The capital asset pricing model sets the theoretical framework for identifying the expected return of a security or portfolio. However, when it comes to identify expected returns in the market practice, there is a number of factors we need to account for when identifying the expected returns. Here, I would like to focus on several popular issues connected with the use of the outcomes based on the CAPM in the real market practice. The first thing I need to talk about is the Beta adjustment. The thing is that the Beta estimate based purely on historical data, also known as the unadjusted Beta, is not a good indicator of the future as a consequence of different choices in the time period used intervalling effect and market index. Different services adjust their regression Betas towards one and use the adjusted Beta to calculate the expected return. Research suggests that over time, there is a general tendency for Betas of all companies to converge towards one. Intuitively, it should not be surprising because most companies tends to grow in size, become more diversified and own more assets. Over time, their Beta values fluctuate less, resulting in what is called Beta mean reversion. Adjusted Beta tends to estimate a security's future Beta. It's a historical Beta adjusted to reflect the tendency of Beta to be mean reversing so the CAPM's Beta value will move towards the market average or one over time. Here you can see the formula which was proposed by Marshall Bloom in 1975. According to Bloom, there is a tendency of Betas to converge towards the mean of all Betas. He describes these tendency by correcting historical Beta's to adjust the Beta, to revert to one and assuming that adjustment in one period is a good estimate in the next period. Another problem which also holds for the portfolio theory is that the historical volatility measures both the upside and the downside volatility. The thing is that the upside volatility may not be considered as a big problem for investors. Indeed, there is not a problem if you get a higher return that you're expected, the true problem is getting the return below the expected value. Thus a Beta is used as a part of the CAPM, which is designed to calculate the overall expected return of the asset. While downside Beta measures, downside risk or the possibility of negative movement. CAPM can also be modified to include upside Beta. Both upside and downside Beta are defined as the scaled amount by which an asset moves compared to a benchmark. Downside risk is calculated on days when the benchmarks return is negative, while upside Beta is calculated when it's positive. A capital asset pricing model that is based on international diversification of assets across different countries is called the global capital asset pricing model. Another name for it is the International Capital Asset Pricing Model. It's incorporates factors that could influence pricing in the international context. This implies that investors do not only hold the local asset, but also a portfolio of globally diversified assets. Then of the market portfolio, it can be constructed using the assets from different countries and different markets and regions. This model of CAPM takes into account such factors as inflation, transaction costs, exchange rates risks and barriers to foreign investment in expected return computation. However, when it comes to investing in a particular overseas country, we need to adjust our expected return estimation by what is called the Country Risk Premium. In general, by Country Risk Premium, we mean the additional return demanded by investors in order to compensate them for high risk associated with investing in a foreign country compared to investment at domestic markets. Overseas investment opportunities are accompanied by high risk because of geopolitical and macroeconomic risk factors that need to be considered. The Country Risk Premium is generally higher for developing markets compared to developed markets. Here are the factors which accounts for the country risk. This factors includes political instability, inflation risks, sovereign debt burden, and default probability as well as the fluctuations at the foreign exchange markets and some adverse government regulation, for example, the expropriation or currency controls. How can we estimate the Country Risk Premium? There are two commonly used methods of estimating this premium. The first one is called the sovereign debt method. In this case, the country risk premium for a particular country can be estimated by comparing the spread on sovereign debt yields between the country and a mature market like the United States. Another method is called the equity risk method. Here, the country risk premium is measured on the basis of relative volatility of equity market returns between a specific country and some developed nation. Here you can see the screenshot from the Bloomberg screen where the country risk premium for different countries are estimated based on such factors as the historical dividend yield for the national stock market, the average growth rate, the dividend payout ratio, and the market return. We also take into account the risk-free rates which are also different in each particular market. We can incorporate the risk premium that we have worked out into the capital assets pricing model using several different ways. The first approach assumes that every company in the foreign country is equally exposed to the country risk. Well, this approach is commonly used, it makes no distinction between any two companies in the foreign country even if one of them is a huge export-oriented firm, and the other one is just a small local business. In such cases, the country risk premium would be simply added to the mature market expected return, so that the CAPM equation will be modified in the following way. The second approach assumes that a company's exposure to country risk is similar to its exposure to other market risks. Thus, we add the country risk premium to the market risk premium like this. By using this method, we anticipate that the companies with higher betas are more exposed to the country risk than the companies with a lower beta, which is quite a reasonable assumption. Finally, the third approach considers country risk as a separate risk factor, multiplying the country risk premium with a variable which is generally denoted as lambda. In general terms, a company that has significant exposure to a foreign country by virtue of getting a large percentage of its revenues from that country or having a substantial share of its manufacturing located here would have a higher lambda value than a company that is less exposed to that country. Many investors and researchers use country risk premium to adjust the estimations of expected returns by using the capital asset pricing model. However, some of the researchers object from using the country risk premium. They say, that the global CAPM would capture a single global equity risk premium. Relying on the asset beta to determine volatility. A final major argument rests on the belief that the country risk is better reflected in the company's cash flow than the utilized discounts rate. Adjustments for possible negative effects within a nation, such as political and, or economic instability would just be worked into expected cash flow, therefore, eliminating the need for adjustments elsewhere in the calculation. Finally, another method for estimating the expected returns is based on the figures from the local markets only. This is called the local CAPM. In this sense, investors don't have access to opportunities associated with international diversification of risk. This implies that the capital markets of individual countries would be completely segmented from an international perspective. According to this type of the capital assets pricing model, the beta is measured relative to the country's market index. The equity premium to be used is the local market premium. Of the major weaknesses of model is that it doesn't tackle the issue of currency risk, though it does exist in the real world. There is a number of other modifications of the CAPM which are used in practice, and in various empirical studies. We can use these modifications to make a better estimation of expected returns. However, we need to remember that all these modifications of the CAPM are based on empirical findings and do not have the theoretical background as the general Capital Asset Pricing Model has.