1 Introduction

This procedure monitors the performance of the portoflio and it calculates the MARKET RISK.
The stocks of 5 companies traded on the Frankfurt Stock Exchange are selected:

  1. Hugo Boss (BOSS_X), Trading System: Xetra, ISIN: DE000A1PHFF7

  2. E.on Se (EON_X), Trading System: Xetra, ISIN: DE000ENAG999

  3. Heidleberg Druckmaschinen (HDD_X), Trading System: Xetra, ISIN: DE0007314007

  4. Continental (CON_X), Trading System: Xetra, ISIN: DE0005439004

  5. Siemens (SIE_X), Trading System: Xetra ISIN: DE0007236101

The portfolio is composed by:

  • 3 shares of Hugo Boss
  • 2 shares of EON
  • 4 shares of Heidelberg
  • 4 shares of Continental
  • 6 shares of Siemens

for a total of 19 shares.

The data are downloaded from Quandl.com, which is a platform for financial, economic and alternative data that serves investment professionals.
The data cover a time period from 02-01-2014 till the last trading day available.
The stocks and the portfolio values are daily updated and the calculations of risk measures are on time.

2 Portfolio Performances

The portoflio value today is:

2018-02-14 2014-01-02 Delta % change
1814.488 1569.14 245.348 14.53

2.1 Plot the values of the portfolio

 
Plot the development of PF value for the last 100 trading days: from 2017-09-11 to 2018-02-14.

2.2 Performances of the portfolio

2018-02-14 2018-02-13 2018-02-12 2018-02-09 2018-02-08 2018-02-07 2018-02-06 2018-02-05 2018-02-02 2018-02-01 2018-01-31
Value 1814.488 1786.922 1791.88 1771.908 1803.14 1851.44 1818.98 1846.82 1869.30 1905.48 1950.26
% change 1.530 -0.280 1.12 -1.750 -2.64 1.77 -1.52 -1.21 -1.92 -2.32 0.08

3 Stocks Performances

3.1 Plot development of stock prices

3.2 Last prices of stocks

2018-02-14 2018-02-13 2018-02-12 2018-02-09 2018-02-08 2018-02-07 2018-02-06 2018-02-05 2018-02-02 2018-02-01 2018-01-31
BOSS price 72.800 72.600 73.100 71.020 71.98 72.70 70.94 71.84 72.90 73.98 73.98
% change 0.280 -0.690 2.890 -1.340 -1.00 2.45 -1.26 -1.46 -1.47 0.00 -0.35
EON price 8.100 7.885 8.018 7.992 8.08 8.23 8.10 8.29 8.24 8.37 8.46
% change 2.690 -1.670 0.320 -1.100 -1.84 1.59 -2.32 0.60 -1.57 -1.07 -0.59
HDD price 2.852 2.798 2.666 2.686 2.81 2.67 2.57 2.68 2.81 2.85 2.91
% change 1.910 4.830 -0.750 -4.510 5.11 3.82 -4.19 -4.74 -1.41 -2.08 2.08
CON price 228.200 223.600 223.600 222.500 225.70 233.10 227.70 230.90 233.40 238.80 241.70
% change 2.040 0.000 0.490 -1.430 -3.23 2.34 -1.40 -1.08 -2.29 -1.21 -0.37
SIE price 109.280 107.960 108.580 107.020 109.50 112.30 111.48 113.40 114.88 116.70 122.16
% change 1.220 -0.570 1.450 -2.290 -2.52 0.73 -1.71 -1.30 -1.57 -4.57 0.81

3.3 Correlation matrix of stock prices

3.4 Descriptive statistics of the returns:

Mean Median St. Dev. Kurtosis Skewness
HugoBoss -0.00033 0.00050 0.01875 22.85933 -2.26206
EON -0.00046 0.00000 0.01998 5.72336 -0.69058
Heidelberg 0.00006 0.00000 0.02362 7.85652 -0.67599
Continental 0.00036 0.00050 0.01639 2.07511 -0.19500
Siemens 0.00010 0.00011 0.01399 2.84080 -0.04024

4 Market Risk

The market risk of the portfolio is computed applying 5 methodologies:

  1. Variance Covariance method

  2. Historical Simulation

  3. Monte Carlo simulation with a Normal distribution

  4. Monte Carlo simulation with a Student-t distribution

  5. POT (Points Over Threshold) with a Generalized Pareto Distribution

In the following table, it is possible to see the maximum loss expected (in Euro), that the portfolio can experience on 2018-02-15 with a probability at 99%.

VaR ES
Var-cov. 56.19 64.42
Hist. sim. 67.65 84.17
MC (normal) 55.27 63.18
MC (Student t) 66.71 90.41
POT 65.73 84.83

5 Backtesting

In this section, the market risk is tested, in order to check the reliability of the model and if it is able to predict the maximum expected loss on 2018-02-15.
The VaR calculated with a Monte Carlo with multivariate t-Student distribution is selected.
The Back Test is evaluated from 2017-07-03 to 2018-02-14.

 

Let’s compare the VaR and Profit/Loss realized by the portfolio in the last 10 trading days:

2018-02-14 2018-02-13 2018-02-12 2018-02-09 2018-02-08 2018-02-07 2018-02-06 2018-02-05 2018-02-02 2018-02-01 2018-01-31
Value of PF in Euro 1814.49 1786.92 1791.88 1771.91 1803.14 1851.44 1818.98 1846.82 1869.30 1905.48 1950.26
Return of PF in Euro 27.57 -4.96 19.97 -31.23 -48.30 32.46 -27.84 -22.48 -36.18 -44.78 1.64
VaR in Euro -65.94 -65.90 -65.30 -66.23 -68.14 -66.56 -67.51 -68.56 -69.85 -71.36 -70.99

Percentage of exceptions occured, i.e. how many times the Loss experienced was higher than the VaR predicted :

## [1] "0 %"

Now, the Conditional Coverage Test (Christoffen 1998) is implemented, which tests that the probability of observing an exception on a given day is independent if whether or not an exception was recorded on the previous day.
The Conditional Coverage Test states that:

\(H_{0}\) : the exceptions are serially independent

## [1] "The null hypothesis of Conditional Coverage Test cannot be rejected"

If the \(H_{0}\) cannot be rejected, the model can react promptly to new information.