Welcome to our next installment on all things options math and probabilities. Today we’ll discuss Option Alpha’s Alpha metric, or the anticipated return on risk per trade.

We’ll dive into what Alpha is, how it’s calculated, and how it came to be. We’ll study its accuracy and usefulness as an options trading tool and explore its power in the context of Trade Ideas – trading technology only available at Option Alpha.

## What is Alpha in Trading?

In the traditional financial lexicon, Alpha (usually denoted as the lowercase Greek, α) is used to gauge an investment strategy’s ability to outperform the market or a designated benchmark.

Essentially, Alpha represents the excess returns generated by an asset, portfolio, or trading strategy over a given time period, above and beyond what can be produced by simply investing in the market directly by buying the index. The objective for any investor or trader is often termed "finding Alpha" or "generating Alpha," which means identifying opportunities that provide a return above the risk-adjusted market average.

In algorithmic and systematic trading, the quest for Alpha becomes a computational and quantitative endeavor. Trading algorithms are rigorously tested over diverse market conditions to evaluate their capability to generate Alpha. Here, the focus is on employing statistical models, machine learning techniques, and other algorithmic strategies to scrutinize market data and execute trades.

"Finding Alpha" in this context is not merely limited to identifying profitable trades; it extends to optimizing the trading strategy for transaction costs, slippage, and market impact. Algorithmic strategies often rely on high-frequency trading and other automated techniques to exploit minuscule price discrepancies or market inefficiencies that can generate Alpha. However, given the speed at which modern markets operate and adapt, Alpha in algorithmic trading may be ephemeral, requiring constant strategy updates and recalibration.

## What does Alpha mean at Option Alpha?

In the framework of Option Alpha's Trade Ideas technology, Alpha emerges as a more nuanced metric designed to offer an anticipatory measure of the return on risk per trade. The concept of Alpha is a natural evolution that begins with the idea of theoretical Reward/Risk and its subsequent realized Return on Risk (RoR). It follows that if we know the *expected* average reward over a large number of trades, we can compare that value to the maximum potential loss as well. And thus we arrive at Alpha, or normalized Expected Value (EV). The mathematical representation of Alpha is:

\[\text{Alpha} = \frac{\text{EV}}{\text{Max Loss}}\]

Here, EV signifies the Expected Value of the trade, while Max Loss indicates the maximum loss that the trade could incur.

EV provides a dollar-valued measure of the average expected return of a trade, but this dollar value lacks context when compared to other trades with different risk profiles.

This is where Alpha comes into play. By taking the Expected Value and dividing it by the Max Loss, we normalize the metric, making it possible to compare trades with different risk profiles on a one-to-one basis. Alpha, in essence, is EV that has been normalized, much like the Reward/Risk ratio.

It serves as a composite metric that provides traders with a forward-looking evaluation of a trade's potential profitability, considering both the prospective returns and the associated risks. This makes Alpha an invaluable tool for comparing the risk-adjusted profitability of various trading strategies.

## Market Makers, Pricing Models, and the Spread

Market makers play a crucial role in the liquidity and efficiency of options markets. They are obligated to provide buy and sell quotes for options contracts to ensure that traders can enter or exit positions at any time. To do so, they employ intricate pricing models. These models take into account various factors such as the underlying asset price, volatility, time to expiration, interest rates, and dividends to generate what they consider to be a "fair" market price for an option contract.

### Skimming the Spread as a Revenue Model

The primary revenue model for market makers is the bid-ask spread, which is the difference between the price at which they are willing to buy an option (the bid) and the price at which they are willing to sell it (the ask). Market makers essentially "skim" this spread as their profit margin.

For example, if the bid price for an option is $1.00 and the ask price is $1.05, the market maker stands to make a $0.05 profit from every round-trip transaction (buying at $1.00 and selling at $1.05). Given that market makers engage in high-frequency trading and process thousands of transactions per second, even a narrow spread can result in substantial profits.

### The Unfair Advantage Over Retail Traders

This model places retail traders at an inherent disadvantage for several reasons:

1. **Information Asymmetry:** Market makers have access to more comprehensive and real-time market data, which enables them to adjust their pricing models continuously. This is in contrast to retail traders, who generally rely on delayed or less granular data.

2. **Computational Resources**: The computational power and sophisticated algorithms at the disposal of market makers far outstrip those available to the average retail trader, enabling more accurate and dynamic pricing models.

3. **Transaction Costs**: Retail traders incur a cost every time they cross the spread. These costs can accumulate and significantly erode profits over time.

4. **Speed:** Market makers often have their servers co-located with the exchange's infrastructure, giving them a speed advantage in both receiving market information and executing orders.

## The Strategic Advantage of Retail Traders: Choice and Market Inefficiency

While market makers maintain several advantages in terms of computational resources, speed, and information, retail traders possess a strategic edge that often goes unacknowledged: the power of choice. Unlike market makers, who are obligated to quote buy and sell prices and maintain liquidity in the market, retail traders have the discretionary ability to enter or exit trades as they deem fit. This flexibility affords them several unique advantages:

1. **Timing:** Retail traders can choose the timing of their trades, allowing them to act on market inefficiencies or discrepancies in option pricing that even the most sophisticated market-making algorithms may not immediately detect.

