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:

2018-12-21 2014-01-02 Delta % change
1263.652 1569.14 -305.488 -21.65

2.1 Plot the values of the portfolio

 
Plot the development of PF value for the last 100 trading days: from 2018-07-31 to 2018-12-21.

2.2 Performances of the portfolio

2018-12-21 2018-12-20 2018-12-19 2018-12-18 2018-12-17 2018-12-14 2018-12-13 2018-12-12 2018-12-11 2018-12-10 2018-12-06
Value 1263.652 1263.314 1275.982 1283.25 1277.784 1287.678 1304.432 1301.924 1288.85 1269.252 1288.146
% change 0.030 -1.000 -0.570 0.43 -0.770 -1.290 0.190 1.010 1.53 -1.480 -3.330

3 Stocks Performances

3.1 Plot development of stock prices

3.2 Last prices of stocks

2018-12-21 2018-12-20 2018-12-19 2018-12-18 2018-12-17 2018-12-14 2018-12-13 2018-12-12 2018-12-11 2018-12-10 2018-12-06
BOSS price 53.320 52.960 53.860 53.640 54.880 56.880 58.000 57.300 59.040 58.760 59.420
% change 0.680 -1.690 0.410 -2.290 -3.580 -1.950 1.210 -2.990 0.480 -1.120 -1.900
EON price 8.864 8.895 8.965 8.899 8.970 9.231 9.220 9.092 8.933 8.694 8.821
% change -0.350 -0.780 0.740 -0.790 -2.870 0.120 1.400 1.760 2.710 -1.450 -2.310
HDD price 1.536 1.526 1.603 1.603 1.631 1.694 1.738 1.745 1.716 1.656 1.756
% change 0.650 -4.920 0.000 -1.730 -3.790 -2.560 -0.400 1.680 3.560 -5.860 -0.230
CON price 122.700 122.550 123.250 124.050 122.800 122.650 125.600 126.950 124.900 121.800 124.800
% change 0.120 -0.570 -0.650 1.010 0.120 -2.380 -1.070 1.630 2.510 -2.430 -3.890
SIE price 98.170 98.390 99.510 100.320 99.580 100.200 100.440 99.510 97.900 96.960 97.670
% change -0.220 -1.130 -0.810 0.740 -0.620 -0.240 0.930 1.630 0.960 -0.730 -3.350

3.3 Correlation matrix of stock prices

3.4 Descriptive statistics of the returns:

Mean Median St. Dev. Kurtosis Skewness
HugoBoss -0.00052 0.00057 0.01836 21.04156 -2.16242
EON -0.00031 0.00000 0.01898 6.08201 -0.64582
Heidelberg -0.00044 0.00000 0.02389 6.68010 -0.69125
Continental -0.00020 0.00000 0.01698 5.22867 -0.56570
Siemens -0.00001 0.00031 0.01362 2.79942 -0.06887

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 multivariate Normal distribution

  4. Monte Carlo simulation with a multivariate 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 2018-12-24 with a probability at 99%.

VaR ES
Var-cov. 38.07 43.58
Hist. sim. 45.05 57.15
MC (normal) 37.44 42.76
MC (Student t) 44.92 61.03
POT 45.09 57.32

5 Backtesting

This section checks if the portfolio survives real market conditions.
The VaR is calculated with a Monte Carlo with multivariate t-Student distribution.
The Back Test is evaluated from 2017-07-03 to 2018-12-21.

 

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

2018-12-21 2018-12-20 2018-12-19 2018-12-18 2018-12-17 2018-12-14 2018-12-13 2018-12-12 2018-12-11 2018-12-10 2018-12-06
Value of PF in Euro 1263.65 1263.31 1275.98 1283.25 1277.78 1287.68 1304.43 1301.92 1288.85 1269.25 1288.15
Return of PF in Euro 0.34 -12.67 -7.27 5.47 -9.89 -16.75 2.51 13.07 19.60 -18.89 -43.63
VaR in Euro -44.78 -45.38 -45.65 -45.45 -45.54 -46.46 -46.57 -45.66 -45.47 -45.75 -47.18

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

## [1] "0.55 %"

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.