Answer to Practice Midterm Exam

International Financial Markets/International Finance (FIN 442/644), Winter 2024

1.   Multiple Choice

Note: Explanations below for Q1 are unnecessary. They are provided for pedagogical purposes. Even if you provide one, it will not be graded and no partial credit will be given.

a)   CIBC quotes 1.42$/€ bid and 1.45$/€ ask. RBC quotes 1.41$/€ bid and 1.44$/€ ask. TD quotes 1.45$/€ bid and 1.47$/€ ask. What is the largest profit you can make if you start by buying €1 at CIBC?

a. ¢0    b. ¢1    c. ¢2     d. ¢3    e. ¢4     f. ¢5     g. ¢6    h. None of the above

Answer: a. If you start by buying €1 at $1.45 at CIBC, your best selling price is 1.45$/€ at TD. Thus, you make a ¢0 profit. To make a positive profit, you need to buy €1 at RBC.

b)  One Indian rupee (INR) is worth 0.9 Philippine pesos (PHP). One Brazilian real (BRL) is worth 25 Philippine pesos. What is BRL/INR?

a. 0.036           b. 0.040           c. 0.044            d. 1.11             e. 22.5

f. 25                g. 27.8             h. None of the above

Answer: a. SPHP/INR  = 0.9PHP/INR and SPHP/BRL  = 25PHP/BRL. So, SBRL/INR  = 0.9/25 = 0.036BRL/INR.

c)   In the Dozier Industries case, Rothschild, the CFO of Dozier, “was not entirely convinced [the pound] would continue to fall, or at least not as much as the forward rate indicated.” What is the parity condition he is implicitly evaluating?

i. Put-call Parity

Answer: d. He is comparing the forward rate and the expected future spot rate. This is the Forward Parity.

d)  The gold price in India rises 20% in rupee. The pound falls 15% against the rupee. What is the gold return in pound?

a. -35%            b. -29.2%        c. -5%              d. -2%              e. 2%

f. 5%               g. 29.2%          h. 35%             i. 41.2%          j. None of the above

Answer: i. The relative change in the gold price in India is Pt+1INR/PtINR – 1 = 0.2.

The relative change in the pound value is St+1INR/₤/StINR/₤  – 1 = –0.15. Converting the INR price of gold to pounds and computing the return, we get (Pt+1INR/St+1INR/£)/(PtINR/StINR/£) – 1 = 1.2/0.85 – 1 = 0.412.

e)  You shorted a call option on one Polish zloty (PLN) with strike 3PLN/$. What is the dollar payoff of your position when the terminal spot rate is 2.8PLN/$?

g. –3                h. 1/3               i. –1/3              j. 0.2                k. –0.2             l. 5

m. –5               n. 1/2.8 – 1/3   o. 1/3 – 1/2.8   p. None of the above

Answer: o. Your counterparty will exercise the call option. You are forced to deliver one zloty at 3PLN/$ or 1/3$/PLN, when it is worth 1/2.8$/PLN in the spot market. Therefore, your dollar payoff is negative, 1/3 – 1/2.8 $/PLN.

2.   Short Questions

a)   Since the Real Interest Parity holds, so does the International Fisher Relation:

We will receive $1.0402 in one year.

b) Approximation and Decomposition. Compute the inflation rate differential and the relative change in the nominal ¥/$ exchange rate:

π¥ – π$ = 0 – 0.03 = –0.03,

Δs¥/$ = 98/100 – 1 = –0.02.

So, the relative change in the real ¥/$ exchange rate is

Δx¥/$ ≈ Δs¥/$ – (π¥ – π$) = –0.02 – (–0.03) = 0.01,

or 1%. Canada’s position has been hurt because

•   the 3% higher Canadian inflation rate outweighs:

•   the -2% stronger (2% weaker) dollar.

Exact formula. If you are asked to use the exact formula, compute

or 0.94%. This slightly differs from the approximation,  1%, because the  exact formula is multiplicative while the approximation formula is additive.

c)  Recall that the theoretical delta of the yen spot rate with respect to the yen futures is

∆S$/¥/∆F$/¥ = (1 + i¥)/(1 + i$),

which equals S$/¥/F$/¥ by the Interest Rate Parity, if the interest rates are constant over the range in which the small ∆ changes are taken (which is true in a partial- derivative sense: dS$/¥/dF$/¥  = (1 + i¥)/(1 + i$)). This is the theoretical hedge ratio. To hedge the ¥1 billion import obligation, we should buy the following number of the yen futures contract:

¥1 billion×(S$/¥/F$/¥)/¥12.5 million

= 1000×(F¥/$/S¥/$)/12.5 = 1000×(95/100)/12.5 = 76 contracts.

There is a maturity mismatch because the import payment is due in six months while the futures contract matures in nine months (there is basis risk; luckily there is no size mismatch).

Note: S and F in the first line above have the yen in the denominator of the superscript to represent the prices of the yen, while those in the second line bring the dollar to the denominator to fit the quotes. This is done by inverting the quote, S$/¥ = 1/S¥/$, and similarly for F.

