Kelly Criterion Allocator

Optimal Bitcoin position sizing using the continuous-time Kelly formula

Formula:f* = (mu - r_f) / sigma²|mu = expected return, r_f = risk-free rate, sigma = volatility

Scenario

Expected Annual Return

Typical: 15-80%

Risk-Free Rate

Current T-bill ~4.5%

Annualized Volatility

BTC historical: 50-90%

Portfolio Size

Risk Profile

Allocation Results

Raw Kelly f* = 80.9%

Fraction	Allocation	$ Amount	Growth Rate	Max Drawdown	Years to 10x	P(Ruin)
Full Kelly (100%)	80.9%	$808.9k	22.90%	70.3%	10.1y	28.81%
Half Kelly (50%)Recommended	40.4%	$404.4k	18.30%	45.5%	12.6y	1.87%
Quarter Kelly (25%)	20.2%	$202.2k	12.55%	26.2%	18.3y	<0.01%
Eighth Kelly (12.5%)	10.1%	$101.1k	8.81%	14.1%	26.1y	<0.01%
Conservative (10% cap)	10.0%	$100.0k	8.77%	13.9%	26.3y	<0.01%

Allocation Across Scenarios

Simulate:

Monte Carlo Simulation

10,000 paths · 10-year horizon · Half Kelly

10th Percentile

$13.0k

-99% return

Median

$36.3k

-96% return

90th Percentile

$89.3k

-91% return

Sensitivity Analysis

Full Kelly allocation (%) varying expected return and volatility by ±10%

Return \ Vol	65%	70%	75%	80%	85%
40%	84%	72%	63%	55%	49%
45%	96%	83%	72%	63%	56%
50%	108%	93%	81%	71%	63%
55%	120%	103%	90%	79%	70%
60%	131%	113%	99%	87%	77%

Recommendation & Guidance

Based on your moderate risk profile, consider Half Kelly (50%)

This means allocating 40.4% of your portfolio ($404.4k) to Bitcoin, with an expected growth rate of 18.3% per year.

Why full Kelly is almost never recommended for Bitcoin

The Kelly Criterion assumes you know the true expected return and volatility with certainty. In reality, BTC return estimates are highly uncertain, and BTC exhibits fat tails (extreme moves beyond what a normal distribution predicts). Estimation error alone can turn an "optimal" allocation into a path to ruin. Academic research consistently shows that half-Kelly or less delivers ~75% of the growth rate with dramatically less variance and drawdown risk.

Practical rules of thumb

• Most practitioners use half-Kelly or quarter-Kelly as their upper bound.
• Never allocate more than 50% of net worth to a single volatile asset, regardless of what the formula says.
• If your calculated f* is negative, the expected return doesn't justify the risk — consider zero allocation.
• Re-run this analysis quarterly as your return/volatility assumptions change.

Rebalancing

Kelly is a continuous-time formula that assumes constant rebalancing. In practice, rebalance monthly or quarterly to stay near your target allocation. More frequent rebalancing incurs transaction costs; less frequent rebalancing increases drift from the optimal fraction. A good rule: rebalance when your actual allocation drifts more than 5% from target.