# Asset Pricing

Comprehensive articles on how to price financial assets. Understand the main pillars of Asset Pricing, including choice theory, portfolio theory, equilibrium pricing, and arbitrage pricing.

## Second Derivative of Utility Function: Why Is It Negative?

The second derivative of a utility function is negative to reflect risk aversion and decreasing marginal utility. A negative second derivative implies a concave function, which illustrates that the more money you have, the less satisfaction you get from additional…

## Quadratic Utility Function (Mean-Variance Preferences)

A quadratic utility function is a type of utility function used in economics and finance to describe a person’s preferences over different outcomes. In other words, how people make choices under uncertainty. The quadratic utility has special importance in finance…

## Arrow-Debreu Securities: Definition, Pricing, Example

This post is a brief and somewhat incomplete look at Arrow-Debreu pricing theory, based on my lecture notes. Hope it helps! What is an Arrow-Debreu Security Arrow-Debreu securities (or state-contingent claims, or simply state claims) are financial instruments that pay…

## How to Calculate Certainty Equivalent from Utility Function

The certainty equivalent of a lottery is the amount you would accept to receive to pass on the possibility of playing said lottery. In other words, it’s the maximum amount a person is willing to pay for a gamble. You…

## Why Are Low Coupon Bonds More Volatile? (Full Answer)

Low coupon bonds are more volatile because the face value received at the maturity date as a lump sum is a big chunk of the total bond’s value. Interest payments along the way are not as significant. This means changes…

## CARA Utility Function: Definition, Formula, Is It Realistic?

The Constant Absolute Risk Aversion (CARA) utility function is a measure of risk aversion. It is characterized by a constant absolute risk aversion coefficient, meaning risk aversion is the same for all levels of wealth. This is unrealistic, as wealthy…

## Understanding the Opposite of Risk Averse (in 4 Easy Steps)

The opposite of risk aversion is risk-seeking behavior. Risk-seeking investors are willing to put up with higher risk for a higher chance of better returns. Risk averse investors on the other hand, prefer a lower risk investment such as government…

## Optimal Risky Portfolio: 5 Things You Must Understand

The optimal risky portfolio (also called tangency portfolio) is a portfolio composed of risky assets in which the amount you invest in each asset will make it so the portfolio gives you the highest possible return for a given level…

## What is CRRA Utility Function: Explained in 6 Easy Steps

In this post, you’ll learn what is CRRA utility function (also called power utility function). We’ll go over 6 things you must know to understand the CRRA formula and the CRRA utility function properties. CRRA stands for Constant Relative Risk…

## Understanding Asset Pricing: How to Value Future Cash Flows

An asset is nothing else than the right to future cash flows, whether they are interest payments from bonds, dividend payments from stocks, insurance payments, or capital gains from investments. To price an asset, all you need to do is…

## Valuing Risky Cash Flows: What is Utility Theory in Finance?

Utility theory in finance measures how much benefit you, as an investor, get from a given asset, and how that will affect your decision to buy that asset over another. We know supply and demand determine the price of an…