# Capital Asset Pricing Model CAPM Vs ARBITRAGE PRICING THEORY APT

2023-11-01 18:49## Capital Asset Pricing Model CAPM Vs ARBITRAGE PRICING THEORY APT

# Capital Asset Pricing Model CAPM Vs ARBITRAGE PRICING THEORY APT

The advisor’s investment manager can take this information and compare it with the company’s past performance and its peers to see if a 13% return is a reasonable expectation. Assume in this example that the peer group’s performance over the last few years was a little better than 10% while this stock had consistently underperformed, with 9% returns. The investment manager shouldn’t take the advisor’s recommendation without some justification for the increased expected return. The CAPM and the SML make a connection between a stock’s beta and its expected risk. Beta is found by statistical analysis of individual, daily share price returns compared with the market’s daily returns over precisely the same period.

In this example the factor-based attribution analysis (Table 12.59) provides a similar picture as the Brinson-type analysis, which for the sake of comparison is given in Table 12.60. The difficulty in applying the APT model in practice results from the task of identifying those factors that cover the commonalities of the securities (and fulfill the model requirements, which will not be discussed in detail). The rule of no-arbitrage pricing states that an identical price will be obtained whichever way one chooses to analyse the bond. Therefore, such bonds pay a lower rate of interest, or yield, than bonds issued by less-established companies with unsure profitability and comparatively larger default risk.

APT provides an alternative approach to asset pricing that takes into account multiple factors influencing an asset’s return. Historical returns on securities are analyzed with linear regression analysis against the macroeconomic factor to estimate beta coefficients for the arbitrage pricing theory formula. The limitation of APT is that the theory does not suggest factors for a particular stock or asset (Bodie and Kane). The price of an oil company stock, like Royal Dutch Shell, will be more sensitive to factor like oil price changes compared to that of a pharma company stock.

- Other companies may have untraded debt or use complex sources of finance such as convertible bonds.
- CAPM and APT are two popular models that differ in their approach to measuring accuracy.
- Could be forecasted with the linear relationship of an asset’s expected returns and the macroeconomic elements that affect the asset’s risk.
- The main problem with APT, however, is that it tries to accurately measure the risk for all assets.
- If the business risk of the investment project is different to that of the investing organisation, the CAPM can be used to calculate a project-specific discount rate.
- It assumes that market action is less than always perfectly efficient, and therefore occasionally results in assets being mispriced – either overvalued or undervalued – for a brief period of time.

The main difference is that while CAPM is a single-factor model, the APT is a multi-factor model. In the CAPM, the only factor considered to explain the changes in the security prices and returns is the market risk. The CAPM has gained widespread use because it provides restrictions for investors’ portfolios and asset prices and returns that appear to be validated by data on a variety of securities.

## Re – The expected rate of return on the risky asset

Having determined that value, traders then look for slight deviations from the fair market price, and trade accordingly. While CAPM assumes that assets have a straightforward relationship, APT assumes a linear connection between risk factors. That means if there is no linear relationship, the models cannot accurately determine outcomes. Since the CAPM is a one-factor model and simpler to use, investors may want to use it to determine the expected theoretical appropriate rate of return rather than using APT, which requires users to quantify multiple factors.

- It provides a simpler way to estimate the expected return of an asset based on its beta coefficient.
- In the CAPM model, the expected return of an asset is a linear function of market risk, while in APT model, the expected return of an asset is a linear function of numerous unknown risk factors.
- Beta is found by statistical analysis of individual, daily share price returns compared with the market’s daily returns over precisely the same period.
- One of these is arbitrage pricing theory (APT), a multi-factor model that looks at multiple factors, grouped into macroeconomic or company-specific factors.

And while they may be rational and objective when studying risk levels, their opinions will reduce the quality of their mathematical projections. The position is then offset by accepting delivery of the asset and paying for the asset via proceeds from the loan. We make the additional assumption in this example that there are no corresponding storage, transportation, or transaction costs (Kolb, 1993). In this example we demonstrate how the investor can earn a risk-free profit without any cash investment by purchasing the asset in the sport market via a loan and simultaneously selling a Futures Contract to lock in a profit. Thus, the idiosyncratic terms ϵ play no role, that is, the idiosyncratic risks can be diversified. In order to illustrate the factor-based attribution analysis by means of an example we will analyze a portfolio and its benchmark with the Wilshire “Global 6-Regions Equity”-model.

For example, one common difficulty is finding suitable proxy betas, since proxy companies very rarely undertake only one business activity. The proxy beta for a proposed investment project must be disentangled from the company’s equity beta. The return on a stock market is the sum of the average capital gain and the average dividend yield. In the short term, a stock market can provide a negative rather than a positive return if the effect of falling share prices outweighs the dividend yield.

## Estimating the Risk Premium

Another drawback is that CAPM calculations are made for just one period, with the formula being too linear. The biggest issue, though, is that calculations are not even consistent with empirical or actual results. At Kesity.com, we provide professional and reliable finance homework help services to students seeking academic assistance. Research has shown the CAPM https://1investing.in/ stands up well to criticism, although attacks against it have been increasing in recent years. Until something better presents itself, though, the CAPM remains a very useful item in the financial management toolkit. The CAPM suffers from several disadvantages and limitations that should be noted in a balanced discussion of this important theoretical model.

