PORTFOLIO THEORY – EXERCISES 1
EXERCISE 1
The security S pays 990 euro after eight months and it costs 900 euro.
If there is a 20% tax on financial profits and the inflation rate is 2% per year, what is the real annual return paid
by security S after taxes?
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.
EXERCISE 5
A risky investment is estimated to deliver the following returns.
After 9 months:
• 𝑅 = −0.15 with a 20% probability
• 𝑅 = 0.1 with a 70% probability
• 𝑅 = 0.25 with a 10% probability
After 24 months:
• 𝑅 = −0.2 with a 20% probability
• 𝑅 = 0.15 with a 60% probability
• 𝑅 = 0.3 with a 20% probability
The annual inflation rate is 3%.
What is the real cumulative expected return after 24 months?
EXERCISE 6
Consider the following series of unadjusted monthly closing prices (in euro) of a stock that undergoes the
corporate events indicated next to the price.
January: 7
February: 6.5 Dividend of 1 euro per share is paid
March: 7.5
April: 7.2
May: 4 2 for 1 stock split
June: 4.5
Compute the adjusted stock returns.