Prof. Stefao Mazzotta Keesaw State Uiversity Fixed Icome Securities FIN4320. Fall 2006 Sample First Midterm Exam Last Name: First Name: Studet ID Number: Exam time is: 80 miutes. Total poits for this exam is: 400 poits Prelimiaries This is a closed book ad otes exam. Oe had writte formula sheet is allowed. (No photocopy or prit out). Remove all other paper from your desk. Explai carefully whe aswerig each questio. Show all relevat calculatios i the space provided uder each questio. Use the back of each page for extra space ad for scrap paper. Simply showig solutio, eve if correct, may ot give you full credit. All exams must be tured i the day of the exam ad durig the class graded exams are reviewed. This exam is subject to KSU s Code of Coduct, as published i the Udergraduate ad Graduate Catalogs. Violators will be prosecuted.
SAMPLE QUESTIONS Questio (50 poits) What is the price of a 5-year bod with a omial value of $100, a yield to maturity of 7% (with aual compoudig frequecy), a 12% coupo rate ad a semi aual coupo frequecy? t CF DF DCF 1 6 0.97 5.80 2 6 0.93 5.60 3 6 0.90 5.41 4 6 0.87 5.23 5 6 0.84 5.05 6 6 0.81 4.88 7 6 0.79 4.72 8 6 0.76 4.56 9 6 0.73 4.40 10 106 0.71 75.15 120.79151 Questio (50 poits) A ivestor has a cash of $10,000,000 at disposal. He wats to ivest i a bod with $1,000 omial value ad whose dirty price is equal to 105%. 1. What is the umber of bods he will buy? 2. Same questio if the omial value ad the dirty price of the bod are respectively $100 ad 97%. Solutio 1. The umber of bods he will buy is give by the followig formula Number of bods bought = Cash / ( Nomial Value of the bod dirty price) Here, the umber of bods is equal to =10000000 / (1000 * 105%) = 9523.81 ad = 10,000,000/ (100 * 97%) = 103093
Questio (50 poits) O 05/31/2002, a ivestor buys $1 millio US T-Bill with maturity date 06/27/2002 ad discout yield 1.76% o the settlemet date. (Recall that the settlemet date is the ext busiess day ad the day covetio is 360.) 1. What is the price of the T-Bill? 2. What is the equivalet moey-market yield? Solutio The settlemet date of the trasactio is 06/1/2002 (tradig date plus 1 workig day). There are 26 caledar days betwee the settlemet date ad the maturity date. The price P of the T-Bill is equal to 100 (1 1.76% 26/360)= 99.8729 2. The equivalet moey-market yield is equal to (1.76% 360)/ (360 26 1.76%) =1.76224% Questio (50 poits) Show that the price of a cosol bod (perpetuity) is P = cn/r Without loss of geerality assume cn = 1 P = (1+r) -1 + (1+r) -2 + (1+r) -3 + (1+r) -4 Hece P(1+r) = 1+ (1+r) -1 + (1+r) -2 + (1+r) -3 + (1+r) -4 Subtract the first equatio from the secod P(1+r) - P = 1 Which implies P = 1/r, or P = cn/r uder the assumptio that cn =1.
Questio (50 poits) If a ivestmet has a cumulative 63.45% rate of retur over 3.78 years, what is the aual cotiuously compouded rate of retur? Solutio. The aual cotiuously compouded rate of retur R is such that 1.6345 = exp(3.78rc) We fid Rc = l(1.6345)/3.78 = 13%.
Questio (50 poits) How would you compute the yield to maturity of a bod with that matures i 6 years, has a coupo rate of 4% paid aually, a face value of 1000, ad a price equal to 970? a) Write the equatio b) Use the space below to write the cash flows, discout factor, ad discouted cash flows for a arbitrary rate of 5%. c) Compute the price with your fiacial calculator d) Explai how you would fid the yield solvig the appropriate equality i excel e) Compare the price you computed with the market price. Is the yield higher or lower? Ca you compute it with your fiacial calculator? 970 =40/(1+y) + 40/(1+y)^2 +. +1040/(1+y)^6 Solve for y. rate 0.05 time CF DF DCF 1 2 3 4 5 6 price 970 Differece Istruct the solver to make the sum of discouted cash flows equal to the price Rate is 0.045832
Questio (50 poits) What are the three mai compoets affectig the chage i the yield curve? Sketch them i three differet plots. Aswer. Check your slides.
Questio (50 poits) What does the pure expectatio theory of the yield curve say? What does the Risk premium theory of the yield curve say? What does the Preferred habitat theory of the yield curve say? How does the Pure Risk premium theory explai a hump shaped yield curve Aswer. It does t.
Questio (50 poits) Explai the basic differece that exists betwee the preferred habitat theory ad the segmetatio theory. Aswer I the segmetatio theory, ivestors are supposed to be 100% risk-averse. Therefore, risk premia are ifiite. It is as if their ivestmet habitat were strictly costraied, exclusive. I the preferred habitat theory, ivestors are ot supposed to be 100% risk averse. So, there exists a certai level of risk premia from which they are ready to chage their habitual ivestmet maturity. Their ivestmet habitat is, i this case, ot exclusive.
Questio 7 (50 poits) At date t = 0, we observe the followig zero-coupo rates i the market: Maturity Zero- Coupo Maturity Zero-Coupo Years Rate 1 5.0% 2 6.0% 3 6.5% 4 6.8% 5 7.0% a) Draw the yield curve b) What are the 1-year maturity forward rates F(0, t, 1) implied by the curret term structure? c) Draw the Forward rate ad the zero curve o top of each other. Maturity Zero-Coupo Maturity Zero-Coupo Years Rate Forward 1 5.0% 2 6.0%F(0,1,1) 7.0095% 3 6.5%F(0,2,1) 7.5071% 4 6.8%F(0,3,1) 7.7051% 5 7.0%F(0,4,1) 7.8038%
Questio 8 (50 poits) Show that 360 rbey P = r BD Where r BEY is the Bod equivalet yield, r BD is the bak discout yield ad P is the price of a bod with face value equal to $1. Solutio P= 1 r P = 1+ r BD 360 1 BEY 1 = 1 rbd 1+ r 360 BEY Solve for rbd 1 1 = rbd 1+ r 360 BEY 1+ rbey 1 360 = rbd 1+ r BEY 1 360 rbey = r 1+ r BEY 360 rbey P = rbd BD