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Investors are risk averse and evaluate their investment portfolios solely in terms of expected return and standard deviation of return measured over the same single holding period. Capital markets are perfect in several senses: all assets are infinitely divisible; there are no transactions costs, short selling restrictions or taxes; information is costless and available to everyone; and all investors can borrow and lend at the risk-free rate.
Investors all have access to the same investment opportunities.
Investors all make the same estimates of individual asset expected returns, standard deviations of return and the correlations among asset returns.
2¼‰ The drawbacks of CAPM
1. The model assumes that either asset returns are normally distributed random variables or that investors employ a quadratic form of utility. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings occur in the market more frequently than the normal distribution assumption would expect. 
2. The assumption of CAPM model is inconsistent with the reality. a) efficient-market hypothesis: in actuall situation, we have trade cost, information cost and taxes. It is an im-perfect market. b) the borrowing rate=risk-free rate: the truth is that borrowing interest rate is higher than loan interest rate. c) CAPM can only be used for capital asset but not human assets. d) the estimated Î² represents the past variability, but not the future variability.But the investors concern about the variability of future price. e) the risk-free property and the market investment portfolio may not exsist.
3. The model assumes that the probability beliefs of investors match the true distribution of returns. A different possibility is that investors' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of behavioral finance, which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel and Avanidhar Subrahmanyam (2001).
4. The model assumes that given a certain expected return investors will prefer lower risk (lower variance) and given a certain level of risk they will prefer higher returns. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.
5. The model assumes that there are no taxes or transaction costs, but in realistic situation, there are taxes and transaction costs.
6. The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital). In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable.
7. CAPM provides a simple calculation for asset pricing, but it lacks of effective explanations about some abnormal phenomenon. The root cause is that CAPM is built on all investors have the same estimation and judgement about the expected risk and return. Efficient Market Hypothesis considers there is no asymmetric information and market frictions, the only thing affect the future average income is the invest risk.
3¼‰ The formula
The simple CAPM would appropriate for valuing dollarâ€dominated CF from a foreign target subject to no greater segmentation or political risk than the bidder faces.
Ke= Rf +Î²i*(Rm-Rf)
Ke is the expected return on the capital asset.Rf is the risk-free rate of interest such as interest arising from government bonds. (beta coefficient) is the sensitivity of the expected excess asset returns to the expected excess market returns.
The assumptions of ICAPM
International investors should hold assets of each country in proportion to the country share in the world market portfolio.This implies that all countries, in a world without transaction and information costs, would hold the same portfolio and would diversify their investment in other countries in proportion to the size of their financial markets.
The drawbacks of ICAPM
The benchmark portfolio that is used to measure risk could be improperly specified.
There could be problems with the returns data caused by infrequent trading of the component stocks.
International CAPM implies that if international markets are fully integrated then the world market risk is the only relevant pricing factor, and the assets with the same risk have identical expected return irrespective of the market. The notion that risk can be defined as the sensitivity to the changes in world market returns is contingent on the assumption of complete market integration. As the amount of segmentation increases, risk takes on a new definition as a security's sensitivity to local-market factors. In integrated world capital markets the sensitivity to many local events can be hedged by a diversified portfolio. That is, a negative event in one country may be offset by positive news in another country. However, if capital markets are segmented, the sensitivity to local events can have significant effects on the required returns for the securities that trade in the local markets.
As investors are holding in their portfolios assets from different markets, the relevant measure of the stock's risk (Î²) is its covariance relative to the variance of returns on the global market portfolio.
Ke= Rf +Î²wi*(Rwm-Rf)
Rf is the risk free rate.
Î²wi is the beta of the asset i, that is, the covariance of returns on asset i relative to the global equity portfolio (such as the Morgan Stanley Capital International (MSCI) Index) divided by the variance of the MSCI Index.
Rwm-Rf is the equity market risk premium on the global portfolio
The Multifactor Model
The assumptions of The Multifactor Model
The assumptions of the Multifactor model come from the Arbitrage Pricing Theory (APT).
1. All securities have finite expected values and variances
2. Some agents can form well diversified portfolios
3. There are no taxes
4. There are no transaction costs
The multifactor model has considerably fewer assumptions than the CAPM.
The drawbacks of The Multifactor Model
The Multifator model's failure to identify the factors specifically in the model may be a statistical strength, but it is an intuitive weakness. The solution seems simple: replace the unidentified statistical factors with specific economic factors and the resultant model should have an economic basis while still retaining much of the strength of the arbitrage pricing model. That is precisely what multi-factor models try to do. Once the number of factors has been identified, their behavior over time can be extracted from the data. The behavior of the unnamed factors over time can then be compared to the behavior of macroeconomic variables over that same period to see whether any of the variables is correlated, over time, with the identified factors.
There might be errors that can be made in identifying the factors. The economic factors in the model can change over time, as will the risk premia associated with each one. It is a problem when we try to project expected returns into the future, since the betas and premiums of each of these factors now have to be estimated. Because the factor premiums and betas are themselves volatile, the estimation error may eliminate the benefits of Multifactor model.