2. **Positive Expected Value:** By carefully analyzing the risk and reward of an options contract, retail traders can identify trades that offer a positive expected value. Unlike market makers, who aim for a risk-neutral portfolio and have to account for the bid-ask spread, retail traders can focus solely on trades that align with their market outlook and risk tolerance, aiming for a higher expected value.

3. **Low-Frequency, High-Quality Trades:** Market makers engage in high-frequency trading and are obligated to make markets continually, exposing them to a gamut of risks and forcing them to maintain a diversified portfolio. Retail traders, on the other hand, can engage in low-frequency, high-quality trades that offer a high Alpha ratio.

Market markets are not omniscient. While they do use sophisticated models, these models are not infallible, and they can't predict sudden macroeconomic news, geopolitical events, or shifts in market sentiment that can lead to option mispricing. A retail trader, who is not bound by the same quoting obligations, can capitalize on these inefficiencies.

Trade Ideas is the search for market inefficiencies, Alpha is the gauge. If we can demonstrate that Alpha does what it claims to do, then we, the patient and savvy traders, can engage in trading opportunities on our terms and only when it is most favorable to us.

If you knew the card count for each table on the blackjack floor before you sat down, would you ignore it? You wouldn’t, but only if you could trust that the count was correct in the first place.

We’ve already shown that EV is remarkably accurate when compared to the realized P/L of Trade Ideas in Trade Ideas Probability & Performance: Expected Value vs. Realized P/L.

Let’s find out if analyzing Alpha produces the same results.

## Methodology

To study Alpha, we used a very similar technique to our previous studies on raw expected value. We borrowed the “bucketing” technique – but this time we’re putting Alpha into 5% buckets, and instead of comparing it to raw P/L dollars, we compare it against the average Return on Risk.

Stated another way, if Alpha is the anticipated RoR per trade over many trades, then the realized RoR should match Alpha once the sample count is high enough. But Alpha is a rational number with potentially many decimal places. So instead of comparing identical Alpha trades to one another, we group them into a range or "buckets" of Alpha.

If the lower and upper bounds of the bucket are 5% and 10%, respectively, then we should expect the average of all Alpha values to be very close to 7.5%. If that is true and Alpha is a true representation of the anticipated RoR, then the realized RoR should also be 7.5%. We can plot this 1:1 relationship as the theoretically “perfect” RoR line.

We grouped all trades in our current Trade Ideas dataset into 5% buckets as a decimal percentage throughout the entire Alpha range, -1 to 1, with sample counts of how many trades were observed producing an Alpha value in that range.

We’ve been collecting Trade Ideas data each market day at 3:55 PM ET since mid-July 2023, and the database has grown to millions of trades. In this study, we sampled 960k already expired positions across 3 strategy types (short put spread, short call spread, and iron condors), 155 underlying symbols, with expirations out to 72 days, though most days to expiration fall within 1 - 45 DTE. We also skipped trades that crossed earnings or ex-dividend dates and assumed cash settlement to record partial profits and losses at expiration.

## Data Analysis

In Figure 1, we observe all data as we’ve defined above in our Methodology, without exclusion. It is fascinating to see how closely Alpha tracks where we expect the average realized RoR to be. Metaphorically speaking, this graph shows us the hidden blackjack tables’ counts, that only we at Option Alpha can see, are indeed accurate.

Out of curiosity, we also wanted to see if this observation held for both ETFs and equities independently.

Look what happens in Figure 2 when considering only the 30 ETFs in our dataset. We observe that Alpha is actually understating the anticipated RoR. In other words, Alpha seems to wield more power for ETFs as a predictor of return per trade.

Figure 3 shows us what happens if we limit our analysis to the remaining 125 stock symbols. The average RoR is definitely overstated in the positive Alpha domain. But don’t fret. Any RoR above the horizontal zero line technically means we’re still making money over time. It will be interesting to see if this trend continues to hold over many more occurrences or if it’s indicative of the current market environment.

Reading this, you may be thinking, “Great, I’ll just trade ETFs then!” You could. But as practitioners, we shouldn’t relish in nitpicking how these trade samples are filtered because we could endlessly filter the data to show exactly what we want.

We should instead care about the accuracy and balance of the broadest application of Alpha, and that’s exactly what Figure 1 shows us.

A balanced, targeted, and predictable RoR can only be achieved by trading both ETFs and equities.

## Conclusions

The flexibility to choose when to participate in the market provides retail traders with a unique set of advantages that can, under the right conditions, counterbalance the technological and informational advantages of market makers. By focusing on high-quality trades with a favorable Alpha, retail traders can, in fact, achieve positive expected values, even in a market landscape seemingly dominated by more resourceful participants.

The technology, information, and regulatory advantages that market makers (or other powerful participants) enjoy often make it an uneven playing field, raising ethical questions about fairness and access. Consequently, retail traders need to exercise caution and arm themselves with as much knowledge and as many analytical tools as possible to navigate this complex landscape.

The retail trader's strategic edge lies in the judicious exercise of choice, backed by powerful technology to meticulously analyze the favorability of a trade.

The development of Alpha represents not just a computational but also a conceptual evolution, aligning with Option Alpha’s commitment to providing a transparent, mathematically robust, and empirically validated framework for options trading.

Over almost 1 million trades, Alpha proves to be scarily accurate at anticipating RoR. We also observed that Alpha on ETFs tends to be slightly understated, while Alpha on stocks tends to be slightly overstated. But in practice, in order to achieve the RoR we anticipate, we can’t artificially limit ourselves to one or the other, we need to trade both.