Portfolio Theory is a theory of investment which try to maximize portfolio expected return for a given amount of portfolio risk, or evenly minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. The expected return on a portfolio is calculated on the stocks which comprise the portfolio. The weights reflect the proportion of the portfolio invest in the stock. This can be expressed as follows: Where: = expected return on the portfolio = number of stocks in the portfolio =the proportion of the portfolio invested in stock i = expected return on stock i For a portfolio consisting of two assets the equation can be express as: Portfolio Theory also assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, an investor will prefer the less risky one. Thus, an investor will take on increased risk only if it gains higher expected returns. Conversely, an investor who wants higher expected returns must accept more risk. The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on individual risk aversion characteristics. The implication is that a rational investor will not invest in a portfolio if a second portfolio exists with a more favorable risk-expected return profile. According to Portfolio theory, investors should focus on the significance of diversification to reduce the total portfolio risk, but they also learn how they can effectively diversify. Portfolio theory has had a marked impact on how investors perceive risk, return and portfolio management. The theory demonstrates that portfolio diversification can reduce investment risk.In other words Portfolio Theory of Investment highlights the importance for an investor not to invest in one stock but to invest in a Portfolio of stock and bonds and Treasury Bills so that he can minimize risk and maximize his return given his risk preference. As well, Portfolio Theory of Investment can be used if one knows the beta of stocks to calculate the expected return of equity using the Capital Asset Pricing Model, which is essential to evaluate capital budgeting decision making. That is, Portfolio Theory of Investment is the basis of the Capital Asset pricing Model and is used in modern financial management of a company. Capital Asset pricing Model (CAPM) on its part provides an expression which relates the expected return on an asset to its systematic risk (Systematic risk is a risk of security that cannot be reduced through diversification).The relationship between is known as the security market line (SML) equation and the measure of systematic risk is called the Beta. The CAPM define systematic risk as beta. In the CAPM model, because all the investors are assumed to hold the market portfolio, an individual asset owned by an investor will have a risk that is defined as the amount of risk that it adds to the market portfolio.
Systematic risk is due to risk factors that affect the entire market such as investment policy changes, foreign investment policy, change in taxation clauses, shift in socio-economic parameters, global security threats and measures whereas unsystematic risk is due to factors specific to an industry or a company like labor unions, product category, research and development, pricing, marketing strategy. Risk, standard deviation of return% Unsystematic risk (unique risk) Total systematic risk risk (market risk) The greater is the systematic risk, the greater is the return expected out of the asset. The relationship between the expected returns and systematic risk is what the CAPM explains. The Security Market Line Equation is as follows: Where: = the expected return on asset i = the risk-free rate =the expected return on the market portfolio = the beta on asset i = the market risk premium The graph below depicts the SML. The SML is equal to which is the market risk premium and the SML intercepts the Y-axis at the risk-free rate. SML I In capital market equilibrium, the required return on an asset must equal its expected return. Thus, the SML can also be used to determine an asset’s required return given its Beta. The Beta ( for a stock is calculated as follows: Where: = the covariance between the return on asset I and the market portfolio = the variance of the market portfolio
Where: N=the number of states = the probability of the state i =the return on the stock in state i = the expected return on the stock The beta of the market portfolio equals 1 and the beta of the risk-free asset equal to 0 An asset’s systematic risk therefore depends upon its covariance with the market portfolio. The market portfolio is the most diversified portfolio as it consists of every asset in the economy held according to its market portfolio.
R Levered portfolio of risky assets E M all the wealth is in risky assets L some wealth is in risk free assets All the wealth is in risk-free asset The formula of capital market line is as follows: E The CML results from the combination of the market portfolio and the risk-free asset (the point L). All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier, with the exception of the Market Portfolio, the point on the efficient frontier to which the CML is the tangent. From a CML perspective, this portfolio is composed entirely of the risky asset, the market, and has no holding of the risk free asset, i.e., money is neither invested in, nor borrowed from the money market account.
Zero transaction costs. The CAPM assumes trading is costless so investments are priced to all fall on the capital market line. If not, some investment would hover below the line- with transaction cost discouraging obvious swaps. But however, many investments involve significant transaction costs. Homogeneous investor expectations. The CAPM assumes invests have the same beliefs about expected returns and the risks of available investments. But there is massive trading of stocks and bonds by investors with different expectations and also that investors have different risk preferences. Thus it may be that the capital market line is fuzzy amalgamation of many different investors’ capital market lines. Beta as full measure of risk. The CAPM assumes that risk is measured by the volatility (Standard deviation) of an asset’s systematic risk, relative to the volatility of the market as a whole. Somehow investor face other risk such as inflation risk which mean that returns may be devalue by the future inflation and also liquidity risk that is investors in need of funds or wishing to change their portfolio’s risk profile may be unable to readily sell at current market prices. Moreover standard deviation does not measure risk when returns are not evenly distributed around the mean. ADVANTAGES OF THE CAPM: It generates a theoretically-derived relationship between required return and systematic risk which has been subject to frequent empirical research and testing. It is generally seen as a much better method of calculating the cost of equity than the dividend growth model (DGM) in that it explicitly takes into account a company’s level of systematic risk relative to the stock market as a whole. It considers only systematic risk, reflecting a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated. DISADVANTAGES OF THE CAPM Problems can arise when using the CAPM to calculate a project-specific discount rate. 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. One way to do this is to treat the equity beta as an average of the betas of several different areas of proxy company activity, weighted by the relative share of the proxy company market value arising from each activity. However, information about relative shares of proxy company market value may be quite difficult to obtain. In order to use the CAPM, values need to be assigned to the risk-free rate of return, the return on the market, or the equity risk premium, and the equity beta.
Portfolio theory and Capital Asset pricing Model are important for managers as well as investors as it helps them in their decision making and a good decision making in its turn will allow then to gain more in term of return. It will also allow them to know the level of risk associated with an investment and generally the greater the risk the higher the return should be. However the CAPM is not perfect but its spirit is to provide a usable measure of risk that helps investors determine what return they deserve for putting their money at risk and in order to be successful, an investor must understand and be comfortable with taking risks. Creating wealth is the object of making investments, and risk is the energy that in the long run drives investment returns.
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