Group number: 1
Lieuwe Bil - 2104794
Sander Slegers - 2014239
Niek van den Hurk - 2079279
Bart Sprangers - 2108613
Introduction:
To complete the assignment, we collected data of 75 different stocks, over a time-period ranging
from 1981 until 2022 (no data on 2023 was available). We selected companies with share code
of 10 or 11 and collected all the necessary data. We randomly chose 75 companies based on the
returns per company. While answering the questions below, we added more columns and
calculations to the dataset. The used PERMNO’s are included in Appendix 1.
Question 1: Suppose you are a US investor who invests in a market-value weighted
portfolio that contains stocks that you collected. (i) Calculate the market-value weighted
portfolio. (ii) What is the average monthly return? (iii) What is the risk as measured by
standard deviation? (iv) What is the annual 99% Value at Risk (VaR) for an investment of
€200.000, -? (v) Finally, calculate the monthly 10% GUISE as has been explained during
class.
(i) To answer this question, we used the full dataset of 75 stocks. To calculate the market-value
weighted portfolio, we first need to find the weights of the portfolio. The weights are calculated
by dividing the market capitalization of the individual stock by the sum of all 75 market
capitalizations in the portfolio. Summing up all the weights of the individual stocks equals one.
(ii) The average monthly return of our portfolio of 75 stocks is 1.07%. So, on average the
portfolio gained 1.07% each month from 1981 up until 2022.
(iii) The standard deviation of the portfolio has been calculated using the portfolio returns and
average return calculated for question 1.ii. As we have the monthly returns, the mean of the
monthly returns and the number of observations the following general formula can be used:
√
n
∑ ( xi−μ )2
i =1
σ=
n
As the dataset contains monthly returns the formula calculates monthly standard deviation. To
calculate the annual standard deviation, we multiplied the monthly standard deviation of 5.30%
by the square root of twelve which returned an annual standard deviation of the portfolio of
18.37%
1
, (iv) To calculate the Value at Risk (VaR) we use the following formula:
VaRt = Wt * (2.33 * SD - 𝜇) = 200.000 * ABS ((2.33 * 18,37%) - 13,56%) = €58.341.
Meaning we can say with 99% confidence that within a year not more than €58.341 out of the
€200.000 investment will be lost.
(v) To calculate the 10% GUISE, we used the Excel provided on Canvas and the lecture slides.
The assumptions made in the lecture are the same assumptions we are using during our
calculations of the GUISE. As the monthly GUISE is asked and the returns in the dataset are also
monthly returns the Arithmic GUISE can be used. This is because any compounding within the
month is already in the monthly returns. The yearly costs are assumed to be 0.5% and the initial
costs are estimated to be 2.00%. The invested amount is €200.000.
In the bad state of the world, the investor will get an expected payoff of €179.522 for his
€200.000 investment. The GUISE calculation is included in Appendix 2.
Question 2: (i) Draw the mean-variance frontier based on the 6 assets when short sales are
allowed. (ii) Next, in the same figure, draw the mean-variance frontier when short sales are
NOT allowed. (iii) Moreover, put these 6 assets and the value-weighted portfolio of those
assets in the figure as well. (iv) Explain the results.
(i) & (ii) & (iii)
2
Lieuwe Bil - 2104794
Sander Slegers - 2014239
Niek van den Hurk - 2079279
Bart Sprangers - 2108613
Introduction:
To complete the assignment, we collected data of 75 different stocks, over a time-period ranging
from 1981 until 2022 (no data on 2023 was available). We selected companies with share code
of 10 or 11 and collected all the necessary data. We randomly chose 75 companies based on the
returns per company. While answering the questions below, we added more columns and
calculations to the dataset. The used PERMNO’s are included in Appendix 1.
Question 1: Suppose you are a US investor who invests in a market-value weighted
portfolio that contains stocks that you collected. (i) Calculate the market-value weighted
portfolio. (ii) What is the average monthly return? (iii) What is the risk as measured by
standard deviation? (iv) What is the annual 99% Value at Risk (VaR) for an investment of
€200.000, -? (v) Finally, calculate the monthly 10% GUISE as has been explained during
class.
(i) To answer this question, we used the full dataset of 75 stocks. To calculate the market-value
weighted portfolio, we first need to find the weights of the portfolio. The weights are calculated
by dividing the market capitalization of the individual stock by the sum of all 75 market
capitalizations in the portfolio. Summing up all the weights of the individual stocks equals one.
(ii) The average monthly return of our portfolio of 75 stocks is 1.07%. So, on average the
portfolio gained 1.07% each month from 1981 up until 2022.
(iii) The standard deviation of the portfolio has been calculated using the portfolio returns and
average return calculated for question 1.ii. As we have the monthly returns, the mean of the
monthly returns and the number of observations the following general formula can be used:
√
n
∑ ( xi−μ )2
i =1
σ=
n
As the dataset contains monthly returns the formula calculates monthly standard deviation. To
calculate the annual standard deviation, we multiplied the monthly standard deviation of 5.30%
by the square root of twelve which returned an annual standard deviation of the portfolio of
18.37%
1
, (iv) To calculate the Value at Risk (VaR) we use the following formula:
VaRt = Wt * (2.33 * SD - 𝜇) = 200.000 * ABS ((2.33 * 18,37%) - 13,56%) = €58.341.
Meaning we can say with 99% confidence that within a year not more than €58.341 out of the
€200.000 investment will be lost.
(v) To calculate the 10% GUISE, we used the Excel provided on Canvas and the lecture slides.
The assumptions made in the lecture are the same assumptions we are using during our
calculations of the GUISE. As the monthly GUISE is asked and the returns in the dataset are also
monthly returns the Arithmic GUISE can be used. This is because any compounding within the
month is already in the monthly returns. The yearly costs are assumed to be 0.5% and the initial
costs are estimated to be 2.00%. The invested amount is €200.000.
In the bad state of the world, the investor will get an expected payoff of €179.522 for his
€200.000 investment. The GUISE calculation is included in Appendix 2.
Question 2: (i) Draw the mean-variance frontier based on the 6 assets when short sales are
allowed. (ii) Next, in the same figure, draw the mean-variance frontier when short sales are
NOT allowed. (iii) Moreover, put these 6 assets and the value-weighted portfolio of those
assets in the figure as well. (iv) Explain the results.
(i) & (ii) & (iii)
2
