Why Stochastic Discount Factors Depend on Investor Utility

Summary

The document raises a foundational asset-pricing question: why risky-asset prices may depend on an investor’s preferences, and why the stochastic discount factor (SDF) is linked to those preferences. It frames the issue through the contrast between pricing under real-world probabilities and using a risk-neutral measure, noting that investors can differ in risk aversion.

The text does not provide the equation it references, an example, or an answer to its questions. It therefore identifies the conceptual issue rather than deriving the SDF or explaining how utility and marginal value across states determine prices. Readers should treat it as a prompt for understanding preference-based pricing, not as a self-contained account of the relationship or a worked valuation method.

Key ideas

• The document asks why risky-asset prices can vary with investor risk aversion.
• It connects investor preferences to the stochastic discount factor and risk-neutral pricing.
• No pricing equation, worked example, or explanation is provided in the text.
• The document frames a conceptual question rather than presenting a complete pricing method.

Tags

# Relationship between an Investor's utility function and Stochastic Discount Factor (SDF)


# Relationship between an Investor's utility function and Stochastic Discount Factor (SDF)












In real world, it is difficult to arrive at a single price for a risky asset since pricing of a risky asset would depend on the level of risk aversion of the investor. The following equation gives the reason to use risk neutral measure instead of real world measure.

My question is: Why does the pricing of an asset depend on the investor? Specifically, why does the SDF depend on the investor? An example would be great.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.