Suppose two zero-coupon bonds are available for trading that have face values of $100 each.Current yields are 2 percent for the two-year bond and 5 percent for the ten-year bond.As the economy is expanding,you believe that the Federal Reserve Bank will raise short-term rates by 25 basis points (or 0.25 percent)to prevent the economy from overheating.The Fed has no influence over long-term interest rates and you expect them to remain unchanged.If you set up a spread strategy and it works as conjectured,then you will make a profit of:

Question

Quizplus · Accepted Answer

To set up the spread strategy, we need to create a synthetic bond by selling two of the two-year bonds and buying five of the ten-year bonds.

Sell 2 two-year bonds at face value of $100 each = $200. 
Buy 5 ten-year bonds at face value of $100 each = $500.

The total initial investment is $300.

If short-term rates increase by 25 basis points, the price of the two-year bond will decrease by approximately 0.50% (using modified duration). Thus, the value of the two-year bonds held will decrease by 0.50% * $200 = $1.

However, the price of the ten-year bond will not change, as expected.

Therefore, the new value of the portfolio will be $299. If we divide this by the initial investment of $300, we get a rate of return of -0.00333 or -0.33%. However, we received a coupon of 5% on the ten-year bonds, which would be $25.

If we subtract the coupon of $25 from the return of -$0.33, we get a total return of $24.67.

Therefore, the profit from this spread strategy would be $24.67 - $24.20 (the value of the portfolio without the increase in the short-term rate) = $0.47.

The correct answer is C, $0.47.

Suppose Two Zero-Coupon Bonds Are Available for Trading That Have