An annual coupon paying bond (denoted by B) with a face value of $1,000 and a coupon rate of 7.5% expires in three years. Its's YTM is 6.39%. If bond B’s current price is $1,000, would there be an arbitrage opportunity that could be exploited? If so, explain how an investor can exploit the arbitrage opportunity. That is, indicate which securities an investor should buy or sell, as well as the quantities of each security.

The answer is you buy B, and simultaneously sell 7.5% of Z1, 7.5% of Z2, and 107.5% of Z3. This operation generates an arbitrage profit of $29.44 (i.e., $1,029.44 - $1,000) per trade.

My question is how do you come up with this answer? What is the formula behind it?

Bond	Maturity (Years)	Price of $1,000 Par Bond (Zero-Coupon)
Z1	1	$961.54
Z2	2	$898.45
Z3	3	$827.85