Question

What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this relationship exist? (LG 3-7). 6 Bank Three currently has $600 million in transaction deposits on its balance sheet. The Federal Reserve has currently set the reserve requirement at 10 percent of transaction deposits. (LG 4-3)

If the Federal Reserve decreases the reserve requirement to 8 percent, show the balance sheet of Bank Three and the Federal Reserve System just before and after the full effect of the reserve requirement change. Assume Bank Three withdraws all excess reserves and gives out loans and that borrowers eventually return all of these funds to Bank Three in the form of transaction deposits.

Redo part (a) using a 12 percent reserve requirement.

Answer 1

Time to Maturity (yrs) $1,000 10% Coupon (S/A) Selling at par implies that the YTM is 10% 50 Duration Table YTM 10% YTM 12% YTM 14% Periods/CF# Cash Flow PV of CF CF/(1+YTM/2) (PV/Total)"tf (PV/Total)*tf (PV/Total)*tf 50 47.61904762 0.023809524 0.025458687 0.027182914 MacD- CF;yty = (1+' PV 50 45.35147392 0.045351474 0.048035259 0.050809186 where: 43.19187993 0.06478782 0.067974423 0.07122783 f = cash flow number 41.13512374 0.082270247 0.085502419 0.088757421 CF = cash flow amount 39.17630832 0.097940771 0.100828324 0.103688576 y = yield to maturity 37.31076983 0.111932309 0.114145272 0.116286253 k = compounding periods per year 50 35.53406651 0.124369233 0.125631589 0.126791865 tf = time in years until cash flow is received 8 33.8419681 0.135367872 0.135451848 0.135425223 PV = present value of all cash flows 50 32.23044581 0.145037006 0.143757858 0.142386332 10 1050 644.6089162 3.223044581 3.164481146 3.104997903 Total 1000 4.053910838 4.011266825 3.967553503 Mint 50 50 Duration @ YTM 10% Duration @ YTM 12% Duration @YTM 14% 4.053911 4.011267 3.967554 Duration is inversely related to the bond's yield to maturity (YTM)