Final answer:
The one-year forward rate four years from now, given specific spot rates, is approximately 14.09%. Duration reflects the price sensitivity of a bond to interest rate changes and balances capital gains/losses with reinvestment income. The overall effect of interest rate changes includes impacts on both the bond's present value and reinvestment opportunities of future cash flows.
Step-by-step explanation:
To compute the one-year forward rate four years from now, given the spot rates R2, R3, R4, R5, and R6 are 5.749%, 6.33%, 6.868%, 9%, and 10% respectively, we use the formula which equates the investment return from investing for five years at the five-year rate with the return from investing for four years at the four-year rate and then one year at the forward rate. Through this process, the one-year forward rate four years from now is calculated to be approximately 14.09%.
Duration is a measure of the sensitivity of a bond's price to a change in interest rates, representing the weighted average time until a bond's cash flows are received. Graphically, it is depicted as the point on the price-yield curve where the bond's price is stable to small changes in yield. Additionally, duration can be used to show how capital losses due to increased rates can be offset by higher reinvestment income due to these same higher rates, and vice versa.
Interest rate changes affect both the present value of future cash flows (capital value) and the reinvestment income. For a bond portfolio, as the interest rate rises, the present value of future cash flows decreases (leading to capital loss), but the reinvestment rate for the cash flows (the coupon payments) increases, potentially mitigating some or all of the capital loss. Conversely, a decreasing interest rate would lead to capital gain but reduced reinvestment income.