Financial Calculators

# CAPM Calculator

Use this CAPM calculator to explain the relationship between the expected return and the risk of security.

#### Capital Asset Pricing Model Calculator

#### Table of contents

◦CAPM Calculator |

◦Capital Asset Pricing Model (CAPM) |

◦Problems with the CAPM |

◦The CAPM & the Efficient Frontier |

◦The practical value of the CAPM |

## CAPM Calculator

The Capital Asset Pricing Model (CAPM) is used in finance to explain the relationship between the expected return and the risk of security. This Capital Asset Pricing Model Calculator (CAPM) can be used to calculate the expected return on a security. It uses the stock's beta, market return, and the risk-free rate.

## Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model, (CAPM), describes the relationship between systematic risks and expected return for assets, especially stocks.1 CAPM is used in finance to price risky securities and generate expected returns for assets given their capital cost and risk.

Investors expect to receive compensation for risk and the money value. The risk-free rate is part of the CAPM formula. It accounts for the time value. The investor takes on additional risk by using the other components of the CAPM formula.

The beta value of potential investments is a measure of how risky the investment will be to a portfolio similar to the market. A beta greater than one indicates that a stock is riskier than the market. A stock with a beta lower than one is assumed to reduce portfolio risk.

The market premium is the expected return from the market that exceeds the risk-free rate. This is multiplied by a stock's beta. The market risk premium and the stock's beta are then added. This should give investors the required returns and discount rates that they can use to determine the asset's value.

The CAPM formula evaluates whether a stock's risk and time value are comparable to its expected return.

## Problems with the CAPM

The CAPM formula is based on several assumptions that have been proven to be false. Two assumptions underpin modern financial theory: First, that securities markets are highly competitive and efficient (that's, information about companies is quickly and universally available and absorbed), and second, that these markets are dominated by rational, risk-averse investors who seek maximum satisfaction from their investments.

Despite these problems, the CAPM formula continues to be widely used. It is simple and allows easy comparisons between investment options.

Beta is included in the formula because it assumes that stock price volatility can be used to measure risk. Price movements in either direction are not equally dangerous. Because stock returns (and the risk associated with them) are not generally distributed, the look-back period used to determine stock volatility is not standard.

The CAPM assumes that the risk-free interest rate will not change over the discounting period. In the previous example, the interest rate on U.S. Treasury Bonds rose to 5% or 6 during the 10-year period. A rise in the risk-free rate could also increase the capital cost and make the stock more expensive.

The market portfolio used to calculate the market risk premium is a theoretical value only and cannot be bought or invested in as an option to stock. Investors will substitute the market most of the time using a major stock index like the S&P 500. This is an imperfect comparison.

The CAPM's assumption that future cash flows can easily be predicted for discounting is its most serious flaw. The CAPM wouldn't be needed if an investor could accurately predict the future return on a stock.

## The CAPM & the Efficient Frontier

An investor's ability to manage their risk by using the CAPM when building a portfolio is supposed to help. The following graph shows how an investor could use the CAPM in order to optimize their portfolio's return relative risk.

This graph illustrates how higher expected returns (y-axis), require greater risk (x-axis). Modern Portfolio Theory states that portfolios with a risk-free rate will have a higher expected return. A portfolio that is compatible with the Capital Market Line is superior to any other portfolio. However, at some point, it's possible to construct a theoretical portfolio using the CML that has the highest return for the risk taken.

Although the CML and efficient frontier are difficult concepts to understand, they illustrate an important concept for investors: investors must make a choice between higher return and greater risk. It is difficult to build a portfolio that meets the CML. Investors are more likely to take on too many risks in order to achieve additional returns.

The following chart shows two portfolios that were designed to follow the efficient frontier. Portfolio A is expected to return 8% per annum and has a 10% risk level or standard deviation. Portfolio B will return 10% per annum, but it has a 16% standard deviation. Portfolio B's risk rose faster than its expected returns.

The efficient frontier assumes the same assumptions as of the CAPM, and can only theoretically be calculated. A portfolio that existed on the efficient frontier would provide the highest return for the risk it takes. It is impossible to predict future returns so it is impossible for a portfolio to be on the efficient frontier.

The CAPM is a trade-off between return and risk. However, the efficient frontier graph can be modified to show the trade-off for individual assets. The following chart shows that the CML has been renamed the Security Market Line. Instead of the expected risk being shown on the x-axis the stock's beta is used. The illustration shows that beta is increasing from one to two and the expected return also increases.

The CAPM, SML, and SML establish a link between a stock's beta level and expected risk. Higher betas mean more risk, but portfolios of high beta stocks can exist on the CML where this trade-off is acceptable.

These assumptions about beta and market participants reduce the value of these models. Beta does not take into account the relative riskiness of stocks that are more volatile than the market and have a higher frequency of downside shocks, as compared to other stocks with a similar beta but that experience less price movement to the downside.

## The practical value of the CAPM

It might seem difficult to see how the CAPM could be of any use given the criticisms and assumptions it is based on in portfolio construction. The CAPM can still be useful in evaluating future expectations and comparing them.

Imagine an advisor proposing to add a stock to a portfolio at $100 per share. To justify the price, the advisor uses the CAPM with a 13% discount rate. This information can be compared to the past performance of the company and other peers by the advisor's investment manager to determine if 13% is reasonable.

Consider this: The performance of the peer group over the past few years was slightly better than 10%, while the stock has consistently underperformed with only 9% returns. An investment manager should not accept the recommendation of an advisor without a justification for the higher expected return.

Investors can also use concepts such as the efficient frontier and CAPM to assess their portfolio or individual stock performance relative to the rest. As an example, let's say that an investor's portfolio returned 10% per year over the past three years. However, this assumes that there has been a standard deviation (risk) of 10%. The market averages returned 10% over the past three years, with a risk level of 8%.

This observation could be used by the investor to review their portfolio and determine which holdings are not on the SML. This could help explain why the portfolio of an investor is not in line with the CML. Investors can identify holdings that are disproportionately affecting returns or increasing risk in the portfolio and make adjustments to increase returns.

To determine a security's fair value, the CAPM applies Modern Portfolio Theory principles. It is based on assumptions about investor behavior, risk and return distributions, and market fundamentals. These assumptions are not consistent with reality. The underlying concepts of CAPM, and the efficient frontier that it creates, can help investors better understand the relationship between expected reward and risk so they can make better decisions when adding securities to their portfolio.

Article author

Parmis Kazemi

Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

###### CAPM Calculator English

Published: Tue May 03 2022

In category Financial calculators

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