Cap return model

Extracted Attributes

• Purpose

  To manage venture capital funding while maintaining a nonprofit mission

• Mechanism

  Limits investor returns to a predetermined multiple, directing surplus to a nonprofit

• Primary User

  OpenAI

• Corporate Structure

  Capped-profit entity (Nonprofit to For-profit Conversion)

• Investment Strategy Alignment

  Power law (investing strategy)

Timeline

• The All-In Podcast (Episode 147) discusses OpenAI's use of the cap return model in the context of its corporate governance and nonprofit to for-profit conversion. (Source: Document f1f8a42e-2cea-4c01-807a-ca2f99837b2e)

  2023-09-29

Capital asset pricing model

In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cost of equity capital is determined only by beta. Despite its failing numerous empirical tests, and the existence of more modern approaches to asset pricing and portfolio selection (such as arbitrage pricing theory and Merton's portfolio problem), the CAPM still remains popular due to its simplicity and utility in a variety of situations.

Web Search Results

• Capital asset pricing model - Wikipedia

  Wikipedia The Free Encyclopedia ## Contents # Capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta "Beta (finance)") (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. [...] | Component | Equation / Derivation | Description & Logic | --- | Reward-to-Risk Ratio | : E ( R i ) − R f β i = E ( R m ) − R f {\displaystyle {\frac {E(R\_{i})-R\_{f}}{\beta \_{i}}}=E(R\_{m})-R\_{f}} {\displaystyle {\frac {E(R_{i})-R_{f}}{\beta _{i}}}=E(R_{m})-R_{f}} | Shows that the risk premium per unit of beta is constant for all assets in the market. | | Standard CAPM | : E ( R i ) = R f + β i ( E ( R m ) − R f ) {\displaystyle E(R\_{i})=R\_{f}+\beta \_{i}(E(R\_{m})-R\_{f})} {\displaystyle E(R_{i})=R_{f}+\beta _{i}(E(R_{m})-R_{f})} | Obtained by rearranging the reward-to-risk equation to solve for E ( R i ) {\displaystyle E(R\_{i})} {\displaystyle E(R_{i})}. This is the primary model for determining the required return of an asset | [...] | Black CAPM | : E ( R i ) = E ( R z ) + β i ( E ( R m ) − E ( R z ) ) {\displaystyle E(R\_{i})=E(R\_{z})+\beta \_{i}(E(R\_{m})-E(R\_{z}))} {\displaystyle E(R_{i})=E(R_{z})+\beta _{i}(E(R_{m})-E(R_{z}))} | A version for restricted borrowing; replaces R f {\displaystyle R\_{f}} {\displaystyle R_{f}} with the return of a zero-beta portfolio ( E ( R z ) {\displaystyle E(R\_{z})} {\displaystyle E(R_{z})}). |

• [PDF] The Capital Asset Pricing Model: Theory and Evidence - Dartmouth

  One implication of the expected return equation of the three-factor model is that the intercept i in the time-series regression, Rit  Rft
  i  iMRMt  Rft  isSMBt  ihHMLt  it, is zero for all assets i. Using this criterion, Fama and French (1993, 1996) find that the model captures much of the variation in average return for portfolios formed on size, book-to-market equity and other price ratios that cause problems for the CAPM. Fama and French (1998) show that an international version of the model performs better than an international CAPM in describing average returns on portfolios formed on scaled price variables for stocks in 13 major markets. [...] When there is risk-free borrowing and lending, the expected return on assets that are uncorrelated with the market return, E(RZM), must equal the risk-free rate, Rf. The relation between expected return and beta then becomes the familiar Sharpe-Lintner CAPM equation, Sharpe-Lintner CAPM ERi
  Rf  ERM  Rf]iM, i
  1, . . . , N. In words, the expected return on any asset i is the risk-free interest rate, Rf, plus a risk premium, which is the asset’s market beta, iM, times the premium per unit of beta risk, E(RM)  Rf. Unrestricted risk-free borrowing and lending is an unrealistic assumption. [...] The last step in the development of the Sharpe-Lintner model is to use the assumption of risk-free borrowing and lending to nail down E(RZM), the expected return on zero-beta assets. A risky asset’s return is uncorrelated with the market return—its beta is zero—when the average of the asset’s covariances with the returns on other assets just offsets the variance of the asset’s return. Such a risky asset is riskless in the market portfolio in the sense that it contributes nothing to the variance of the market return.

