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On Russia

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The russion CB hiked the policy rate tonight form 10.5% to 17.0%. In the market this lead to a nearly parallel shift of the yield curve with steepening in the 1-5 year range.

rus_yield_curve

For me, this leads to some question:

  • How large is the duration mismatch of the Russian banks?
  • Assuming it is not trivial, how long will the banks survive the inverted yield curve?

The macro problems of Russia show all the symptoms of dutch disease – a strong ressource sector leading to real appreciation of the Ruble, making the rest of the economy less competetive. The current abrupt reversal following the decline in oil prices kills the forex inflow on which domestic consumption of imports relied, making the interest rake hike necessary. This finally kills investments in the private sector, which would be necessary to capitalize on the new terms of trade by increasing exports and consumption of domestic goods.

 

PS: Gone with the wind – after gaining  10% in early trading after the hike, the ruble lost all gains before lunch.

Differences in Draft and Final Delegated Acts (Solvency II)

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2

The Solvency II Delegated Acts have been published by the EU commission yesterday. My last draft version was from July of this year, so I wanted to compare the versions for any differences. I exported the text from PDF to .txt files and uploaded them into a gist as revision 1 and 2. The github diff stops at a certain point, so you would have to download the text versions and use your own diff software.

On the whole, this version has only very minor changes, with the exception of the treatment of securitisations in the spread risk module. On first glance it seems to be that the defintition of type 1 securitisations has been tightend, and the capital charge for this type has been reduced, which would fit to the recitals 91 and 92.

If anybody wants to diff the more widely circulated March version of the draft with the final version, I would suggest to save that work and just use the annotated pdf available on Petter Svensons site for the July version.

Here are the material differences that I can spot:

  • Added explanatory memorandum
  • New recital 67: Rationalization for the operation risk module of the standard formula.
  • Enhanced recital 91 (former 90) and new recital 92: Stressing importance of regulating use of securisitations.
  • Art. 13, new point 6 – allowing for valuation of related undertakings according to local gaap under conditions.
  • Article 177: Fine-tuning, which securitisations belong to type 1 or type 2.
  • Article 178: Lowering spread risk for securitisation type 1 with CQS 2 or 3.
  • Article 204: Technical Provisions can be adjusted for transitional adjustments when calculating OpRisk.
  • Article 250, 251: Technical Provisions can be adjusted for transitional adjustments when calculating linear component of MCR.

 

Scratching that itch from ifelse

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Okay, as I wrote yesterday, ifelse is rather slow, at least compared to working in C++. As my current project is using ifelse rather a lot, i decided to write a small utility function. In the expectation that I will collect a number of similar functions, I made a package out of it and posted it on github: https://github.com/ojessen/ojUtils

I get a speedup of about 30 times, independent of the target type.

Feedback and corrections greatly appreciated.

Thanks to the people at Travis for providing a free CI server which works directly with github. This of course is a tiny example, but it is good to know that the workflow to set this up can be done in 5 minutes.

And thanks to Romain Fraoncois for showing some Rcpp sugar:

Some data:

require(ojUtils)
## Loading required package: ojUtils
require(microbenchmark)
## Loading required package: microbenchmark
test = sample(c(T,F), size = 1e5, T)
yes = runif(1e5)
no = runif(1e5)

microbenchmark(ifelse(test, yes, no), ifelseC(test, yes, no))
## Loading required package: Rcpp
## Unit: microseconds
##                    expr   min      lq  median      uq    max neval
##   ifelse(test, yes, no) 31925 33404.8 34065.1 58083.5  71891   100
##  ifelseC(test, yes, no)   620   647.5   721.8   817.7 209254   100
test = sample(c(T,F), size = 1e5, T)
yes = rep("a", 1e5)
no = rep("b", 1e5)

microbenchmark(ifelse(test, yes, no), ifelseC(test, yes, no))
## Unit: milliseconds
##                    expr    min     lq median     uq   max neval
##   ifelse(test, yes, no) 57.313 58.763 59.626 72.435 87.92   100
##  ifelseC(test, yes, no)  1.747  1.837  1.926  2.749 29.56   100
test = sample(c(T,F), size = 1e5, T)
yes = rep(1L, 1e5)
no = rep(2L, 1e5)

