Uncertainty Pricing: The Hidden Cost of Volatility Drag in Options Pricing

The Hidden Cost of Volatility Drag

As investors, we're always on the lookout for ways to maximize our returns while minimizing risk. One strategy that has been proven time and again is the Kelly Criterion. This simple yet powerful approach can help you grow your capital as fast as possible, but it's essential to understand its limitations.

The Problem with Most Investors

Most investors underestimate the importance of expected log portfolio return when making investment decisions. In fact, research has shown that a portfolio strategy that maximizes this expected value will outperform any other strategy over the long run, despite being inferior in terms of accumulated wealth. However, the proof requires that asset returns be IID (Independent and Identically Distributed), which is notoriously difficult to obtain in reality.

The Kelly Criterion

The Kelly Criterion is a straightforward equation: f = (bp - q)/b, where b is the bet's payout, p is your probability of winning, and q is your probability of losing. To apply this formula precisely, you need accurate knowledge about the probability distribution of asset returns. Without it, even with optimal leverage, you'll experience unacceptable drawdowns.

Practical Considerations

While the Kelly Criterion can be a useful tool for traders, it's essential to remember that applying it exactly as stated would require an unrealistic estimate of your probability of winning. To balance volatility in earnings and rate of growth, you should aim for 7% or 8% if you're unsure about your edge.

An Alternative Approach

Thierry Michel suggests using R = mu^2 / 2*sigma^2 as a more general alternative to the Kelly Criterion. This approach is useful when dealing with asset returns that are heavily skewed, but it's not tailored to writing options or other strategies with complex outcome distributions.

Conclusion

The Kelly Criterion offers a powerful tool for investors looking to maximize their returns while minimizing risk. However, its limitations should be carefully considered before applying it exactly as stated. By understanding the underlying assumptions and practical considerations, you can use this strategy to balance volatility in earnings and rate of growth.