Individual HW 3 — FX & Parity Relationships

Due: May 29 (Week 9) at the start of class

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1. From September 2011 until January 2015, the Swiss Central Bank actively intervened to prevent the Euro from costing less than 1.2 Swiss Francs. The exchange rate is S = SFr/€.

(a) When the exchange rate jumps down in January 2015, is the Swiss Franc appreciating or depreciating relative to the Euro?

(b) Based on the FT article “Swiss franc’s return to peg level opens options for central bank”:

(i) The article says the SNB used negative interest rates to weaken the Swiss Franc. Are negative interest rates loose or tight monetary policy? Explain briefly.
(ii) Should negative interest rates lead to higher or lower inflation?
(iii) Should negative interest rates lead to appreciation or depreciation of the Swiss Franc? Use the international parity relations.
(iv) Describe the balance sheet entries for the SNB and Credit Suisse if the SNB buys €100M of German Bunds from Credit Suisse at S = SFr/€ 1.20.
(v) Describe how QE of this type should affect the value of the Swiss Franc.

2. Absolute PPP. The market exchange rate is S = Mex$/$ 18.70. A BigMac costs $5.26 in the US and 48 Pesos in Mexico.

(a) What is the exchange rate implied by absolute PPP applied to BigMacs?

(b) Is the Peso over- or undervalued at market rates?

3. Inflation data for 9 countries is provided.

(a) If relative PPP holds, which currency would you expect to depreciate the most? Why?

(b) Using the log-linear approximation to relative PPP, compute by how much that currency will depreciate against: (i) the Yen, (ii) the Swiss Franc, (iii) the Canadian Dollar.

4. The nominal interest rate in the US is 4% and in the Eurozone is 2%.

(a) Calculate the expected rate of change in the $/€ exchange rate.

(b) If the current rate is S = $/€ = 1.2, what is the expected exchange rate in one year?

(c) If the expected rate in one year is S = $/€ = 1.26 and the current rate is 1.2, calculate the US nominal interest rate given the Eurozone rate is 2%.

5. The 1-year US Treasury rate is 2.54% and the 1-year Swiss government bond rate is −0.70%. The current exchange rate is S = $/SFr = 1.01. Use 4-decimal rounding.

(a) Using exact (discrete) uncovered interest rate parity, what is the expected S = $/SFr in one year?

(b) Does UIRP predict appreciation or depreciation of the US Dollar relative to the Swiss Franc?

(c) If you expect the dollar to appreciate to 0.95 $/SFr, is the dollar more attractive as a funding currency or investment currency?

(d) Borrow 1 Swiss Franc, convert to dollars, invest in 1-year US Treasuries, convert back at your predicted rate of 0.95 $/SFr. What is the profit per Swiss Franc borrowed?

6. The spot rate is S = $/€ = 1.2. US interest rate is 3%, Eurozone rate is 1%.

(a) Calculate the 1-year forward rate F = $/€.

(b) Predict the future spot rate assuming the forward unbiased hypothesis holds.

(c) If the actual future spot rate is 1.25 $/€, did an investor who entered a forward contract at the rate from (a) gain or lose? Calculate the gain or loss per EUR.

Synthesis Question

7. Client Question — Should We Hedge Our Japanese Equity Exposure?

Your firm manages a US-based global equity fund that recently allocated $10 million to Japanese equities. The portfolio manager asks: “The yen has been weak for years. Should we hedge our yen exposure back to dollars, or leave it unhedged? What do the parity relations tell us?”

Current data:

	United States	Japan
1-year nominal interest rate	4.5%	0.75%
Current inflation rate	3.0%	2.5%
Spot rate	S = $/Yen = 0.00667 (i.e., 1 USD = 150 Yen)

(a) UIRP Analysis: Using uncovered interest rate parity, what is the expected $/Yen exchange rate in one year? Does UIRP predict the yen will strengthen or weaken against the dollar? By approximately what percentage?

(b) Relative PPP Analysis: Using the log-linear approximation to relative PPP, what exchange rate change does the inflation differential predict? Is this prediction consistent with or contradictory to UIRP? Explain intuitively why both relations might point in the same direction here.

(c) Hedging Cost: Using covered interest rate parity, calculate the 1-year forward rate F = $/Yen. If the fund hedges by selling yen forward, what is the annualized cost of hedging? Explain why the cost of hedging is directly related to the interest rate differential.

(d) Unhedged Scenario Analysis: Suppose the Japanese equity portfolio returns 10% in yen terms over the next year. Calculate the fund’s return in US dollar terms under three exchange rate scenarios:

(i) Yen strengthens to 140 Yen/Dollar (S = $/Yen = 0.00714)
(ii) Yen stays flat at 150 Yen/Dollar
(iii) Yen weakens to 160 Yen/Dollar (S = $/Yen = 0.00625)

Compare these to the hedged return (using the forward rate from part c with the same 10% yen return).

(e) In July 2024, the yen carry trade dramatically unwound when the Bank of Japan unexpectedly raised rates, and the yen surged from around 160 Yen/Dollar to 142 Yen/Dollar in just a few weeks. Briefly explain why this episode is relevant to the hedging decision above. What does it illustrate about the risks of being unhedged (or of running a carry trade)?

(f) Write a 1-paragraph memo to the portfolio manager (4–6 sentences) with your hedging recommendation. Reference the cost of hedging (from the interest rate differential), what the parity relations predict, the asymmetry of currency risk for a US-based investor holding yen assets, and the lessons from the 2024 carry trade unwind.