There’s this old saying, often applied to strategic games as well as warfare, that “**the best defense is a good offense.**” Another variation of this is that “the only good defense is an *active* defense.” Let’s transform it a bit: the best of “defensive strategies” has an effectively “aggressive (offensive) component.”

What we’re trying to say here is not that the two–defense and offense–are linked (which they are), but that one can easily shift to the other when the situation calls for it.

As it relates to trading, a “defensive” posture can be tweaked to take on an “aggressive” function. In other words, “risk management” is as much an aggressive concept as it is a defensive strategy. You manage risk to calibrate profit potential, not just to avoid losses. Here’s an example that explores this notion.

## Risk Management Strategy Squeezes Profit From Losing Trades

Imagine two traders–Trader Joe and Trade Giuseppe.

**Similarities**

Both traders have a starting balance of $10,000. Both are trading the Dow Jones futures. Both are following the same trading signals.

**Differences**

Trader Joe trades a *fixed position* of one contract, which ticks at $5 per point. Trader Giuseppe uses a *2% risk strategy,* so he trades both the YM and the MYM to fine-tune his position size.

**The trades were losers but Trader Giuseppe ended the day with a profit**

There were a total of five trades–all of which, when combined, **ended in a loss **of -130 points. Though Trader Joe ended the day down only -$650, Trader Giuseppe went home with +$1,068 profit.

*How was that even possible?*

How could two traders following the same signals for the same instrument have such a disparity in profit and loss? The answer, which you can guess, is risk management. It’s not that Trader Giuseppe* lost less* due to his risk management strategy, it’s that his strategy allowed him to *win more*. In short, risk management was not just a defensive strategy but an aggressive one as well. Let’s break it down to see how both traders ended up with their results.

## Breaking Down the Trades

Position | Stop Loss | Profit Target | Point P/L |

1 contract | -65 | 100 | -65 |

1 contract | -75 | 100 | -75 |

1 contract | -10 | 100 | 100 |

1 contract | -75 | 100 | -75 |

1 contract | -15 | 100 | -15 |

-130 |

The total system loss amounted to -130 points. Quite a big loser.

The exit rules in this system are simple: close out at the maximum profit target or allow your position to get stopped out (at the stop loss).

Now, here’s where the interesting results begin–**how Trader Joe ends up with a relatively sizable loss, when Trader Giotto generates a win.** Let’s start with Trader Joe.

## Trader Joe’s Losing Strategy

Position | Stop Loss | Profit Target | Point P/L | $ P/L |

1 contract | -65 | 100 | -65 | -$325 |

1 contract | -75 | 100 | -75 | -$375 |

1 contract | -10 | 100 | 100 | $500 |

1 contract | -75 | 100 | -75 | -$375 |

1 contract | -15 | 100 | -15 | -$75 |

-130 | -$650 |

Trading a fixed amount, in this case one contract, will give you a result that matches a systems PL once adjusted for value. In this case, Joe’s one contract has a $5 per tick value. So a loss of -130 points amounts to (-130*5 = -325) a -$650 loss.

How did Trader Giotto’s results end up so different and on the opposite side of the PL spectrum? All he did was use a simple 2% risk management strategy–namely, don’t risk more than 2% on any single trade. Let’s dig deeper into how this happened.

## Trader Giotto’s Aggressive Risk Management Strategy

*Note: at this point, we’re about to get very detailed. But when managing risk, position sizing can become a very detailed endeavor–one that requires you to constantly check your balance against % risk. So, let’s go over it blow by blow.*

- To come up with 2% risk, Giotto multiplies his trading account size with 0.02 (Account x 2%).
- To come up with his max dollar-per-tick value, he divides his max risk by his stop loss (e.g. look at the first trade–$200 divided by 65 = $3.07 maximum dollar-per-tick value).
- He then selects the number of contracts to match the exact amount of his dollar-per-tick (or slightly below it).

Let’s walk through each trade.