3.   TexMesq

a)   0.80×(1 + 0.025/2)/(1 + 0.01/2) = $0.80597/CHF.

b)  In the forward hedge, the firm will sell CHF 10 per unit forward in 6 months at $0.80597/CHF.

c)   The firm should buy the put option with strike 0.75$/CHF. The future value of the premium is

FV(P) = 0.020×(1 + 0.025/2) = $0.02025.

(i) When the terminal spot rate is ST = 0.65$/CHF, the put option is in the money (ITM). The profit of the option is the payoff (K – ST) less the future value of the  premium,

K – ST – FV(P) = 0.75 – 0.65 – 0.02025 = 0.07975$/CHF.

The profit of the hedged position adds the value of the export position, ST, to the above, which is equivalent to

K – FV(P) = 0.75 – 0.02025 = 0.72975$/CHF.

(ii) When the terminal spot rate is ST = 0.95$/CHF, the put option is out of the   money (OTM). The profit of the option is the payoff (0) less the future value of the premium,

0 – FV(P) = 0 – 0.02025 = -0.02025$/CHF.

The profit of the hedged position adds the value of the export position, ST, to the above,

ST – FV(P) = 0.95 – 0.02025 = 0.92975$/CHF.

d)  A zero-cost scheme for an exporter finances the purchase of the OTM put option from Part c) by shorting a call option. The range forward shorts an OTM call option, while the participating forward shorts a fraction of the ITM call option with the same strike price as the OTM put option.

(1) Range forward

Strategy: buy the 0.75 put and sell the 0.85 call, each on CHF10 per unit. Net receipt of premium = ¢2.4 (call) – ¢2.0 (put) = ¢0.4/CHF.

FV(net premium) = 0.004 × (1 + 0.025/2) = $0.00405.

(i) When the terminal spot rate is ST = 0.65$/CHF, the call option is out of the money (OTM), while the put option is in the money. Since you can sell the

franc at the put’s strike (KP), the profit of the hedged position is KP + FV(net premium) = 0.75 + 0.00405 = 0.75405$/CHF.

(ii) When the terminal spot rate is ST = 0.95$/CHF, the call option is in the money (ITM), while the put option is out of the money. Since you are obliged to sell the franc at the call’s strike (KC), or equivalently from the diagram below, the profit of the hedged position is

KC + FV(net premium) = 0.85 + 0.00405 = $0.85405/CHF.

(2) Participating forward

Strategy: for each 0.75 put bought, sell the 0.75 call on CHFy. Equate the premiums:

1 × ¢2.0 = y × ¢6.0

→ y = 2.0/6.0 = 0.33333

So, multiplying the CHF amount, buy the 0.75 put on CHF 10 per unit and sell the 0.75 call on CHF 3.3333 per unit.

Net receipt of premium = ¢6.0×y (call) – ¢2.0 (put) = ¢0/CHF. FV(net premium) = 0 × (1 + 0.025/2) = 0.

(i) When the terminal spot rate is ST = 0.65$/CHF, the call option is out of the money (OTM), while the put option is in the money. Since you can sell the franc

at the put’s strike (common K), the profit of the hedged position is K + FV(net premium) = 0.75 + 0 = 0.75$/CHF.

(ii) When the terminal spot rate is ST = 0.95$/CHF, the call option is in the money (ITM), while the put option is out of the money. From the diagram below, the profit of the hedged position is

K + (ST – K)×(1 –y) = 0.75 + (0.95 – 0.75)×(1 –y) = 0.88333$/CHF.

(3) Synthetic forward (invalid)

Note: A synthetic forward is invalid because it does not provide an upside benefit as instructed. However, here is the strategy for review.

Strategy: buy the 0.75 put and sell the 0.75 call, each on CHF10 per unit. Net receipt of premium = ¢6.0 (call) – ¢2.0 (put) = ¢4.0/CHF.

FV(net premium) = 0.04 × (1 + 0.025/2) = 0.0405$/CHF.

Regardless of the terminal spot rate, the profit of the hedged position is 0.75 + 0.0405 = 0.7905$/CHF.

e)   Extra analysis for review: The firm’s manufacturing cost is $6.7 per unit. Its profit goal is $0.7 per unit. Compute the lowest possible profit after the manufacturing cost in dollars per unit for each of the hedging schemes in Parts b), c), and d). Does the scheme achieve the profit goal in any exchange-rate scenario?

Part b) The final dollar profit is

CHF 10×$0.80597/CHF – $6.7 = $1.3597 > $0.7/unit,

which achieves the profit goal.

Part c) The lowest possible profit is, from Case (i),

CHF 10×0.72975 – $6.7 = $0.5975 < $0.7/unit,

which does not achieve the profit goal.

Part d) (1) Range forward: The lowest possible profit is, from Case (i),

CHF 10×0.75405 – $6.7 = $0.8405 > $0.7/unit,

which achieves the profit goal.

Part d) (2) Participating forward: The lowest possible profit is, from Case (i),

CHF 10×0.75 – $6.7 = $0.8 > $0.7/unit,

which achieves the profit goal.

Part d), synthetic forward (invalid): Final profit is always

CHF 10×0.7905 – $6.7 = $1.205 > $0.7/unit,

which achieves the profit goal.