This model allows the required rate of return of a security to be function of the risk free rate plus the exposure of the stock market to various factors. The following macroeconomic factors are usually included:
1. World stockâ€market price risk (risks arising from the volatility of the returns on the global equity market portfolio)
2. Country stockâ€market price risk (risks arising from the volatility of the returns on the country's equity market portfolio)
3. Industry price risk
4. Exchange rate risk
5. Political risk
6. Liquidity risk
Ri-Rf=ai+Î²i/w(Rw-Rf)+ Î²i/c(Rc-Rf)+ Î²i/I(RI-Rf)+ Î²Ex(REx-Rf)+ Î²D(RDc-RAAA)+ Î²L(RLoL-RHiL)+Îµ
f=risk free rate
W=global equity portfolio
C=Country equity portfolio
I= Industry equity portfolio
Ex=Portfolio of foreign currency deposits
D=Sovereign debt instrument of the company's home country (C)
AAA=highest rated sovereign debt instrument
L=portfolio of low or high liquidity bonds
Îµ=regression error term
In the CAPM, investors care about one risk factor-the overall market. InICAPM, they are also concerned about real currency fluctuations. This insight leads to a model of expected returns involving not only the beta of an asset versus the overall market, but also the betas of the asset versus currency movements and any other risk that is viewed differently by different investor segments.
The Î² of ICAPM consists of 3 factors, including the domestic stock market volatility, the worldwide stock market volatility and the correlation of the world stocks. The Î² of CAPM cannot deal with the correlation of the world stocks.
The standard CAPM cannot explain returns in a cross-section of national value portfolios.
The ICAPM leads to a multi-factor solution for the pricing of assets. The new factors are the excess returns on assets that are perfectly correlated with the exchange rate appreciations for each currency but the benchmark currency. Utility varies not just because of variation in wealth but also because of variation in the purchasing power of the wealth. For given returns denominated in the foreign currency their purchasing power would be less when the domestic currency appreciates. Investors in the foreign market may hedge against this kind of risk by holding their own currency.
The beta of Multifactor Model, whether measured against a single factor or against multiple world sources of risk, appears to have some ability to discriminate between high and low expected return countries.
The CAPM and Multifactor Model are different approaches to assetpricing, but they are not contradictory. The idea behind the Multifactor Model is that investors require different rates of return from different securities, depending on the riskiness of the securities.
The CAPM and Multifactor Model assume that only market risk is rewarded and they derive the expected return as a function of measures of this risk. The CAPM makes the most restrictive assumptions about how markets work but arrives at the model that requires the least inputs, with only one factor driving risk and requiring estimation. The Multifactor Model makes fewer assumptions but arrives at a more complicated model, at least in terms of the parameters that require estimation.
5. The extent to which these techniques may be properly applied in light of the recent crisis in financial markets.
After the financial crisis, a court in the USA declared that all bubles are going to burst. The bigger the buble is, the bigger the lost is. This seems to pronounce the illegality of Efficient Market Hypothesis (EMH). But many people are still unwilling to admit the problems of EMH.Because of the CAPM which is based on Efficient Market Hypothesis, the investors turn a blind eye to the giant buble and let the buble develop. They thought the market can reflect all kinds of informations. Although a lot of people don't believe in Efficient Market Hypothesis, but they trust CAPM. The problem of CAPM is that it is based on a series of hypothesis which are of problems, such as investors can buy or sell any stock without affect the stock price.
CAPM can lead to pricing anomalies. a) Value Premium puzzle: firms with high Book-to-MKT ratios (value stocks) perform better than those with low ratios (growth stocks).
b) Size Premium puzzle: Small firms do better than large firms. c) Mean reversion in 'long term' returns (over-reaction). d) Momentum in 'short term' returns (under-reaction). e) Accounting-based anomalies (accruals, pension funding, etc.).
In practice market portfolio does not exist, when using proxies we find that there are many othe sources of risk which are relevant for investors. We need to set both the portfolio selection and the pricing problems in the context of Multifactor model.
Multi-factor models are used to construct portfolios with certain characteristics, such as risk, or to track indexes. When constructing a multi-factor model, it is difficult to decide how many and which factors to include. Datas are evaluated on history statistic, which cannot accurately forecast future values.
CAPM cannot explain the average returns of many investment opportunities: we need factors, sources of priced risk, beyond changes in the market portfolio in order to explain cross sectional variations in average returns. Multifactor models extend the CAPM precisely in this sense, attributing high average returns to positive correlation with additional risk factors other than movements in market risk. In general, the CAPM has the advantage of being a simpler model to estimate and to use, but it will under perform the richer Multifactor model when an investment is sensitive to economic factors not well represented in the market index.
It is important to realize that the only reason why investors are willing to take risk is their perception of a positive expected return (in excess of the risk free rate). In an international framework, for instance, many investors do not have strong convictions about future currency movements. In other words, they do not have a positive expected return on any currency. If this is the case, currency movements induce additional risk in the portfolio that is not remunerated by a positive risk premium. Such risk should then be hedged.
This leads us to the concept of the International CAPM, which is used in this study. The first source of risk is the "World Market risk", for which investors anticipate a positive return. The main equity regions considered in this study react more or less to changes in this world market portfolio. This is measured by beta coefficients. The other sources of risk of an international investor are the above-mentioned currency risks. The investor's portfolio has, of course, exposures to these risk sources (measured by currency beta coefficients), and to each source of currency risk there is an associated currency risk premium.