Current location - Trademark Inquiry Complete Network - Futures platform - What is the interest rate of Japanese gold futures?
What is the interest rate of Japanese gold futures?
Suppose an investor buys an ounce of gold in the quantity of m, then when he buys it at $560, he needs to pay $560 million, and when he sells it at $559, he can get back $559 million.

In addition, investors can borrow money at an annual interest rate of 6% or 5.5%. If investors choose to borrow money, they need to repay the principal plus interest after one year. If he borrows X dollars, he needs to pay x*( 1+6%)= 1.06x dollars. On the contrary, if investors choose to lend funds, they can recover the principal and interest after one year. If they lend Y dollars, they can recover Y * (1+5.5%) =1.055Y dollars.

If investors arbitrage, two conditions should be met:

The capital needed to buy gold is not higher than the borrowing cost.

That is, 560m ≤1.06x.

The proceeds from the sale of gold shall not be lower than the loan interest.

That is, 559m ≥1.055y.

By sorting out the above two formulas, we can get:

m/x ≤ 1.06/560

m/y ≥ 1.055/559

Since m is the quantity of gold purchased, it must be a positive number, so the first inequality requires that the left side should not be less than zero, that is, x ≥ (1.06/560) m. Take the reciprocal of the right side and multiply it by 560 to get 560x≥ 1.06m, that is, x ≥ (1.06/560).

m/( 1.055/559) ≤ y

Similarly, because Y is a loan fund, it must be a positive number, so the above formula requires that the right side should not be less than zero, so there is y≥( 1.055/559)m, and the left side is multiplied by (1.055/559) to get:

( 1.055/559)m ≤ y

Combining the above two inequalities, we can get:

( 1.055/559)m≤y≤m/( 1.06/560)

That is to say, the precondition for investors to carry out arbitrage is that the gold price fluctuates in the range of [( 1.055/559) × 560, (1.06/560) × m]. In other words, investors can arbitrage only when the price of gold rises or falls beyond this range.