Expected Value

We encourage all readers to apply the following principles with all investment-related activities, be it trading strategy, fund / investment performance etc.

In a zero-sum game, strategies act as proxies for the battle between the smartest, peak-performing, and highest-paid individuals in the world. Although markets can feel isolating when working with just an execution platform and a monitor, make no mistake: each tick of movement on the screen represents millions of dollars deployed by the best and brightest in the field. With Formula-One-like disciplined execution and R&D budgets in the realm of eight figures, uninformed participants are left light-years behind professional traders in the financial capitals of the world. How does one compete with these market-moving giants? How does one compare strategies objectively? And moreover, what is considered an excellent strategy? The answer lies in Expected Value.

What is Expected Value?

Expected Value, or EV, tells us the average return a strategy is likely to produce over its lifetime on a trade by trade basis. Here’s the basic formula:

Where:

• EV = Expected Value

• win% = Percentage of profitable trades

• RR = Profit per unit of risk (Risk-Reward ratio)

• loss% = Percentage of unprofitable trades

• R = Standard unit of risk

Generally, the higher the EV, the better the profit potential. Each of these components adds insight into how a strategy works - something often overlooked by traders and investors (we’ll dive deeper into this below).

Basic Prerequisites

Before exploring the ‘sexy’ elements of the topic, we need to cover a few essentials. The saying “garbage in, garbage out” highlights that no matter how good the analysis is, using poor data will lead to poor results. The same is true with EV calculations. Since markets are always changing, we need to ensure we’re using quality data for EV calculations by:

1. Ensuring a big enough sample size of trades;

2. Using reliable market data;

3. Applying consistent execution rules.

We’ll go deeper into robustness principles in future newsletters. For now, a minimum of 150 trades over two years is a good standard for short-term strategies. Testing with three samples of 50 trades (our team calls this “non-consecutive sample testing”) provides a better estimate of performance. Why three samples? To prevent strategies from being too tailored to a specific market condition—a problem called curve-fitting. Lastly, make sure all trades follow the same entry, exit, signal, time, and risk criteria to avoid biased results.

Warning: Don’t skip these three steps.

Strategy Archetypes

Most strategies focus on three elements: trade frequency, risk-reward, and win rate. Usually, two of the three elements are prioritised (unfortunately, there is no free lunch prioritising all three). With that said, for most, sacrificing frequency by prioritising risk-reward and win rate comes at the expense of high exposure

The Consistency Approach - High Win Rate & Adequate Frequency

A high win rate leads to low-variance, or steady returns over time. This approach is often used by newer traders and investors to build confidence and to reduce stress. Consistency-focused strategies are simple to execute, require little maintenance, and work across many markets. For high-net-worth individuals and family offices, consistency is key seeing that their goals often lend themselves to stable income as opposed to outperforming the S&P 500.

However, the tradeoff with consistency is lower returns. Since these strategies are simpler, accuracy is sacrificed. As such, risk models tend to focus on gradually increasing position size as the strategy proves effective to stimulate performance. These strategies typically achieve win rates of 65%-85% with a risk reward between 0.5 and 1.5. Here’s an EV example of a common strategy in this realm - take note that the average return per trade lower than the risk of the trade, or less than 1:

(70% x 1.2) - (30% x 1) = 0.54R

The High-Performance Approach - High Risk Reward & Adequate Frequency

At Apex Capital and the Athena fund, we specialise in high-performance strategies. Here, win rate is relaxed in favour of higher risk-reward. Given win rates can’t exceed 100%, marginal reduction in win rates lead to exponential growth in risk-reward. These strategies are often suited to experienced traders and sophisticated investors like hedge funds and proprietary trading firms, as they can be more challenging to execute and often require proprietary techniques to create and maintain. These strategies often have win rates between 25%-65%, with risk rewards ranging from 1.5 to as high as 10 (sometimes even 30).

(65% x 1) - (35% x 1) = 1.65R

With this approach, we can see that marginal reductions in win rate can lead to exponential increases in performance - note that the average return is larger than the risk of the trade, or larger than 1. Risk models for high-performance strategies focus on exposure reduction, as these strategies are generally more sensitive to changing market conditions.

Benchmarking Expected Value Strategies: The Good, The Bad, and The Risky

Each strategy type has its own set of risks. Consistent strategies risk underperformance, while high-performance strategies can face larger drawdowns if not carefully managed. Ultimately, risk tolerance varies depending on the type of investor. Hedge funds face higher pressure to outperform than family offices, for example. At Apex, we use both types of strategies, setting the following benchmarks: consistent strategies must achieve an EV of at least 0.8R to be viable, while high-performance strategies need an EV of 1.45R or greater without compromising win rates below 50%.

As a final note, strategies tend to see a 30% decline in performance from backtesting to live execution on average. Ensure that there is enough margin within strategy EV during the testing phase to cover the decline in performance as a rule of thumb.

Key Takeaways

• Expected Value (EV) represents the average return of a strategy on a per-trade basis over time. The higher the EV, the stronger the strategy’s profit potential.

• Before calculating a strategy’s EV, ensure that data quality is high by using an adequate sample size, reliable historical data, and consistent execution variables. A checklist can help keep backtesting thorough. Think, ’garbage in, garbage out’.

• Strategies typically fall into one of two categories: consistency-oriented or performance-oriented. Consistent strategies prioritise win rate and trade frequency, while high-performance strategies focus on risk-reward and frequency. Each strategy type has specific risk model requirements.

• Risk varies in a professional context. Hedge funds face a higher risk of underperformance than family offices, seeing that the latter seeks consistency.

• Our benchmarks: consistent strategies must reach an EV of 0.8R, while high-performance strategies need an EV of 1.45R or more.

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