Investment management in three dimensions

How we use options and why they are a core part of any sophisticated investment process.

Investing with options is often seen as daunting, complex, and a second-order consideration for most investors. In this note, we aim to challenge that perception by presenting options from first principles – showing how they unlock the dimensions of time and probability, revealing a more complete picture of price and risk than the underlying alone. When understood this way, they become an essential and powerful tool for sophisticated investment management.

We can demonstrate this by showing how Fulcrum incorporates options into its investment process across four key areas:

• As a tool for providing information content about the expected path of underlying prices
• Expressing views and achieving upside asymmetric returns
• Implementing smart hedges
• As an independent alpha return stream

We explore each of these in the following analysis.

The information content of options

Option prices reflect the collective uncertainty about where underlying prices are likely to settle. Most managers maintain an underlying price-centric view, but in doing so, they overlook the additional dimensions of time and probability that are embedded in options. But it is precisely these dimensions that define the complete forward distribution of outcomes.

Figure 1 – Terminal distribution of 2026 Euro Stoxx 50 dividends on October 10th, 2025, showing key statistics.

For illustrative purposes, consider the European dividend market, where investors trade futures contracts on the total dividends paid by companies each year. From option prices on these contracts, we can reliably extract the implied distribution of future outcomes, which can be summarised through key statistics:

• Mean: The expected value of dividends. This coincides with the level implied by current futures prices. While this is the benchmark on which most investors focus, it represents only a slice of the distribution of outcomes.
• Median: The middle point of the distribution. It tells us what the “typical” dividend might be, which differs meaningfully from the mean in a left-tailed market like this.
• Mode: The single most likely outcome. This corresponds closely to where analyst and bottom-up surveys cluster.
• Percentiles (10th, 90th): These capture the tails of the distribution. On the downside, the 10th percentile reflects scenarios such as a recessionary dividend cut/default. On the upside, the 90th percentile reflects the chance of positive surprises in dividend payments.

Importantly, the distribution is left-tailed, meaning that large downside returns carry more weight than large upside returns. It is intuitive that puts are typically more expensive than calls in left-tailed markets like these: they embed compensation for this asymmetric risk.

“I can buy a dividend future today at 159 at a discount to the most probable value of 164 as a compensation for default risk”, is more complete than “I can buy dividends today at 159”. The information derived from the options market paints a more complete picture than just looking at the underlying prices alone.

The information content of options – The S&P 500 and its constituents

Figure 2 – Historical S&P 500 prices (blue) and forward price distributions implied from options on October 10th, 2025.

Another example of a left-tailed market is the S&P 500 index. Figure 2 expands on Figure 1 by showing historical prices alongside the implied distributions at multiple option expiry dates. Three points stand out:

• Uncertainty increases with time. The further out the expiry, the wider the distribution of possible outcomes.
• The mean (forward price) drifts upward due to expected interest rates being higher than dividend yields.
• There is a left skew at every expiry. The SPX implied distributions are persistently left-tailed, so the mean is pulled below both the median and the mode. Consequently, forward prices respond not only to changes in the most likely outcome but also to changes in the perception of risk.

We push this analysis further by looking at the largest six stocks in the S&P 500 by market cap.

Figure 3 – Historical single stock prices (blue) and forward price distributions implied from options on October 10th, 2025.

In contrast to the index, the skew is not uniform. For some distributions, such as Tesla (TSLA), there is a right skew with more weight on upside relative to downside returns. More generally, single stock distributions tend to be more symmetric, lacking the persistent left tail that characterises SPX.

Why this difference? The left tail of an equity index reflects the risk of systemic downturns, where many stocks fall together. Individual stocks, by contrast, reflect idiosyncratic risks, where surprises like earnings can dominate.

The information content of options – US Interest Rates

We can apply the same analysis to the interest rates market by extracting implied probabilities from the Secured Overnight Financing Rate (SOFR) options. Most market commentators tend to focus on expected rate cuts or increases by a certain date, which are derived from forward prices, the green line on Figure 4. Options allow us to go further.

Consider 2026: as of November 3^rd, 2025, the market expects roughly three cuts of 25bp each or 75bps in total. But the percentile bands reveal a much wider range of possible outcomes. At the 90th percentile, total cuts reach 150bps, and at the 10th percentile, we see a rate increase.

This range of outcomes highlights the uncertainty around short-term interest rates that most commentaries overlook. Moreover, Figure 4 reveals that the path of interest rates beyond two years is insignificant relative to the width of uncertainty around it.

Figure 4 – Historical FED fund rates (blue) and forward distributions implied from SOFR options on November 3rd, 2025.

Beyond presenting a more complete picture of price and risk, options are a powerful tool for expressing directional views. In the example above, an investor who believes interest rates will remain above current levels by the end of 2026 can use options to exploit the low probability the market currently assigns to this scenario, as low probabilities are associated with higher potential payout ratios relative to the premium paid.

Asymmetric upside returns

The asymmetry embedded in options allows managers to profit disproportionately when correct.

