EXERCISES
EXERCISE 1
A coupon bond will pay a coupon of 50 euro 3 months from now, another coupon of 50
euro 9 months from now, and final coupon of 50 euro plus the face value of 1000 euro
15 months from now. The yield to maturity is 2% and the current price of the bond is
1123.34 euro. Compute the Macaulay duration.
EXERCISE 2
The log-return of the four assets included in an equally weighted portfolio is:
𝑟1 = 0.1, 𝑟2 = −0.06, 𝑟3 = 0.07, 𝑟4 = 0.05
What is the return of the portfolio?
EXERCISE 3
The returns of a security over four periods are:
𝑅𝑡=1 = 0.2, 𝑅𝑡=2 = −0.1, 𝑅𝑡=3 = 0.08, 𝑅𝑡=4 = 0.04
If we invested 1000 euro in this asset at t=0, how much is our investment worth at t=4?
EXERCISE 4
The vector of weights and the covariance matrix of a portfolio with three assets are:
𝒘 = [
0.5
0.7
−0.2
] 𝜮 = [
0.004 0.006 0.003
0.006 0.008 0.007
0.003 0.007 0.005
]
Compute, using matrix form, the variance of the portfolio.