Alternatives to the Kelly Criterion

This article discusses some alternatives to the Kelly Criterion for position sizing. We will cover the concepts of target volatility, risk parity, and the Sharpe ratio.

Given the limitations of the Kelly Criterion, many practitioners use alternative methods for position sizing. In this article, we will discuss some of the most popular alternatives to the Kelly Criterion.

Target Volatility

Target volatility is a position sizing method that aims to maintain a constant level of volatility for the portfolio. The basic idea is to adjust the leverage of the portfolio in response to changes in the volatility of the underlying assets. When volatility is high, the leverage is reduced, and when volatility is low, the leverage is increased.

The formula for the leverage in a target volatility strategy is:

$f = \frac{\sigma_{target}}{\sigma_{portfolio}}$

Where:

• f is the leverage
• $\sigma_{target}$ is the target volatility
• $\sigma_{portfolio}$ is the current volatility of the portfolio

Risk Parity

Risk parity is a portfolio allocation method that aims to allocate capital to different assets in such a way that each asset contributes equally to the overall risk of the portfolio. The basic idea is to allocate more capital to low-risk assets and less capital to high-risk assets.

The formula for the allocation to each asset in a risk parity portfolio is:

$w_i = \frac{1/\sigma_i}{\sum_{j=1}^{N} 1/\sigma_j}$

Where:

• $w_i$ is the weight of asset i
• $\sigma_i$ is the volatility of asset i
• N is the number of assets in the portfolio

The Sharpe Ratio

The Sharpe ratio is a measure of risk-adjusted return. It is the ratio of the expected excess return of an asset to its volatility. The Sharpe ratio can be used to rank different assets and to allocate capital to the assets with the highest Sharpe ratios.

The formula for the Sharpe ratio is:

$S = \frac{\mu}{\sigma}$

Where:

• S is the Sharpe ratio
• $\mu$ is the expected excess return
• $\sigma$ is the volatility

Comparison of the Methods

The following table compares the Kelly Criterion, target volatility, risk parity, and the Sharpe ratio.

Conclusion

There are a number of alternatives to the Kelly Criterion for position sizing. The best method for a particular trader will depend on their individual goals and risk tolerance. By understanding the different methods, traders can make more informed decisions about how to size their positions. In the next article, we will provide a case study of a leverage optimization strategy.