Position | Balance | Stop Loss | Profit Target | Point P/L | $ P/L |

6 MYM | 10000 | -65 | 100 | -65 | -$200 |

5MYM | $9,800 | -75 | 100 | -75 | -$196 |

3 YM + 8 MYM | $9,604 | -10 | 100 | 100 | $1,921 |

6 MYM | 11525 | -75 | 100 | -75 | -$230 |

3 YM | 11294 | -15 | 100 | -15 | -$225 |

-130 | $1,069 |

**Trade 1**

**Balance:** Giotto begins the day with $10,000.

**2% Risk:** Amounts to $200.

**Stop loss:** 65 points.

**Maximum dollar-per-tick:** He can’t risk more than $3.00 per tick ($3 x -65 = -$200).

**Contract size:** To match the ideal dollar-per-tick value, Giotto needs to trade no more than 6 Micro Emini Dow Jones contracts (MYM) each with a tick value of $0.50.

**Result:** He got stopped out with a -$200 loss (-65 x $0.50 = -$200).

**Trade 2**

**Balance:** $9,800 left.

**2% Risk: **$196.00

**Stop loss:** 75 points

**Maximum dollar-per-tick:** Risk no more than $2.61 per tick (round that down to $2.50).

**Contract size:** 5 MYM contracts maximum (5 contracts x $0.50 = $2.50 per tick).

**Result:** PL of -$196.00

**Trade 3**

**Balance:** Now, Giotto’s account is down to $9,604.

**2% Risk:** $192 is his two percent loss limit.

**Stop loss:** This stop loss is 10 points away–meaning he can have a much larger position.

**Maximum dollar-per-tick:** He can risk as much as $19.21 per tick ($192 divided by 10 = $19.20)

**Contract size:** 3 YM + 8 MYM contracts ($15 + $4 – $19 per tick).

**Result:** A winner, this one yielded a return of $1,921–a big winner. Note that Joe, in the previous trade, only made $500.

**Trade 4**

**Balance:** Giotto’s account is now up to $11,525.

**2% Risk: **Maximum risk has increased to $230.

**Stop loss:** 75 points.

**Maximum dollar-per-tick:** $3.07 (rounded to $3.00).

**Contract size:** 6 MYM contracts.

**Result:** Stopped out with a loss of -$230.

**Trade 5**

**Balance:** Giotto’s account value is down to $11,294.

**2% Risk:$226.**

**Stop loss:** This one is 15 points away.

**Maximum dollar-per-tick:** Because of the small stop loss, to lose 2%, he would have to risk $15.00 per tick.

**Contract size:** 3 YM contracts.

**Result:** Another loser, this ended with a return of -$225.

In the end, Trader Giotto gained $1,069, or a 10.7% profit, as compared with Trader Joe’s -6.5% loss. But what a world of a difference.

## Same Win Rate, Different Profit Factor

In a previous post, we discussed the concept of win rate vs profit factor. Win rate is the frequency of wins, often expressed as a percentage. The profit factor is the ratio of wins to losses.

**The System:**

- The system’s
**win rate**for these last five trades was poor–a 20% win rate, and 80% rate of loss. Granted, these were just five trades. But still, it was a loser. - The system’s
**profit factor**was poor–0.43-to-1, or inversely, -2.31-to-1 (loss factor).

**Trader Joe:**

- Joe’s win rate and profit factor
*mirrored the system’s*, as he used a fixed allocation for each trade.

**Trader Giotto:**

- Giotto’s win rate was the same as the system’s and the same as Joe’s.
- But his profit factor was a surprising 2.25-to-1. For every one unit lost, he gained 2.25 units in profit–the exact opposite of Joe’s.

*To reiterate, the difference between Joe’s loss and Giotto’s win was that the latter used a risk management strategy to guide his position sizing. And the difference turned out to be night and day.*

Since we’re discussing win rate and profit factor, let’s talk about both for a moment.

In our previous post, we mentioned that a system with a high win rate can still be a losing system, especially if its negative returns dwarf its profits. Similarly, a system with a high profit factor can still end up a loser, if it loses frequently enough to begin generating negative returns.

## At What Point Will Win Rate Interfere With Profit Factor and Vice Versa?

Let’s imagine a trading system that had a win rate of only 30% but it made double what it lost.

- If its average win was $100, it’s average loss was $50, can you expect it to generate positive returns? The answer is no, you can’t.
- But what if it made an average of $120 and an average loss of $50. Does it have a
*positive trading expectancy*? Yes, it does.

Let’s play with this idea some more. Let’s take the first example, wherein a system has an average gain of $100 and an average loss of $50.