• Capital Asset Pricing Model (CAPM) | Formula + Calculator

  ## How Does Capital Asset Pricing Model Work? The capital asset pricing model (CAPM) is a fundamental method in corporate finance to determine the required rate of return on an equity investment given the coinciding risk profile. In short, the CAPM establishes the relationship between the risk and expected return on an equity security based on three underlying variables: 1. Risk-Free Rate (rf) 2. Beta (β) of the Underlying Security 3. Equity Risk Premium (ERP) However, the discount rate concept must be comprehended to understand the core components of the capital asset pricing model (CAPM) theory. [...] ## What is CAPM? The Capital Asset Pricing Model (CAPM) estimates the expected return on an investment based on the perceived systematic risk. The cost of equity—the required rate of return for equity holders—is calculated using the CAPM. Generating [...] If plotted on a chart, the capital asset pricing model (CAPM) depicts the relationship between the expected return and trade-off with regard to risk. The CAPM graph implies the expected returns (i.e. the y-axis) rise in tandem as more risk is undertaken by the investor (i.e. the x-axis), and vice versa. Note: The market beta is equal to 1.0 here. Capital Asset Pricing Model Graph (CAPM) ## Refining CAPM Analysis with AI

• The Capital Asset Pricing Model and Your Investment Decisions

  5 min read #### Key Takeaways For investors who want to know what return to expect for a given level of risk, the capital asset pricing model (CAPM) can come in handy. The CAPM is one tool often used across the financial industry to determine whether a stock is fairly valued, and it also plays a key role in financial modeling and asset valuation. The average investor can benefit from CAPM in important ways: understanding risk and return, establishing realistic expectations, and comparing investments. Let’s say you’re sitting down to decide between a couple of different investments. You’d rather put your capital in just one, instead of spreading it out among the group, and you feel equally confident in all of them. [...] How to decide? One tool might be the capital asset pricing model (CAPM), which measures the expected return of an investment relative to the risk assumed. In theory, an investment’s expected return is directly proportional to its risk. The riskier the investment, the higher a return the investor expects to make. Now, a lot of investment risk is managed through diversification, the art and science of putting different investments together to balance each other’s risk out. When one asset class or sector is declining, another, non-correlated one, may likely be ascending. [...] But not all risk can be diversified away, because some risk is inherent in the market itself. Factors like interest rates, exchange rates, geopolitical events, and recessions affect the market as a whole, albeit not evenly.1 The CAPM uses the risk-free rate, the asset’s beta, and the historical market return to describe a return on investment that accounts for the risk the investor has taken on. The investor can then decide whether they think that return is likely over their intended time frame. ### Understanding the Capital Asset Pricing Model Let’s dig into the elements that go into the model.

• CAPM formula | Capital asset pricing model - Intuit

  Expected Return = 2.5 + 6.6 Expected Return = 9.1% This means that your investment or asset will see a return of 9.1% annually. Since these base numbers change over time, regularly reviewing and recalculating these figures is essential for the most accurate information. ## Applications and considerations for the CAPM The CAPM model is one of many accounting formulas that has various use cases: [...] ## CAPM formula components The capital asset pricing model (CAPM) formula calculates an investment’s expected return using three main components: risk-free rate, beta, and market risk premium, resulting in the expected return. [...] By Marshall Hargrave Published on December 18, 2025 What is the CAPM formula? The capital asset pricing model (CAPM) formula is a model that calculates the expected rate of return on an investment. Using the formula you can calculate your expected return: Expected return = Rf + (β \ MRP). Knowing how to make the right investments is key to growing a business. It can help expand product offerings, penetrate new markets, and attract investors who are willing to play the long game. The CAPM formula can help you figure out how much money you expect to make on your investment. This will help you decide if you should take the risk or not. Learn more about what makes up the CAPM formula and how to best leverage it for your business decisions. ## CAPM formula components