | 1/3 | €1,800 | $1/1.00 E | $1,800 |

2 | 1/3 | €2,000 | $1.25/1.00 E | $1.25/1.00 E |

3 | 1/3 | €2,200 | $1.50/1.00 E | $3,300 |

In this case, we calculate 800 for (β). Positive (β) shows that your cash rent varies with the fluctuating exchange rate, and there is a potential economic exposure.

A special factor to notice is that as the Euro appreciated, the rent in Dollars also increased. A forward contract for € 800 at a contract price of $1.25 per €1 can be bought to hedge against the exchange rate risk.

In Table 2, (β) is the correct hedge for Case 1. The Forward Price is the exchange rate in the forward contract and it is the spot exchange rate for a state.

Suppose we bought a forward contract with a price of $1.25 per euro.

● If State 1 occurs, the Euro depreciates against the U.S. dollar. By exchanging € 800 into Dollars, we gain $200, and we compute it in the Yield column in Table 2.

● If State 2 occurs, the forward rate equals the spot rate, so we neither gain nor lose anything.

● State 3 shows that the Euro appreciated against the U.S. dollar, so we lose $200 on the forward contract. We know that each state is equally likely to occur, so we, on average, break even by purchasing the forward contract.

__Table 2 – The Beta is the Correct Hedge for Case 1__

State | Forward Price | Exchange rate | Yield |

1 | $1.25/1 | $1.00/1E | (1.25 – 1.00) × 800 = 200$ |

2 | $1.25/1E | $1.25/1E | (1.25 – 1.25) × 800 = 0 |

3 | $1.25/1E | $1.50/1E | (1.25 – 1.50) × 800 = –200 $ |

Total | $ 0 |

The rents have changed in Table 3. In Case 2, you could now get € 1,667.67, € 2,000, or € 2,500 per month in cash, and all rents are equally likely. Although your rent fluctuates greatly, the exchange moves in the opposite direction of the rent.

__Table 3 – Renting out your Condo for Case 2__

State | Probability | Rent (E) | Exch. Rate | Rent (P) |

1 | 1/3 | 2,500 | $1/1E | $2,500 |

2 | 1/3 | 2,000 | $1.25/1E | $2,500 |

3 | 1/3 | 1,666.67 | $1.50/1E | $2,500 |

Now, do you notice that when you calculate the rent in dollars, the rent amounts become $2,500 in all cases, and (β) equals –1,666.66? A negative (β) indicates that the exchange rate fluctuations cancel the fluctuations in rent. Moreover, you do not need a forward contract because you do not have any economic exposure.

We finally examine the last case in Table 4. The same rent, € 2000, is charged for Case 3 without considering the exchange rate changes. As the rent is calculated in U.S. dollars, the exchange rate and the rent amount move in the same direction.

__Table 4 – Renting out your Condo for Case 3__

State | Probability | Rent (E) | Exch. Rate | Rent (P) |

1 | 1/3 | 2,000 | $1/1E | $2,000 |

2 | 1/3 | 2,000 | $1.25/1E | $2,500 |

3 | 1/3 | 2,000 | $1.50/1E | $3,000 |

However, the (β) equals 0 in this case, as rents in Euros do not vary. So, now, it can be hedged against the exchange rate risk by buying a forward for €2000 and not the amount for the (β). By deciding to charge the same rent, you can use a forward to protect this amount.