Can somebody please assist to review the solution appended below the question? I think they mixed the currency conversion around.

Question:

Rosario Delgado is an investment manager in Spain. Delgado’s client, Max Rivera, seeks assistance with his well-diversified investment portfolio denominated in US dollars.

Rivera’s reporting currency is the euro, and he is concerned about his US dollar exposure. His portfolio IPS requires monthly rebalancing, at a minimum. The portfolio’s market value is USD2.5 million. Given Rivera’s risk aversion, Delgado is considering a monthly hedge using either a one-month forward contract or one-month futures contract.

Assume Rivera’s portfolio was perfectly hedged. It is now time to rebalance the portfolio and roll the currency hedge forward one month. The relevant data for rebalancing are provided in Exhibit 1.

Exhibit 1

One Month Ago

Today

Portfolio value of assets (USD)

2,500,000

2,650,000

EUR/USD spot rate (bid–offer)

0.8913/0.8914

0.8875/0.8876

One-month forward points (bid–offer)

25/30

20/25

Q. Calculate the net cash flow (in euros) to maintain the desired hedge. Show your calculations.

Solution

When hedging one month ago, Delgado would have sold USD2,500,000 one month forward against the euro. Now, with the US dollar-denominated portfolio increasing in value to USD2,650,000, a mismatched FX swap is needed to settle the initial expiring forward contract and establish a new hedge given the higher market value of the US dollar-denominated portfolio. To calculate the net cash flow (in euros) to maintain the desired hedge, the following steps are necessary:

Buy USD2,500,000 at the spot rate. Therefore, the bid side of the market must be used to calculate the outflow in euros.USD2,500,000 × 0.8875 = EUR2,218,750.

Sell USD2,650,000 at the spot rate adjusted for the one-month forward points (all-in forward rate). Therefore, the offer side of the market must be used to calculate the inflow in euros.All-in forward rate = 0.8876 + (25/10,000) = 0.8901. USD2,650,000 × 0.8901 = EUR2,358,765.

Therefore, the net cash flow is equal to EUR2,358,765 – EUR2,218,750, which is equal to EUR140,015.

However, I still don’t understand why selling 2.65M forward produces a cash flow today.

My answer would be the following:

On one hand, you need to buy 2.5M USD to cover the original USD short position. That would cost you 2.5M / 0.8875 = 2,816,901.41 EUR.

On the other hand, you’d receive the EUR from the original fwd contract. Namely, 1 month ago the agreed rate was 0.8913 + 25 points = 0.8938, and hence the EUR received would be 2.5M / 0.8938 = 2,797,046.32 EUR.

The net cash flow would be +2,797,046.32 EUR - 2,816,901.41 EUR = -19,855.09 EUR.

You’re dividing USD 2.5 million by 0.8875; you should be multiplying it by 0.8875. Similarly with 0.8938.

It appears that you’re reading the currency quotes backward; in the CFA world, EUR/USD 0.8875 means that EUR 0.8875 = USD 1.0, not the other way round.

Don’t you need to divide by 0.8875 to buy the 2.5m USD in the spot mkt? So it costs you 2,816.9 kEUR (a bit more expensive than you were saying), for a total CF of -21.7 kEURV?

I agree with your comment, only one point is that I think we should use 0.8914 + 30 to convert previous forward contract. Could you conclude the correct answer?

Assume your exchange rate is correct, we can focus on the step by step solution.
I do not understand clearly CFA’s answer for this question:

One month ago, we hedge our portfolio by sell 2,500.000 USD FORWARD contract (means buy EUR, sell USD) at the Forward rate 1 EUR = 0.8914 + 0.0030 = 0.8944 USD => Today, at the maturity of Forward contract, we have to transfer money (sell 2,500,000 USD, receive EUR 2,795,170 (2,500,000/0.8944).

Today, doing FX swap to square the previous Forward position by Buying 2.5 mio USD in the spot market and pay EUR 2,816,901 (2,500,000 USD/0.8875).

Today, Enter a new Forward contract for new balance of our portfolio: Sell 2,650,000 USD buy EUR at the Forward rate of 0.8876+0.0025 = 0.8901 USD/EUR. Payment will be mad in 1 month, not today.
Sum up, Today Cashflow in EUR: +EUR 2,795,170 -EUR 2,816,901= -21,731 EUR.

I can not understand why CFA’s answer ignored the proceed of 1-month Forward contract signed 1 month ago? And why the proceed of new Forward contract of 2,650,000 USD asset portfolio could be calculated in CFA’s answer although it will be transfer in the next one month, not today?
Please share your idea with me. Thanks!!