The prices of a one-year 4% coupon bond,a two-year 5% coupon bond,and a three-year 6% coupon bond are $101,$100 and $99,respectively.Coupons are paid annually.What is the price of a bond that pays $37 each year?

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Quizplus · Accepted Answer

The price of a bond that pays $37 each year can be calculated using the concept of arbitrage. Arbitrage involves combining the given bonds in such a way that their coupon payments match the desired $37 payment. By doing so, we can determine the price of the desired bond without directly calculating its yield to maturity or using any bond pricing formula.Given:- 1-year 4% coupon bond priced at $101 (pays $4 annually)- 2-year 5% coupon bond priced at $100 (pays $5 annually)- 3-year 6% coupon bond priced at $99 (pays $6 annually)To create a bond that pays $37 annually, we can combine these bonds as follows:- Buy 7 of the 6% coupon bonds: 7 * $6 = $42- Sell 1 of the 5% coupon bonds: -$5- Sell 0 of the 4% coupon bonds: $0This combination results in a net payment of $37 annually ($42 - $5). The cost of this combination is:- Cost of buying 7 of the 6% bonds: 7 * $99 = $693- Proceeds from selling 1 of the 5% bonds: -$100- Net cost: $693 - $100 = $593However, to accurately reflect the price of a bond paying exactly $37 annually, we need to adjust this combination to exactly match the $37 payment. Since the initial combination gives us $42 in coupons and we need to reduce this to $37, we adjust by considering the sale of the 5% bond (which reduces the coupon by $5). The net payment is then exactly $37, and the net cost calculated above ($593) is for a combination that effectively pays $37 annually over the period considered.Given the complexity of directly calculating the exact price without knowing the total number of bonds or the specific combination that would yield exactly $37 in annual payments without any remainder, the approach simplifies to understanding that arbitrage and combination of existing bonds can give us an insight into the pricing of a new bond with desired characteristics. The correct answer, therefore, involves recognizing the principle of arbitrage and the need for a detailed calculation or combination strategy, which was not fully explored due to the initial misinterpretation of the question's requirements.

The Prices of a One-Year 4% Coupon Bond,a Two-Year 5