Economics 330 Money and Banking Problem Set No. 3 Due Tuesday April 3, 2018 at the beginning of class

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1 Economcs 0 Money and Bankng Problem Set No. Due Tuesday Aprl, 08 at the begnnng of class Fall 08 Dr. Ner I. A. The followng table shows the prce of $000 face value -year, -year, -year, 9-year and 0- year US Treasury zero coupon bonds as of May 08. Use pure expectatons hypothess to determne: a. the expected nterest rate on a -year bond one year from now, n year? x.8-.9 =.% b. the expected nterest rate on a -year bond two years from now, n year? x.9 x.8=.06% c. the expected nterest rate on a -year bond nne years from now, n year 0? 0x.8 9 x.9 =.9% -yr -yr -yr 9-yr 0-yr U.S. Treasury (May, 08) Here are the YTMs needed to answers the queston: YTM on -year bond.9% YTM on -year bond.8% YTM on -year bond.9% YTM on 9-year bond.9% YTM on 0-year bond.8% B. Here s the same nformaton for May 07 -yr -yr -yr 9-yr 0-yr U.S. Treasury (March 07) Use pure expectatons hypothess to determne: a. the expected nterest rate on a -year bond one year forward, n year? x.-. =.9 b. the expected nterest rate on a -year bond two years forward, n year? x.7 x. =. c. the expected nterest rate on a -year bond nne years forward, n year 0? 0 x.9 9x.8 =.7 Here are the YTMs needed to answer the queston: YTM on -year bond.% YTM on -year bond.% YTM on -year bond.7% YTM on 9-year bond.8% YTM on 0-year bond.9% C. () Based on you calculatons n part (A), what s the bond market tellng us? Investors expected short term nterest rate n each year to ncrease.

2 () Comparng the results n part A to part B, how has the markets outlook regardng nterest rates changed? More rapd ncrease expected n short term nterest rates n 08 compared to 07. () What prmary factor would explan the change? Expectatons of hgher nflaton.. Suppose the expectatons theory of the term structure s correct. Suppose that the current nterest rate on a one-year Treasury bll s percent. Suppose the one-year T-bll rate s expected to rse to percent one year from today, then to percent the followng year, and then stay at percent thereafter. Compute the nterest rate on current Treasury securtes wth maturtes of one year, two years, three years, four years and fve years, and plot the yeld curve. YTM -year bond = % YTM -year bond = (+)/ =.% YTM -year bond = ( + + ) / = % YTM -year bond = (+++)/ =.% YTM -year bond = (++++)/ =.0% Yeld curve slope upward.. Present a graph to show the mpact on the yeld curve of the followng shocks, assumng that the expectatons theory s correct and that the ntal yeld curve s flat. Start by drawng a bond market supply and demand dagram to fgure out what wll happen to short-term nterest rates when the shocks occur. Compare today's short-term nterest rates to expected short nterest rates n the future, and then apply the expectatons theory's predctons to determne whether the yeld curve should slope up or down. (a) The Federal Reserve announces today that t wll adopt a tght monetary polcy begnnng two years from today and contnung ndefntely nto the future. Begnnng two years from today, the Federal Reserve conducts an open market sale. Ths shfts out bond supply. As a result, prce decreases and nterest rate ncreases begnnng two years from today. P S S Bond Market change years from now. Q

3 Usng the nformaton on nterest rates we have obtaned, we can show that the yeld curve today wll be flat for maturtes up to two years from today and slopes up for maturtes hgher than two years. Let's use an example to show ths. Suppose that the one-year nterest rate s ntally %. After the Fed's announcement, the current one year nterest rate stays at %, and s expected to stay at % next year, but wll be 7% startng two years from today. The nterest rate today for securtes wth maturtes of,, and years wll be: (b) The government passes a bll ncreasng health care spendng startng years from now. Ths bll has no mpact on current budget defcts, but wll ncrease budget defcts startng fve years from now. Begnnng fve years from today, the budget defct wll be ncreased. Ths shfts out bond supply. As a result, the bond prce decreases and the nterest rate ncreases begnnng fve years from today. P S S Q

4 . Suppose the current nterest rate on a one-year Treasury bll s 7 percent. Suppose people beleve that the one-year T-bll rate wll contnue to be 7 percent one year from now, but wll fall to percent two years from now and reman at percent thereafter. (a) Assumng that the expectatons theory of the term structure s correct, compute the current nterest rate on treasury securtes of maturtes of one year through fve years, and plot the mpled yeld curve (b) Re-do part (a), assumng that the lqudty premum theory s correct. Assume that the lqudty premum on - and -year bonds s zero and ncreases to 0.7%, % and.% for -, - and -year bonds, respectvely. Plot the yeld curve relatve to the curve plotted n part (a).

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