Problem1

ConsiderthedatabelowalongsidetheoutputfromarelatedOLSregression.Thepvariableistheleft hand side variable in a regression and captures the price(s) of 5 annual coupon bonds. The 5 xvariables(x1,x2...x5)representthecashflowsdueonthebondsattimes1through5,respectively.

1. Giventhereportedregressionoutput,reportbackthepureyieldcurve,r1-r5.
2. Comparer3totheyieldtomaturityonthe3yearbond.Explainthedifference

p	x1		x2		x3		x4		x5
100.00		101.00		0.00		0.00		0.00		0.00
99.00		1.00		101.00		0.00		0.00		0.00
100.00		2.00		2.00		102.00		0.00		0.00
97.00		2.00		2.00		2.00		102.00		0.00
90.00		1.00		1.00		1.00		1.00		101.00
90.00		1.00		1.00		1.00		1.00		101.00

SUMMARYOUTPUT

RegressionStatistics

MultipleR		1
RSquare		1
AdjustedRSquare		0
StandardError		0
Observations		6
ANOVA
	df		SS		MS	F	SignificanceF
Regression		5		55410	11082	#NUM!	#NUM!
Residual		1		0	0
Total		6		55410
Coefficients StandardError tStat P-value Lower95%	Upper95%
Intercept	0	#N/A		#N/A	#N/A	#N/A	#N/A
x1	0.99009901		0	65535	#NUM!	0.99009901	0.99009901
x2	0.970395059		0	65535	#NUM!	0.970395059	0.970395059
x3	0.941951097		0	65535	#NUM!	0.941951097	0.941951097
x4	0.894069703		0	65535	#NUM!	0.894069703	0.894069703
x5	0.853499853		0	65535	#NUM!	0.853499853	0.853499853

Problem2

Basedontheyieldcurveabove,solvefor

1. f_1,2
2. f_2,3
3. f_3,4
4. f_4,5
5. f_1,3

Problem 3 Assume for a moment that not only is the expectations hypothesis correct, but in this case, the realized path of interest rates follows expectations exactly. What will the one year holding period returns to 1, 2, 3, 4, and 5 year zero coupon bonds be (ret⁽ⁿ⁾_t,t+1)? What about the 2 year holding period returns (ret⁽ⁿ⁾_t,t+2)?

Problem4 Suppose instead, the path of interest rates does not follow the expectations consistent with problem 3. Given the alternative path of rates, the one year return on a two year zero is 0.01 (ret(²⁾_t,t+1= 0.01). The annualized one and two year returns on the current 3 year zero (from t to t+1 and t to t+2) are 0.01 and 0.01 (ret⁽³⁾_t,t+1= 0.01 and [1 +ret⁽³⁾_t,t+2]^0.51 = 0.01. Solve for the actual path of one year rates, r_0,1, r_1,2, r_2,3 that would generate these returns. Where and how did the path of interest rates diverge from expectations generated under the expectations hypothesis (note: if you can't solve this mathematically, think simply about what expected holding period returns would be under the expectations hypothesis)?

Bonus: What was the change in the two year rate r_1,3 r_0,2 and what was the forecast change in the 2-year rate relative to the expectations hypothesis?

Problem5

Suppose expected short rates at all horizons (E(r_0,1) =E(r_1,2) =E(r_2,3),...)are flat at 0.01. HowdoyouinterprettheforwardratesgeneratedinProblem2aand2b?

Problem 6 Interpret the regression below: ret⁽²⁾_t,t+1r₁=a+b(f_1,2r₁) +e Describe and interpret what we found in the data when we ran this regression. What does it have to do with the change in r1 from t to t+1 predicted by the expectations hypothesis?