Отлично защищённая курсовая работа по предмету "Fixed Income securities" . Написана на английском языке
QUESTION 1 [a total of 60 marks]
Consider an MBS pass-through security with principal $300 million. The original
mortgage pool has a weighted average maturity of WAM=360 months (30 years)
and a weighted average coupon WAC=7%. The pass-through security pays a
coupon equal to 6.5%. Assume a flat term structure with constant 5.65%yield.
The corresponding discount with maturity T is then r T T Z T e (0. )* (0, ) .
a) What is the main difference between a pool of mortgages and a passthrough
security from the same pool? Discuss. (8 marks)
b) What types of risks appear in an MBS security? What is the sensitivity of
an MBS in interest rate movements and what are the effects on PSA?
Discuss. (12 marks)
c) Assume a constant PSA150%. Compute the price of the pass-through
security by using an Exce
Показать всеl spreadsheet. Explain your calculations on how
to price the pass through security. (12 marks)
d) Compute the duration of this security assuming that the PSA remains
constant. (8 marks)
e) Compute the effective duration of this security assuming that the PSA
increases to 200% if the term structure shifts by 50 basis points, while it
decreases to 120% if the term structure shifts up by 50 basis points.
Discuss any difference that you find compared to your result in part d).
f) Compute the effective convexity of this security under the same PSA
assumption as in part e). Interpret your results. (10 marks)
Page 4 of 4
QUESTION 2 [a total of 40 marks]
This question requires to carry out an empirical study on the yield curves, zero-coupon and forward, of the US government debt markets. You need to implement the steps listed below. Data can be downloaded from the ST Louis Federal bank’s web site (a manual with instructions can be found on Moodle). Alternatively you can collect the data from Yahoo.com/finance.
a) Select a recent business day (e.g. 5 May 2014) and download ytms (yield to maturity), bond prices and coupons for different maturities ranging from 1month to 10 years (NB you will need to collect the data for about 20 different maturities with each observation being about 6 month apart). Arrange them in a spreadsheet in columns, i.e. maturity in years (fractions of years are ok), ytm, coupon price. The order will be the maturities ascending one1.
b) Create a scatter plot between ytm and maturity (maturity on the X axis).
c) Fit a (continuous line) curve through the plot. You can use some functions/options in excel to fit this line curve.
d) With your fitted line for yields, generate a new table of YTM, and bond prices, each observation being six months apart. Hence, if your last maturity bond is of ten years, you will have 20 periods of a half year each. Call this Table 2. Remember that your fitted line gives you yield as a function of maturity. Hence, for maturities t = 0.5; 1; 1.5; 2, 2.5, 3, …9.5, 10, you will compute matching yields.
e) Using this table of ytms, prices, and coupons, compute (i) the zero-coupon rates and (ii) forward rates for all maturities in the table. Call this Table 3.
f) Present a time series plot of the (i) ytm curve, (ii) zero-coupon rate curve, and (iii) forward rate curve against time to maturity on the same graph. Call this Plot 3.
g) Now, as an alternative, show how you can use Table 1 with a regression method to derive discount factors and zero-coupon rates. Feel free to make any simplifying assumptions here. Create a table of zero-coupon rates spaced half a year apart. Call this Table 4.
h) Plot the zero-coupon curve from Table 3 versus the one from Table 4, and comment. Call this Plot 4.
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MBS are highly sensitive to interest rates, however. The asset class can be hurt in two ways: 1) by a sharp increase in rates, which causes prices to fall, and 2) a sharp decline in rates, which prompts homeowners to refinance their mortgages, which can lead to return of principal (which needs to be reinvested at lower rates) and a lower yield than investors were anticipating (since there is no interest paid on the retired principal). MBS therefore tend to perform best when rates are stable.To be clear interest movements are effects on PSA we have to review an example:Consider Table 8.4:-The first two columns show the impact of interest rates on the price of the pass through, when the speed of prepayment is kept constant at 200% PSA.-The next three columns show the case in which as the i
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