Free lesson · Prediction foundations

From probability to a decision price

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A probability is a belief about an outcome; a trading decision compares the value of that belief with the ask and all costs.

Under risk neutrality and no discounting, a $1 binary claim has expected payout equal to its probability in dollars. This converts a probability estimate into a break-even purchase price under a specific utility assumption.

A price also reflects risk preferences, capital constraints and market access. A model disagreement is a research hypothesis, not evidence that other traders are wrong. Include uncertainty in the forecast and use the appropriate event horizon.

Apply it in a strategy

• Translate probability forecasts into cost-aware candidate decisions at a defined horizon.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Uncalibrated probabilities and correlated forecast errors can overwhelm a small modeled edge.

Research deliverable

Build and explain a from probability to a decision price worksheet. Translate probability forecasts into cost-aware candidate decisions at a defined horizon.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def expected_profit(probability,ask,cost,shares):
    if not 0<=probability<=1 or not 0<=ask<=1 or min(cost,shares)<0: raise ValueError("Invalid forecast or cost")
    return shares*(probability-ask-cost)

print(expected_profit(.66,.62,.01,100))