The first question is merely an application of interest rate parity:
JPYfut/USDfut = JPYspot/USDspot × [(1 + rJPY)/(1 + rUSD)]^t
= JPY124.30000/USD1.0 × [(1.001)/(1.038)]^½
For the second question, you should normally have to decide which currency to borrow initially, but they saved you the trouble. So the steps are straightforward:
- Borrow USD at the USD risk-free rate
- Convert USD to JPY at the spot rate, and enter into a forward contract to pay JPY and receive USD; the amount will be the future value of the JPY
- Invest JPY at the JPY risk-free rate
- Wait 3 months
- Convert JPY to USD at the forward rate you locked in 3 month ago
- Pay off the USD loan, including interest
- What’s left over is your profit in USD
- To get your profit in JPY, convert USD to JPY at the prevailing JPY/USD spot rate
I wrote an article on pricing currency forwards that may help you step through this stuff: http://financialexamhelp123.com/covered-interest-rate-parity-irp-pricing-currency-forwards/.
So when the Spot > Forward (124.3 > 123.2605) You borrow US Dollars You sell the forwad (you received 1 000 000 * (0.35)^(0.25) = 1008637.446 and you paid 124325155.9127 But in the same time you invest the borrowed dollars in rf Yen with the spot rate 124.3 You received with this investment 124 300 000 * (1.005)^(0.25) The final Payoff is 129 928.61 —> The raisonning is correct ? What will be the raisonning if the Spot is lower than Forwad ? You buy Forwad ? Please explaine me because it’s not clearly explained in your website. Thanks
You’re not comparing the spot price with the forward price; you’re comparing the actual forward price with the arbitrage-free forward price.
If the actual forward price (in JPY/USD) is _ higher _ than the arbitrage-free forward price (in JPY/USD), then you’ll be getting _ more _ JPY in the future than you should; thus, you want to start and end with JPY: borrow JPY today to get things rolling.
If the actual forward price (in JPY/USD) is _ lower _ than the arbitrage-free forward price (in JPY/USD), then you’ll be getting _ fewer _ JPY in the future than you should; this is equivalent to saying that you’ll be getting _ more USD _ in the future than you should. Thus, you want to start and end with USD: borrow USD today to get things rolling.
Okay But what I don’t understand it’s the point 2
- Convert USD to JPY at the spot rate, and enter into a forward contract to pay JPY and receive USD; the amount will be the future value of the JPY It mean for this example that you Buy a forward contract that give you foreign currency (dollar) for domestic currency (Yen) ? But it’s a exceptional case because we borrow the dollar but without this requirement the trader must Borrow Yen and sell a forward (Pay dollar to receive Yen ) ? It’s the requirement that gives me trouble Are you agree with this raisonning ?
Let’s do all of the calculations:
- Borrow USD1,000,000 for 3 months at 3.5% (effective annual) interest.
- Convert USD1,000,000 to JPY124,300,000 at the spot rate of JPY/USD 124.3. Enter into a 3-month forward contract to pay JPY and receive USD at the forward rate of JPY/USD123.2605, in the amount of JPY124,455,085.
- Invest JPY124,300,000 for 3 months at 0.5% (effective annual) interest.
- Wait 3 months; the JPY investment grows to JPY124,455,085.
- Convert JPY124,455,085 to USD1,009,692 at the forward rate of JPY/USD123.2605.
- Pay off the USD loan plus interest for USD1,008,637.
- Your profit is USD1,054.
If you want your profit in JPY, then change the amount on the forward contract (step 2) to JPY124,325,156. Then, when you convert that amount to USD (step 5), you’ll have USD1,008,637: enough to pay off the loan plus interest. Your profit will be JPY129,929 (= JPY124,455,085 – JPY124,325,156).