- At its current 30% win rate, it’s a loser.
- What if its win rate were 32% instead? It’s still a loser.
- What if its win rate was slightly higher, at 35%?. In this case, it’s potentially a big winner.

How did we just figure this out? Simple, we calculated the *trading expectancy.*

## Introducing Trading Expectancy

Trading expectancy is a calculation you can use to theoretically predict the favorability of a trading system–whether winning or losing–based on its* win rate* and its* average wins and losses* (almost like profit factor).

It can help answer the following questions: “How low can the win rate go before the system begins losing; and how low can the profit factor go before it begins losing?”. Likewise, it inversely tells you how high the win rate or profit factor must be for a system to be profitable.

Trading expectancy sets a limit at zero. If a system’s trading expectancy is below zero, it’s a loser. If it’s above zero, it’s a potential winner.

Here’s how to calculate it:

**(Win % x Average Win) – (Loss % x Average Loss) = Trading Expectancy**

With this calculation, you no longer need to worry whether you’re focusing too much on a system’s win rate or profit factor. All you have to do is plug in the numbers, and you’ll be able to forecast whether a system will likely “make” or “take” your money.

Let’s illustrate this concept with a simple example of a coin toss.

## Trading Expectancy of a Coin Toss and a Weighted Coin Toss

Someone presents you with a coin toss bet. If the coin shows heads, you win a dollar; tails, you lose a dollar. You know right off the bat, it’s a 50/50 bet. How might it look in terms of trading expectancy?

Win rate = 50%; Loss rate = 50%

Average win = $1.00; Average loss = -$1.00.

Plug in the numbers: (0.50 x 1) – (0.50 x 1) = 0 trading expectancy. Over time, it’s neither a winning nor a losing bet. You do, however, lose time, effort, and you pay an opportunity cost; missing out on a more favorable gambit.

**But what if that same person presented a slight variation–a weighted coin toss: **

- The coin is weighted so that it tends to land “heads” 75% of the time…however…
- A heads win will return $1 and a loss of $2.50
- A tails win will return $2.50 and a loss of $1.

Would you bet heads or tails?

The winning bet would still be heads, with a trading expectancy of 0.125–not the biggest winner, it’s still the only bet that won’t lose over time.

## Using Trading Expectancy to Analyze Trades

If you understood the examples above, you can easily transfer this to the domain of trading performance.

Here are three systems, each presented with their Win Rates and average wins and losses:

System 1 wins only 20% of the time, returns an average of $425, loses an average of $100.

System 2 wins 95% of the time, returns an average of $50, loses an average of $975.

System 3 wins 65% of the time, returns $200 on average, loses $375 on average.

Which systems can you expect to win and lose over time? Without calculating its trading expectancy, it would be difficult (if not nearly impossible) to *objectively* determine that system 1 is the only winner, as you can see below.

System | Win % | Av Win | Loss % | Av Loss | Expectancy |

1 | 0.2 | 425 | 0.8 | 100 | 5 |

2 | 0.95 | 50 | 0.05 | 975 | -1.25 |

3 | 0.65 | 200 | 0.35 | 375 | -1.25 |

The important takeaway here is that win rate and profit factor, despite being important metrics, can’t give you a big picture view of a system’s performance. Trading expectancy helps complete the picture, *unless the underlying conditions of the market change*.

Although there are many factors that go into “risk management,” we’re hopefully covering a few important and practical ideas that can help your trading. There’s one other that we’d like to go over. We touched upon this in our previous post, but let’s expound upon it now, since many traders don’t always get the big picture behind this very basic concept.

## The Single and Largest Risk That Most Traders Miss

Let’s imagine three really-bad traders who aimed to make upwards of 200% return in the markets–this is a hypothetical figure.

Instead, they all lost 100% of their trading account. Let’s say this amounted to $100,000. That’s quite a dismal performance.

That’s where the similarities end. There’s a big difference between the three.

- Regarding the
**first trader**, $100k was his entire life savings, all distributed to other market participants. A tragic story indeed, as he truly faced financial ruin (or more years in the workforce to make up for what he had lost). - Regarding the
**second trader**, $100k was only 20% of his $500k total investable capital. He kept the rest in cash. Not a “loser,” but not quite a winner either. He put his money to work for him, and it came back empty-handed. The rest of it just slowly lost purchasing power due to inflation. - Regarding the
**third trader**, the $100k lost was also 20% of her total capital, but she invested the rest in stocks, bonds, real estate, and other ventures. She’s the only “bad” trader among the three who ended up with more than just her starting capital.

