A 2 -year bond with a semiannual coupon rate of \(4 \%\) per annum is trading at par \((100 \%)\).

(a) What is its spot semiannual yield?

(b) Assume one can borrow at \(3 \%\) p.a. simple interest rate for three months ( 0.25 years) to purchase this bond on a leveraged basis. What is the forward price for a 3-month forward delivery?

(c) Use the 3-month forward price to calculate its forward yield, i.e., its semiannual yield on the forward date based on the above forward price. Note that in three months, the bond will be in the middle of the coupon period with 21 months left to maturity. Use Formula 2.5 with \(w=0.5\).

(d) A positive carry trade is one where the yield is higher than the financing cost. For bonds, a positive carry trade leads to a positive yield carry defined as the difference between the forward yield and the spot yield. Is purchase of this bond a positive carry trade?

(e) Recalculate the forward yield if the 3 -month borrowing rate is \(5 \%\). Is the yield carry positive?