Solution 1
(1.052)(1.058) = (1 + 1r2)2 = 1.113016; (1 + 1r2) = 1.054996 ⇒ 1r2 = .0550 or 5.50 percent
Solution 2
[1 + E(ir1)] = (1 + 1Ri)i ÷ (1 + 1Ri-1)i-1
[1 + E(4r1)] = (1.0635)4 ÷ (1.06)3 = 1.0741 ⇒ E(4r1) = 7.41 percent for period 4 [1 + E(5r1)] = (1.0665)5 ÷ (1.0635)4 = 1.0786 ⇒ E(5r1) = 7.86 percent for period 5 [1 + E(6r1)] = (1.0675)6 ÷ (1.0665)5 = 1.0725 ⇒ E(6r1) = 7.25 percent for period 6
Solution 3
The implicit forward rates are f2 =[(1+1r2)2/(1+1r1)]–1 f2 = [(1.065)2/(1.055)] - 1 = 7.51% Solution 4
a) If inflation is going up existing bonds, with given nominal values and coupons, do not offer a yield that compensates for inflation (r = real rate + expected inflation). Thus, demand is lowered and prices of bonds fall until they offer the required yield. In addition, if prices are expected to go up it makes sense to consume today (incl. buying capital goods) before prices increase. For business today’s bonds have a low real yield, why it is profitable to increase the supply of bonds and invest more. They will increase the supply of long term bonds and drive prices down. The outcome is a shift up in the yield curve, as the yield adjusts to higher inflation expectations. We can make a case for a steeper slope, in particular if expected inflation is associated with a boom in the economy.
b) Coming bad times means that you have to save more for the bad times going. Cut down on current consumption and buy bonds that mature when the bad times are coming. Say that you expect bad times 18 months from now, then you buy bonds with a maturity, which in turn drives up the price of these bonds and brings down the yield. You could see the yield curve becoming humped shaped with lower mid –term bonds selling at higher prices than long-term