## CALCULATION: How much expected return from the share price :

The model uses beta (β) to measure systematic risk, which is the measure of an asset’s volatility compared to the overall market. CAPM suggests that the expected return on an asset is proportional to the market risk premium (MRP), which is the difference between the expected market return and the risk-free rate of return. A big difference between CAPM and the arbitrage pricing theory is that APT does not spell out specific risk factors or even the number of factors involved. While CAPM uses the expected market return in its formula, APT uses the expected rate of return and the risk premium of a number of macroeconomic factors.

## CAPM formula

In order to mitigate that risk one should also use a standard model by way of comparison. A characteristic of the attribution analysis according to Brinson et al. is the dependence of the results on the chosen partitioning of the investment universe. It is, for instance, possible that for a global equity fund significant interaction terms occur in a sector-based approach, while when switching to a country-segmentation, interaction terms are close to zero. Since they are all derived from the APT model, they deliver similar results for the distribution of allocation and selection effects. Depending on the chosen factors the allocation results may change, however, on a detail level. For the analysis period January 2010 the Wilshire model estimates residual returns in the range from −7.87% (MAN SE) to 8.23% (Siemens) for the four titles contained in the portfolio and the benchmark.

The other components of the CAPM formula account for the investor taking on additional risk. However, market action should eventually correct the situation, moving price back to its fair market value. To an arbitrageur, temporarily mispriced securities represent a short-term opportunity to profit virtually risk-free. The main advantage of APT is that it allows investors to customize their research since it provides more data and it can suggest multiple sources of asset risks. Theoretically speaking, CAPM or APT analysis may lead to lower risk as investors use set mathematical formulae. When analysts come up with risk projections, their subjective decisions can make the picture even more complex.

As you can see in the illustration, as beta increases from 1 to 2, the expected return is also rising. The graph shows how greater expected returns (y-axis) require greater expected risk (x-axis). Modern portfolio theory (MPT) suggests that starting with the risk-free rate, the expected return of a portfolio increases as the risk increases. Before coming up with a beta and risk premium, the investor must select the factors that they believe affect the return on the asset; it can be done through fundamental analysis and a multivariant regression. One method to calculate the beta of the factor is by analyzing how that beta’s affected many similar assets/indices and obtain an estimate by running a regression on how the factor’s affected the similar assets/index.

So, one should, in the next case, start with the Fama French as the null model and then explore alternatives. If the Fama French is not rejected often enough, then it should be accepted as if true. In Frequentist decision theory, you have an acceptance region and a rejection region. If the result of an experiment puts the statistic of interest in the acceptance region, then you accept the null as if true.

Finally, APT is considered to be more flexible than CAPM, as it allows for the inclusion of additional factors that may impact an asset’s expected return. At first glance, the CAPM and APT formulas look identical, but the CAPM has only one factor and one beta. Conversely, the APT formula has multiple factors that include non-company factors, which requires the asset’s beta in relation to each separate factor. However, the APT does not provide insight into what these factors could be, so users of the APT model must analytically determine relevant factors that might affect the asset’s returns. On the other hand, the factor used in the CAPM is the difference between the expected market rate of return and the risk-free rate of return. The intuition of the model is that there would be an arbitrage opportunity if an investment were not priced this way.

The CAPM allows investors to quantify the expected return on an investment given the investment risk, risk-free rate of return, expected market return, and the beta of an asset or portfolio. The risk-free rate of return that is used is typically the federal funds rate or the 10-year government bond yield. Over the years, arbitrage pricing concept has grown in reputation for its relatively less complicated assumptions. However, arbitrage pricing principle is much more troublesome to apply in apply because it requires lots of information and complicated statistical evaluation. The arbitrage pricing concept was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing mannequin (CAPM). For investors looking for a straightforward approach and a model that is widely accepted in the financial industry, CAPM may be the preferred choice.

Both CAPM and APT are essential tools in the field of finance that help investors assess the risks and expected returns of their investments. While CAPM provides a simpler framework focused on a single factor (beta), APT offers a broader approach by considering multiple factors influencing asset prices. It just offers the framework to tie required return to multiple systematic risk components. The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (CAPM). Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.

The return of Deutsche Bank is nearly in its entirety explained by the model factors, so that only a very small residual return of −0.02% is left over. In contrast, the residual return of Commerzbank was equal to 2.61% for the analysis period. The portfolio had thus an overweight position in titles with a negative residual return and an underweight position in titles with a positive residual return, which led to a significant negative selection contribution of −1.98%. Suffice it to say that the fit of the individual approaches depends on the specific investment approach. Analyzing portfolios from different angles by applying several different methodologies simultaneously can sometimes be meaningful in practice. From the discussion above on the differences between CAPM and APT, APT is more accurate since it considers multiple factors and it is an extension of CAPM.