# Utilities and Benchmark Analysis

### Description

A collection and description of utility
and benchmark functions for the analysis
of financial markets. The collection
provides a set of functions for the
computation of returns, for the display
of price charts, and for benchmark
measurements.

The functions are:

`ohlcPlot` | Plots open--high--low--close bar charts, |

`sharpeRatio` | Computes Sharpe Ratio, |

`sterlingRatio` | Computes Sterling Ratio, |

`maxDrawDown` | Computes maximum drawdown. |

### Usage

1 2 3 4 5 6 7 8 9 | ```
ohlcPlot(x, xlim = NULL, ylim = NULL, xlab = "Time", ylab, col = par("col"),
bg = par("bg"), axes = TRUE, frame.plot = axes, ann = par("ann"),
main = NULL, date = c("calendar", "julian"), format = "%Y-%m-%d",
origin = "1899-12-30", ...)
sharpeRatio(x, r = 0, scale = sqrt(250))
sterlingRatio(x)
maxDrawDown(x)
``` |

### Arguments

`date, format, origin` |
[ohlcPlot] - |

`r` |
[sharpeRatio] - |

`scale` |
[sharpeRatio] - |

`x` |
a numeric vector of prices.
For |

`xlim, ylim, xlab, ylab, col, bg, axes, frame.plot, ann, main` |
[ohlcPlot] - |

`...` |
[ohlcPlot] - |

### Details

**Open–High–Low–Close Chart:**

Within an open–high–low–close bar chart, each bar represents
price information for the time interval between the open and the close
price. The left tick for each bar indicates the open price for the
time interval. The right tick indicates the closing price for the time
interval. The vertical length of the bar represents the price range
for the time interval.
The time scale of `x`

must be in Julian dates (days since the
`origin`

).

`[tseries:plotOHLC]`

**Sharpe and Sterling Ratios:**

The Sharpe ratio is defined as a portfolio's mean return in excess of
the riskless return divided by the portfolio's standard deviation. In
finance the Sharpe Ratio represents a measure of the portfolio's
risk-adjusted (excess) return.
The Sterling ratio is defined as a portfolio's overall return divided
by the portfolio's maximum drawdown statistic. In finance the
Sterling Ratio represents a measure of the portfolio's risk-adjusted
return.

`[tseries:sharpe]`

**Maximum Drawdown:**

The maximum drawdown or maximum loss statistic is defined as the
maximum value drop after one of the peaks of `x`

. For financial
instruments the maximum drawdown represents the worst investment
loss for a buy–and–hold strategy invested in `x`

.

`[tseries:maxdrawdown]`

**Get Returns:**

The function computes the return series given a financial security
price series. The price series may be an object of class `numeric`

or a time series object. This includes objects of classes `"ts"`

,
`"its"`

and/or `"timeSeries"`

.

### Value

`ohlcPlot`

creates an Open–High–Low–Close chart.

`sharpeRatio`

`sterlingRatio`

return the Sharpe or Sterling ratio, a numeric value.

`maxDrawDown`

returns a list containing the following three components:
`maxDrawDown`

, double representing the max drawdown or max loss
statistic; `from`

, the index (or vector of indices) where the
maximum drawdown period starts; `to`

, the index (or vector of
indices) where the max drawdown period ends.

### Author(s)

Adrian Trapletti for the ohlcPlot,*Ratio and maxDrawDown functions,

Diethelm Wuertz for the Rmetrics **R**-port.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
## ohlcPlot -
# Plot OHLC for SP500
# ohlcPlot(x, ylab = "price", main = instrument)
## sharpeRatio -
# Sharpe Ratio for DAX and FTSE:
data(EuStockMarkets)
dax = log(EuStockMarkets[, "DAX"])
ftse = log(EuStockMarkets[, "FTSE"])
# Ratios:
sharpeRatio(dax)
sharpeRatio(ftse)
## maxDrawDown -
data(EuStockMarkets)
dax = log(EuStockMarkets[, "DAX"])
mdd = maxDrawDown(dax)
mdd
# Plot DAX:
plot(dax)
grid()
segments(time(dax)[mdd$from], dax[mdd$from],
time(dax)[mdd$to], dax[mdd$from])
segments(time(dax)[mdd$from], dax[mdd$to],
time(dax)[mdd$to], dax[mdd$to])
mid = time(dax)[(mdd$from + mdd$to)/2]
arrows(mid, dax[mdd$from], mid, dax[mdd$to], col = 2)
title(main = "DAX: Max Drawdown")
``` |