Position sizing, expected return, and portfolio results - There is imprecision in trader language

"I only take trades that have an expected return to risk of 3:1 and my average risk position .5 to 1.5% based on my conviction. I expect to generate mid-teens returns with a 10% vol..... bla, bla, bla...." 

This is pretty standard language for many traders describing their strategy, but some of it does not make sense when you look through the numbers, or at least a careful look at the numbers will tell you what has to happen for this all to be true. 

This is where simple cases of imprecise language can lead to confusion. Investors may have problems with understanding what a trader means if all the assumptions concerning trading are not well-defined. Here are some questions that an investor may have when hearing the above phrases.

• If you only take 3:1 return to risk trades and your volatility is 10%, then does this mean your return should be 30%? 
• The idea of risk and return for a trade have to be made precise.
• If you only generate a 10% return in reality, does this mean that 2/3rds of your trades scratched with no gain?
• An ex ante 3:1 trade is not the same as ex post returns. 
• Does it mean that your 3:1 trades were actually only 1:1 trades? 
• The translation from trades to portfolio returns is not always easy to describe.
• How many losing trades did you have? 
• 3:1 trades only give you half the story. Investors need to know the outcomes. 
• How many winners were there of those original trades?
• If ex ante you expect 3:1 trades, what is your success ex post?
• I might prefer 2:1 if your success rate is better.
• If your average risk position is between .5 and 1.5%, you have to come up with a lot of good 3:1 trades to make money. How many "3-baggers" are out there?
• How many good ideas can one trader come up with in one year if you will only take 1% risk per trade?
• Assume you take 1% positions; if you take 100 position, you will need a fair number of successful trades to hit anything close to a 10% return. How much are you willing to lose for those 3:1 trades?
• How long will you wait for those 3:1 trades to be realized? 
• 3:1 trade over different time frames makes a huge difference in returns. 

Using the fundamental law of active management, what does it mean when you say you take 3:1 trades? How many trades do you actually have to take? The fundamental law states that the information ratio is equal to the information coefficient or selection skill times the square root of the number of investment opportunities. Efficiency, the information ratio, is equal to skill times breath. A trader needs a lot of independent trades to make money independent of a benchmark.

Obviously, this original comment can be decomposed and carefully studied to show the potential returns under a number of alternatives. Our important point is to focus on the ambiguity and imprecision of language when these terms are used. Don't take what is said for granted.