1 Introduction

This procedure monitors the performance and the market risk of a portfolio.
The following cryptocurrencies are selected:

  1. Bitcoin, BTC

  2. Ethereum, ETH

  3. Ripple, XRP

  4. Bitcoin Cash. BCH

  5. Cardano, ADA

The portfolio is composed by:

  • 3 shares of Bitcoin
  • 5 shares of Ethereum
  • 20 shares of Ripple
  • 2 shares of Bitcoin Cash
  • 30 shares of Cardano

for a total of 60 cryptocurrencies.

The portfolio was created on 2014-03-24 and the data are available until the last trading day.
The cryptocurrencies and portfolio values are daily updated and the calculations of risk measures are on time.

2 Portfolio Performances

The portoflio value (in Dollar) today is:

2018-03-26 2014-03-24 Delta % change
28933.47 1750.487 27182.99 280.51

2.1 Plot the values of the portfolio

2.2 Performances of the portfolio

2018-03-26 2018-03-25 2018-03-24 2018-03-23 2018-03-22 2018-03-21 2018-03-20 2018-03-19 2018-03-18 2018-03-17 2018-03-16
Value 28933.47 30060.93 30619.66 31394.36 30926.31 31683.66 31664.84 30685.85 29258.34 28431.50 29996.61
% change -3.82 -1.84 -2.50 1.50 -2.42 0.06 3.14 4.76 2.87 -5.36 0.44

3 Crypto Performances

3.1 Plot development of crypto prices

3.2 Last prices of cryptos

2018-03-26 2018-03-25 2018-03-24 2018-03-23 2018-03-22 2018-03-21 2018-03-20 2018-03-19 2018-03-18 2018-03-17 2018-03-16
BTC price 8209.40 8495.78 8668.12 8879.62 8728.47 8929.28 8913.47 8630.65 8223.68 7916.88 8338.35
% change -3.43 -2.01 -2.41 1.72 -2.27 0.18 3.22 4.83 3.80 -5.19 0.45
ETH price 489.95 524.29 526.44 539.62 539.70 561.73 557.17 556.73 538.64 552.78 601.67
% change -6.77 -0.41 -2.47 -0.01 -4.00 0.82 0.08 3.30 -2.59 -8.47 -1.59
XRP price 0.60 0.64 0.64 0.64 0.66 0.69 0.71 0.75 0.66 0.64 0.69
% change -6.84 0.10 -0.30 -3.00 -4.56 -2.30 -5.39 12.85 3.23 -7.75 -1.16
BCH price 919.25 966.88 982.30 1019.43 1011.52 1033.45 1059.12 994.67 938.12 949.78 977.03
% change -5.05 -1.58 -3.71 0.78 -2.14 -2.45 6.28 5.85 -1.24 -2.83 3.48
ADA price 0.17 0.18 0.19 0.19 0.20 0.21 0.20 0.20 0.16 0.15 0.18
% change -9.54 -2.46 -0.03 -7.25 -4.66 3.94 3.63 23.56 0.90 -14.48 -3.75

3.3 Correlation matrix of crypto prices

3.4 Descriptive statistics of the returns:

Mean Median St. Dev. Kurtosis Skewness
Bitcoin 0.00229 0.00203 0.04502 7.90810 -0.19057
Ethereum 0.00538 -0.00075 0.08383 62.65306 -3.55952
Ripple 0.00273 -0.00280 0.08036 26.87614 2.02508
Bitcoin Cash 0.00325 -0.00663 0.11350 3.21691 0.57098
Cardano 0.01082 -0.00362 0.13725 10.93389 2.38030

  Plot the density functions of cryptocurrencies returns

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

The following table displays (in Dollar):

  • VaR : Value at Risk, the maximum loss that the PF can experience on 2018-03-27 with a probability at 99%
  • ES : Expected Shortfall

  • maxReturn : the maximum positive return that the PF can experience on 2018-03-27 with a probability at 99%

    VaR ES maxR
    Var-cov. -3729.05 -4287.15 0.00
    Hist. sim. -4775.16 -5089.21 3980.90
    MC (normal) -3483.35 -3966.07 4255.20
    MC (Student t) -7382.27 -11489.64 10778.19
    POT -3722.42 -4884.01 0.00

5 Backtesting

This section checks if the portfolio survives real market conditions.
The VaR is calculated with the “Point Over the Threshold” method, which exploits the properties of the Generalized Pareto Distribution.
The Back Test is evaluated from 2015-03-24 to 2018-03-26.
The green line shows the maximum return expected for that day.

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

2018-03-26 2018-03-25 2018-03-24 2018-03-23 2018-03-22 2018-03-21 2018-03-20 2018-03-19 2018-03-18 2018-03-17 2018-03-16
Value of PF in Euro 28933.47 30060.93 30619.66 31394.36 30926.31 31683.66 31664.84 30685.85 29258.34 28431.50 29996.61
Return of PF in Euro -1127.45 -558.74 -774.70 468.05 -757.35 18.81 978.99 1427.51 826.84 -1565.11 130.73
VaR in Euro 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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

## [1] "12.65 %"

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 is rejected with confidence level at 0.99"

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