The moral of the story: often, your biggest risk as a trader is “you.” There may be no “safe” trades or investments, but there are certainly “safer” trading and investment practices.

Let’s step back and take a closer look at the third trader, the one who ended up a “winner” despite losing big in her trading endeavors.

She didn’t have great trading skills, apparently. Perhaps, she didn’t have very sophisticated investment skills either. But she held true to a couple of principles:

Her trading expectations had a reward-to-risk scenario of 2-to-1.* The potential payoff was much greater than the loss*. But because the risk was high, she *allocated only 20% of her investable funds*, nothing more. Most importantly, she knew that she had very little in the way of “sophisticated” market knowledge, making it impossible for her to “predict” market and economic trends. So, what did she do? She allocated her capital evenly across the board, *diversifying and expanding her “return sources”* while hedging one economic sector against another. All this while attempting to trade the markets.

The idea of positive vs negative payoff is an important one here when it comes to managing risk.** Ideally, you’d speculate on opportunities whose positive payoff outweighs the negative payoffs. **That’s a simple principle that doesn’t take sophisticated knowledge to put into practice.

To demonstrate this further, and its importance to risk management, let’s talk about a very ancient story about risk–about NOT having sophisticated knowledge, but having solid knowledge on scanning and assessing the odds. This is a story about Thales, one of the Seven Sages of Greece, and to whom Aristotle referred as the first “philosopher,” who not only made a killing in the olive oil market but was one of the first recorded “monopolists” as a direct result of his speculations.

## How to Make a Killing in a Market You Don’t Fully Understand Using Only Basic Risk Management Principles

The story goes like this. One harvest season, Thales speculated that the olive harvest was going to be bountiful. So, he rented all of the olive oil presses in his area and surrounding areas *at a discount*. The weather later that season turned out to be a real boon for the harvest. As Thales owned all of the presses, he rented them out to farmers, became wealthy, and proved to his fellow citizens that he could be a very good businessman should he choose to continue as one.

So, what does this story have to do with risk management? It’s subtle, but it underlies every aspect of the story.

**Success Attributable to Knowledge?**

Aristotle attributes Thales’ fortune to the latter’s knowledge of astronomy. Since Thales was skilled in reading the stars, he was able to predict a good harvest. Thales’ success, according to Aristotle, was based on “knowing” things (astronomy) that most others didn’t understand. Do you buy his explanation? Such knowledge can help, but it’s no surefire guarantee of success–as nobody can predict the future.

**Success Attributable to Risk Management?**

But what if Thales’ astronomical knowledge wasn’t advanced enough to predict the outcome of an entire harvest season? In other words, what if Thales had far less knowledge than Aristotle claimed? *What if given the discount in press rentals, Thales knew that the potential return far surpassed the potential loss?* And what if Thales was able to afford that loss, should he be wrong? In that case, Thales made a fortune by simply managing his risk-taking a “bet” on an opportunity that presented a much higher upside (outcome unknown) than downside (outcome known and fixed…the cost of the rental).

The takeaway here is that by sticking to this rule of thumb–exploiting opportunities with significantly higher upside than downside–you can gain the upper hand on most speculative endeavors, never approaching the risk of ruin.

## The Bottom Line

Risk management is more than just a defensive strategy; it can be used to aggressively pursue opportunities while (secondarily) keeping risks under control. It can also help you better identify the conditions in which trading opportunities or systems may prove more or less favorable in terms of profit potential. Last but not least, we hopefully demonstrated how risk management principles can either enhance or “best” trading knowledge no matter how simple or sophisticated. When you engage the markets, keep in mind the saying we opened with “the best defense is a good offense.” No successful pursuit is sound without a risk management plan that adequately supports it. Remember, you can trade aggressively and safely at the same time.

Thanks Rolf. This is a fantastic article that I will be frequently revisiting to make sure that I never forget to manage risk in every trade to calibrate its profit potential and not just to minimize its loss (which is my natural fearful tendency).