To illustrate this generally, we can simulate the performance of three manager styles with the same forecasting edge, a 53% hit ratio, in a hypothetical market with 20% annualised volatility over 1,000 randomly generated years of daily returns. In this Bernoulli trial, each manager operates under the following constraints:

• A long only manager who alternates between 100% and 0% exposure to the market
• A long/short manager who alternates between 100% and -100%
• An options manager who alternates between buying ‘at the money’ (ATM) call and put options*

*Option prices in this simulation include a premium above the theoretical 20% volatility to reflect real-world effects of higher transaction costs associated with trading options.

Table 1 – Simulation shows trading with options achieves asymmetric upside returns.

Results show the options manager achieves positively skewed returns (1.55) while the long only and long/short managers exhibit essentially no skew. Figure 5a illustrates the point. The blue bars show the distribution of returns from the long/short strategy, while the orange bars show the distribution of returns from the options strategy (scaled to show both strategies on an equal volatility footing). The options manager captures more asymmetric upside returns while losses to the downside are capped.

However, this advantage comes with an important caveat: forecasting volatility is critical. Figure 5b demonstrates that while a 53% hit rate provides a directional edge, the Sharpe ratio declines exponentially when managers systematically overpay for volatility. The compounding effect of consistently buying options when implied volatility (the width of the forward distribution) exceeds realized volatility eventually dominates their directional advantage. This is especially dangerous because options tend to trade at a premium to realized volatility and, with negative returns, positive skewness is ineffective.

Figure 5a – Distribution of returns from long/short and option managers with the same hit-ratio. Showing option managers with more upside skew and limited downside.

Figure 5b – While skew remains constant, the Sharpe ratio of option managers declines exponentially when realized volatility falls below implied volatility.

When volatility is forecasted correctly, however, the combination of directional skill and asymmetric payoffs from options has the potential to create a return profile that delivers a better outcome for investors.

Hedging

The asymmetric payoffs we’ve discussed extend naturally to hedging. In practice, many investors hold long positions that represent existing views, as in equity portfolios for example. While standard put options can provide downside protection, they often feel expensive in bull markets. More sophisticated structures can address this trade-off.

Lookback options illustrate this principle. Figure 6 shows how a lookback put would have performed during the Nasdaq’s dot-com bubble. Unlike a standard put with a fixed strike, a lookback put resets its strike to the highest price reached during its life. This creates an adaptive hedge that performs well in trending bull markets.

Figure 6 – Lookback options show their value hedging the Nasdaq through the dot-com bubble.

Trading distributions against each other

Options can also be traded without directional exposure to the underlying market. Revisiting Figure 3, where we showed different single stocks with non-uniform distributions, we can expand further by comparing these distributions and trading one against the other when dislocations are present.

Figure 7 – META and Adobe normalized prices with implied 10th-90th percentile bands. Despite comparable historical volatility, the options market implies higher future volatility and risk for Adobe.

When one distribution appears mispriced relative to another, whether comparing individual stocks or single names versus the index, options can capture relative value without outright market exposure.

Consider META and Adobe. Figure 7 shows their normalized price histories alongside their implied forward distributions. While both stocks have comparable historical volatility, Adobe’s options imply higher forward-looking volatility and risk.

Divergences like this often reflect technical flows rather than informed views. For example, structured products that systematically sell options for yield suppress implied volatility without regard to future realized volatility. When properly identified, this creates opportunities that can be exploited through relative value volatility and dispersion strategies.

Managers must assess whether the divergence reflects fundamental differences, such as upcoming earnings or other structural effects, rather than true relative mispricing. This requires both quantitative rigor and a deep understanding of market structure.

Common pitfalls and final thoughts

While the applications outlined so far are compelling, exploiting them effectively demands respect for the practical challenges inherent in options markets.

• Asymmetry is not free. On average, options trade above where the volatility of past returns would suggest. This gap, known as the volatility risk premium, is the price investors pay for convexity. Forecasting this premium and knowing when to avoid it and when to participate is important.
• Models are tools, not substitutes for market judgment. The behaviour of West Texas Intermediate options on oil prices during Spring 2020 illustrates this clearly. When crude prices turned negative with the sudden collapse in demand, traditional option pricing models failed. A deep understanding of the market structure from first principles is essential and over-reliance on models in unusual regimes can be dangerous.
• Option markets generate enormous amounts of data. This richness makes it easy to data-mine and overparameterize. Datamined trading models tend to fit history well but fail in live trading. The key is simplicity and generalisation.
• Option bid–ask spreads and execution costs can be significant. Compared to an equivalent forward or futures position, the effective trading cost of an option can be up to ten times higher. This means strategies must be selective and efficient; otherwise, transaction costs erode the benefits investors seek to capture from trading options.

Despite these challenges, when managed skillfully, options are a powerful and indispensable tool for sophisticated investment management. In Fulcrum’s Diversified Absolute Return strategy, we regularly use¹ options to achieve asymmetric returns and in the hedging of our portfolios. Our more focused ‘Equity Dispersion’ strategy, meanwhile, focuses on investing in options, seeking to exploit relative value opportunities between the volatility of individual stocks and broader indices.