microbenchmark(ifelse(test, yes, no), ifelseC(test, yes, no))
## Unit: microseconds
##                    expr     min      lq  median      uq   max neval
##   ifelse(test, yes, no) 30747.6 31868.5 32274.8 32829.0 59412   100
##  ifelseC(test, yes, no)   453.7   548.9   581.5   646.2 27575   100
test = sample(c(T,F), size = 1e5, T)
yes = rep(T, 1e5)
no = rep(F, 1e5)

microbenchmark(ifelse(test, yes, no), ifelseC(test, yes, no))
## Unit: microseconds
##                    expr     min      lq  median      uq   max neval
##   ifelse(test, yes, no) 29331.2 31167.3 31719.7 32455.3 60589   100
##  ifelseC(test, yes, no)   460.1   537.1   566.8   640.7 27118   100

Comparing ifelse with C++ for loop with ifs

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I currently am reading a bit about using Rcpp and its potential for speeding up R. I found one unexpected example in the lecture from Hadley Wickham:

require(Rcpp)
signR <- function(x) {
  if (x > 0) {
    1
  } else if (x == 0) {
    0
  } else {
    -1
  }
}

cppFunction('int signC(int x) {
  if (x > 0) {
    return 1;
  } else if (x == 0) {
    return 0;
  } else {
    return -1;
  }
}')

require(microbenchmark)
microbenchmark(signC(rnorm(1)), signR(rnorm(1)),times = 1e5)

## Unit: microseconds
##             expr   min    lq median   uq  max neval
##  signC(rnorm(1)) 2.832 3.186  3.540 3.54 4130 1e+05
##  signR(rnorm(1)) 2.478 3.186  3.186 3.54 2641 1e+05

As expected, the two versions perform nearly identical. Now for the surprise: I changed the scalar version of signC into a vectorized version:

library(Rcpp)

cppFunction('IntegerVector signCVec(NumericVector x){
int n = x.size();
IntegerVector out(n);
for(int i = 0; i < n; i++){
            if(x[i] > 0 ){
out[i] = 1;
            } else if(x[i] == 0){
out[i] = 0;
            } else {
out[i] = -1;
            }
}
return out;
}

            ')

signRVec <- function(x) {
  ifelse(x > 0,1, ifelse(x == 0,0,-1))
}

Now I would have expected the two functions also to be rather similar in execution, but see for yourself:

x = rnorm(1e6)

microbenchmark(signCVec(x), signRVec(x),times = 10)

## Unit: milliseconds
##         expr    min      lq  median      uq     max neval
##  signCVec(x)   8.07   8.103   8.311   8.761   8.952    10
##  signRVec(x) 571.91 581.988 607.664 620.322 743.546    10

Wow: A 60-odd-times reduction using Rcpp.

Der Effekt, wenn man am Höhepunkt Aktien kauft

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Bei mir hat heute wieder mal der Boulevard-Indikator ausgeschlagen, also die Erkenntnis, dass man sich von Aktien verabschieden sollte, wenn in der Boulevardpresse zur Investition in Aktien aufgerufen wird. Ein Beispiel hierfür sei folgender Artikel vom Manager Magazin:

Der Dax notiert bei knapp 10.000 Punkten. Höchste Zeit, sich von einigen Aktien-Irrtümern zu verabschieden. Zum Beispiel davon, dass man Aktien nur kaufen sollte, wenn sie billig sind.

Um diese Aussage zu überprüfen, sollen folgende Strategien miteinander verglichen werden:
1. Die Buy-High-Strategie: Es wird im Abstand von 400 Handelstagen, also ca. 2 Jahren, am höhchsten Punkt des DAX gekauft, und nach 10 Jahren verkauft. Die Renditen der einzelnen Trades werden gemittelt, und stellen den Ertrag der Strategie dar.
2. Die Buy-Low-Strategie: Es wird im Abstand von 400 Handelstagen, also ca. 2 Jahren, am niedrigsten Punkt des DAX gekauft, und nach 10 Jahren verkauft. Die Renditen der einzelnen Trades werden gemittelt, und stellen den Ertrag der Strategie dar.

