FRE6571 – Asset Backed Securities
Homework Answers
Due 02/25/2011
2. Given the following Par Yield Curve (semi-annually compounded yields), calculate
the corresponding Spot Rate Curve, and the Forward Rates
Period Year Par Spot Forward
1 .5 2.0 2.000 2.000
2 1.0 2.5 2.503 3.007
3 1.5 3.0 3.010 4.028
4 2.0 3.5 3.522 5.066
Spot(1) = Par(1) = 2.000
Spot(2) 100 = 1.25/(1+2/200)1+101.25/(1+x/200)2 x = 2.503
1 2 3
Spot(3) 100 = 1.50/(1+2/200) +1.5/(1+2.503/200) +101.5/(1+x/200) x = 3.010
Spot(4) 100 = 1.75/(1+2/200)1+1.75/(1+2.503/200)2+1.75/(1+3.010/200)3+
101.75/(1+x/200)4 x = 3.522
Forward(1) = Spot(1) = 2.000
Forward(2) (1+2.000/200)(1+x/200) = (1+2.503/200) 2 x = 3.007
2 3
Forward(3) [(1+2.503/200) ][1+x/200] = (1+3.01/200) x = 4.028
Forward(4) [(1+3.010/200)3][1+x/200] = (1+3.522/200) 4 x = 5.066
3. What is the price of a 3 year 0-coupon bond with a BEY of 6%. What is the
Macaulay Duration? What is the Modified Duration?
Price = 100/(1+BEY)n = 100/(1.03)6 = 100/1.19405 = 83.748
Macaulay Duration for 0 coupon bond is same as years to Maturity = 3
Modified Duration = Macaulay Duration/(1+BEY/200) = 3/1.03 = 2.913
4. Your local bank offer 6-month CDs at a rate of 5% and 12-month CDs at a rate of
6%. You want to invest $10,000 for a full year. If you select the 6-month CD as
your investment what rate will the bank need to offer in 6 months for new 6-
month CDs for you to breakeven? (assume all rates are semi-annually
compounded rates)
(1+6/200)2 = (1+5/200)(1+X/200)
(1+X/200) = 1.032/1.025 = 1.035
X = (1.035 – 1)*200 = 7.00%
5. A mortgage backed security has a flat price of 101 an accrued interest of .415, a
MEY (monthly compounded yield) of 5.432 and a Macaulay Duration of 4.5. If
the BEY moves up by 40 basis points estimate the new price.
MEY 6
BEY 200 ((1 ) 1) = 200 x [(1+5.432/1200)^6-1] = 5.494%
1200
MacaulayDuration
ModifiedDuration = 4.5/(1+5.494/200) = 4.380
Yield
1
200
Old Full Price = 101 + .415 = 101.415
Percent Change = -40/100 x 4.380 = -1.752%
New Full Price = (100-1.752)/100x101.415 = 99.638
New Flat Price = 99.638 - .415 = 99.223
Answers to 6 & 7 in Excel Spreadsheet