More than one tenor can sing Rigoletto - at the same time

This mandrigal-like performance of Guiseppe Verdi's La Donne Mobile is interesting because the operatic solo (aria) replaced mandrigals in the early 17th century. Three great tenors here include Jose Carreras, Placido Domingo and Luciano Pavoratti. If you look into the lyrics, it's basically about some guy being flummoxed, perplexed and confused about women.

More than one way to play the violin

It's not just the musical score that can be appreciated, but how someone plays the notes. The musical piece below is Niccolo Paganini's Moto Perpetuo. My favorite performances include those by Michael Rabin, Yehudi Menuhin, Itzhak Perlman and Jascha Heifetz. When you play really, really well, you get the title of 'Virtuoso'. Heifetz is my favorite virtuoso and too bad I couldn't find a video of him performing this piece. You can view him actually playing Paganini's Caprice No. 24. But for our musical selection you'll just have to look at his picture and listen.

More than one way to play a sheet of music

It's interesting that Bach's Cello Suite (Prelude to Suite #1 below) sounds so different depending on who's playing it. Most have probably heard the YoYo Ma rendition in some chick flick. Other cellists you may want to listen to include Mischa Maisky and Mstislav Rostropovich. I've chosen the Pau Casals version mostly because he brought this obscure piece of music back into the public. He found the sheet music in a shop in Barcelona in 1890 and practiced playing it for 12 years before performing it publicly. He was forced into exile in France because of voicing some opinions against Spain's Franco government. That same government promised to amputate his arms if he returned.

A custom Optimization Profile using R

While the backtest gives us a historical perspective on the viability of a trade system, the optimization process illumines how stout, sturdy, strapping and hardy (yes, I know how to research synonyms for robust) our trade system is across a variation of parameter sets. What does this all mean? Well, if a 10/30 moving average crossover system yields spectacular returns, then we'd like to rest assured that the 9/30 or the 10/31 parameter sets are fairly similar in their results. This is a test to weed out lucky systems that have absolutely no predictive value or money-making potential. Most backtesting systems will come with a handy little optimizer. The art of choosing what range to test over is a topic for another day so let's keep it simple for now and pick simple ranges with about equal number of variations per parameter. Using our moving crossover system example, let's test the fast moving average (10-day) between the values of 3 and 18 in steps of 3 for a total of six possible values, and the slow moving average (30-day) between the values of 20 and 45 in steps of 5 for a total of six possible values. To makes things really exciting, let's add a third parameter. How about a Bollinger Band around the slow moving average that confirms the crossover signal? Great. Vary that between .3 and .9 standard deviations in steps of .2 for a total of four possible values.

Programming a custom Backtest Profile in R

One of the many issues with systems trading is trying to make sense of the vast amounts of data you accumulate with the backtest of a system. Historical backtesting is the first step in testing your trading idea. If it is a trading idea that ought to work across many different markets, then you need to test it on many different markets to see how it performs. Yes, you are looking to see how .... robust (I said it) ... your trading idea is in the crucible of historical data. It's easy to get lost in the data and that's why I'm embarking on creating a custom Backtest Profile Report, dubbed version 1.0. I've chosen to create this profile using the R statistical package, which is offered for free to those who elect to use it.