Math 4550: Math of Financial Derivatives. HW #4
Homework assignment for Wednesday, 2/25/2015
1. Over the last 10 years, Apple’s stockprice has increased from (split-adjusted)
$5.85 to $128
a. What is the percentage increase (=`return’) of Apple over these 10
years?
b. What is the average annual percentage return of Apple over this time
period?
c. What is the average annual log return for Apple over this time period?
2. Over the last 8 years, Sear’s stock price has declined nearly 80%, from $168 to
$36.
a. What is the average annual percentage return of Sears over this time
period?
b. What is the average annual log return for Sears over this time period?
3. Suppose that inflation for some country behaved like this: all of year 1 it was 1%,
2% for year 2, 3% for year 3, and so on until it was 20% for year 20.
a. What is the overall (cumulative) inflation for these 20 years?
b. What is the average rate of inflation for these 20 years?
4. If you invest $1000 at 7% compounded continuously, how long will it take until
you have $10000?
5. Suppose you would like to buy a house. You figure you can afford $1000 a month
for mortgage payments. Suppose 30-year-mortgage rates are currently 5%. How
much money can you borrow?
6. Suppose you have the choice between two $100,000 mortgages:
A: One charging a constant 6% interest rate (compounded monthly) for the life
of the mortgage.
B: One charging a constant 5% interest rate (compounded monthly) for the first
5 years, and then 10% for the rest of the life of the mortgage.
a. Suppose you can afford to pay a monthly payment of $700. Calculate for
both mortgages when you would be done paying the mortgage, and how
much in total payments you would have made. Which mortgage deal
would you choose
b. Suppose you can afford to pay a monthly payment of $X. For what value
of X, are the two mortgages equally good?
7. Find the value of a 10-year-bond with annual coupons of $50 and facevalue of
$1000, if the market rate is 6%. Also find its Simple, Macauley and Modified
Duration.