Wenn man sich den Verlauf des DAX anschaut, bekomme ich erste Zweifel,dass die erste Strategie überlegen sein könnte.

## [1] "GDAXI"

plot of chunk unnamed-chunk-1

Zunächst identifizieren wir die Einstiegs- und Ausstiegs-Tage für die beiden Strategien

seq_times = seq(from= 1, to = nrow(GDAXI)-2000, by = 400)
index(GDAXI[seq_times])

##  [1] "1990-11-26" "1992-07-10" "1994-02-09" "1995-09-12" "1997-04-18"
##  [6] "1998-11-23" "2000-06-23" "2002-01-23" "2003-08-21" "2005-03-16"

high_points = low_points =numeric(length(seq_times)-1)

for(point in 2:length(seq_times)){
  high_points[point-1] = seq_times[point-1] + which.max(GDAXI[(seq_times[point-1]):seq_times[point],4]) - 1
  low_points[point-1] = seq_times[point-1] + which.min(GDAXI[(seq_times[point-1]):seq_times[point],4]) - 1
}


high_points_exit = pmin(high_points + 2000, nrow(GDAXI)) 
low_points_exit = pmin(low_points + 2000, nrow(GDAXI)) 

data.frame(high_points = index(GDAXI[high_points]),
           high_points_exit = index(GDAXI[high_points_exit]),
           low_points = index(GDAXI[low_points]),
           low_points_exit = index(GDAXI[low_points_exit])
           )

##   high_points high_points_exit low_points low_points_exit
## 1  1992-05-25       2000-05-11 1991-01-16      1999-01-12
## 2  1994-01-03       2001-12-10 1992-10-06      2000-09-19
## 3  1995-09-06       2003-08-15 1995-03-28      2003-03-11
## 4  1997-03-11       2005-02-08 1995-10-27      2003-10-06
## 5  1998-07-20       2006-06-01 1997-04-22      2005-03-18
## 6  2000-03-07       2008-01-21 1998-12-14      2006-10-26
## 7  2000-07-20       2008-06-04 2001-09-21      2009-08-03
## 8  2002-03-19       2010-01-26 2003-03-12      2011-01-11
## 9  2005-03-07       2012-12-28 2003-09-30      2011-07-28

Anschliessend berechnen wir die Renditen und deren Durchschnitt

high_returns = log(as.numeric(GDAXI[high_points_exit,4]))-log(as.numeric(GDAXI[high_points,4]))
low_returns = log(as.numeric(GDAXI[low_points_exit,4]))/log(as.numeric(GDAXI[low_points,4]))

mean(high_returns)

## [1] 0.3453371

mean(low_returns)

## [1] 1.095384

Wie man auch grafisch sieht, bietet die Strategie, im Tiefpunkt zu investieren relativ verlässliche Renditen von > 100 Prozent auf den 10-Jahres-Horizont, während die Strategie, am Höhepunkt zu investieren, eine sehr gemischte Performance aufweisst.

plot of chunk unnamed-chunk-4

Man kann natürlich einwänden, dass man ja nie weiss, wann der Höhe- oder Tiefpunkt erreicht ist. Daher wird zum Vergleich das Ergebnis dargestellt, wenn man jeweils am mittleren Tag des 400-Tage-Fensters einkauft.

seq_mean = round((seq_times[-length(seq_times)]+seq_times[-1])/2,0)
seq_mean_exit = pmin(seq_mean+2000, nrow(GDAXI))
mean_returns = log(as.numeric(GDAXI[seq_mean_exit,4]))-log(as.numeric(GDAXI[seq_mean,4]))

mean(high_returns)

## [1] 0.3453371

mean(low_returns)

## [1] 1.095384

mean(mean_returns)

## [1] 0.5344595

Das Ergebnis dieser Strategie ähnelt eher dem der Investition am Höhepunkt, kann aber im Durchschnitt eine höhere Rendite erzielen.
plot of chunk unnamed-chunk-6