The Fuck Up Ratio: A Measure of Unexpected Risk in Financial Assets and Its Application to Portfolio Allocation

Abstract

This thesis introduces the "Fuck Up Ratio" (FUR), a novel metric designed to quantify the potential for unexpected adverse price movements—or "fuck ups"—in financial assets, particularly cryptocurrencies. By integrating market capitalization (MC) as a proxy for liquidity and the Average True Range percentage (ATR%) as a measure of observed volatility, FUR highlights latent risks in lower-cap assets that may appear deceptively stable. We derive the formula, provide empirical examples using Bitcoin (BTC) and Shiba Inu (SHIB), and extend it to portfolio allocation via inverse FUR weighting. This approach draws parallels to established risk management strategies like inverse volatility weighting and risk parity, offering a practical tool for risk-adjusted slicing of asset baskets. Data as of October 19, 2025.

Introduction

In financial markets, volatility is a double-edged sword: it drives potential returns but also amplifies the risk of sudden, detrimental price swings—what we colloquially term "fuck ups." Traditional volatility measures, such as standard deviation or the Average True Range (ATR), capture observed price fluctuations but often overlook structural vulnerabilities tied to an asset's size and liquidity. Smaller market cap assets, despite sometimes exhibiting lower nominal volatility, can experience outsized impacts from modest capital flows due to thinner order books. This thesis formalizes this intuition through the Fuck Up Ratio (FUR), a score that penalizes low liquidity and low observed volatility, revealing hidden risks.

The motivation stems from the observation that lower-cap assets may have "higher dollar per price move potential" but also elevated unexpected downside. We propose FUR as a proxy for this risk and demonstrate its use in portfolio construction, inverting it to allocate smaller weights to higher-risk.

Literature Review

Volatility Measurement: Average True Range (ATR)

The Average True Range (ATR), developed by J. Welles Wilder, is a technical indicator that quantifies market volatility by averaging the true range over a specified period, typically 14 days. The true range is the greatest of the current high minus low, the absolute value of the high minus previous close, or the low minus previous close, making ATR sensitive to gaps and large moves. Expressed as a percentage (ATR%), it normalizes volatility across assets of different prices, aiding comparisons. ATR is widely used for setting stop-losses and position sizing, as higher values indicate greater price variability.

Market Capitalization and Asset Volatility

Market capitalization (MC) significantly influences volatility, with an inverse relationship observed: larger-cap assets tend to exhibit lower volatility due to greater liquidity and institutional participation. Empirical studies show that small-cap stocks or assets are more susceptible to volatility spikes from trading volume changes, as modest inflows/outflows can disproportionately affect prices. This effect is pronounced in cryptocurrencies, where low MC correlates with higher tail risks.

Risk-Based Portfolio Allocation

Risk parity strategies allocate capital to equalize risk contributions across assets, often using leverage to balance volatile and stable components. This contrasts with market-cap weighting and aims for true diversification by focusing on risk rather than dollar amounts. A related approach, inverse volatility weighting, assigns weights proportional to the inverse of an asset's volatility, reducing exposure to high-vol assets to minimize portfolio drawdowns. Such methods have shown improved Sharpe ratios and lower maximum drawdowns in backtests. FUR extends these by incorporating MC as a liquidity adjustment, addressing gaps in pure volatility-based models.

Methodology

Defining the Fuck Up Score

The Fuck Up Score for an asset is formulated as:

[ \text{FUR} = \frac{1}{\sqrt{\text{MC}} \times \sigma} ]

Where:

• (\text{MC}) is the market capitalization in USD.
• (\sigma = \frac{\text{ATR\%}}{100}) is the volatility in decimal form.

This structure inverts the product of a size factor ((\sqrt{\text{MC}})) and observed volatility ((\sigma)). The square root on MC draws from financial models where volatility scales inversely with the square root of liquidity or size, reflecting diffusion-like price impacts. Lower MC or lower (\sigma) increases FUR, capturing the intuition that small, seemingly stable assets harbor higher latent "fuck up" potential.

To compute:

1. Obtain ATR% over 14 periods.
2. Convert to (\sigma).
3. Calculate (\sqrt{\text{MC}}).
4. FUR = 1 / ((\sqrt{\text{MC}} \times \sigma)).

Fuck Up Ratio Between Assets

For two assets A and B, the ratio is:

[ \text{FUR Ratio (A/B)} = \frac{\text{FUR}_A}{\text{FUR}_B} = \sqrt{\frac{\text{MC}_B}{\text{MC}_A}} \times \frac{\sigma_B}{\sigma_A} ]

This simplifies comparisons without recomputing absolutes.

Portfolio Allocation Using Inverse FUR

To "slice" a portfolio, use inverse FUR weighting:

For asset (i) in a basket of (n) assets:

• Inverse FUR(_i) = 1 / FUR(_i)
• Total Inverse = (\sum_{i=1}^n) (1 / FUR(_i))
• Weight (w_i) = (1 / FUR(_i)) / Total Inverse

This mirrors inverse volatility strategies but adjusts for MC, allocating less to high-FUR assets.

Empirical Illustration

Using data from October 19, 2025 (MC from CoinGecko, ATR% from Polygon API):

FUR Ratio (SHIB/BTC) ≈ 8.67, indicating SHIB's fuck up potential is 8.67 times BTC's, driven by its ~367x smaller MC despite higher observed volatility.

For a two-asset portfolio:

This allocation reduces exposure to SHIB's risks while maintaining diversification.

Conclusion

The Fuck Up Ratio provides a concise, intuitive metric for assessing hidden risks in assets, particularly those with low market caps. By integrating ATR% and MC, it extends traditional volatility measures and supports risk-aware portfolio slicing via inverse weighting. Future work could incorporate actual liquidity metrics (e.g., trading volume) or test backperformance against benchmarks like risk parity portfolios. This framework empowers investors to mitigate unexpected "fuck ups" in volatile markets.

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