Assumptions of Mean-Variance Space (MVS)

In this section, the assumptions of the MVS will be discussed. In the analysis, it is assumed that the expected returns of both the stocks are similar to the average historical returns. Thus, it is assumed that the historical returns are representative to estimate the future returns, or in other words, the future returns can be reasonable predicted by historical returns. This assumption may not valid in real life, because as we can see, the historical returns of Barclays from the example above, is negative, but it is more relevant to assume that Barclays as the group of company will be more conservatively managed and thus could results in a positive returns in the future. In order to draw the Capital Market Line (CML) in the example above, it is assumed that the relevant risk free rate is 5%. Thirdly, under the mean-variance framework, it is assumed that the relevant risks faced by investors are the volatility of stock prices (Remark: this may not be relevant in case investors do not perceive that volatility is a risk). It is also assumed that the stock returns are normally distributed. Not only that, it is assumed that investors have homogeneous expectations.

Assumptions of Capital Asset Pricing Model (CAPM)

In this section, the assumptions of the Capital Asset pricing Model (CAPM) will be discussed. Under the theory of CAPM, it is assumed that the many investors cannot affect the stock prices through their personal trades. Perfect competitions among investors are assumed. Besides, it is also assumed that all investors have identical holding periods. Thirdly, it is assumed that investors will form the portfolio from the universe of all traded financial assets (i.e., include stock, bond, and any other tradable assets). It is also assumed that all investors have access to unlimited lending or borrowing. Apart from that, it is also assumed that investors do not subject to transaction costs or taxes. Thus, the returns of dividend or capital gains make no differences from the perspective of investors. Besides, it is also assumed that all investors are mean-variance optimizer. They based their investing decision on the efficient frontier and mean-variance framework. Essentially, all of the investors have similar perceptions on the investing world. They have identical expectations on the statistical properties and probabilities of the many financial assets in the universe.

Besides, in the example shown above, as the various statistical data used to construct Security Market Line (SML) is obtained from the historical calculation of the returns relevant to IBM and Barclays five years of historical monthly returns; several assumptions applied in MVS do apply here as well. To explain: it is assumed that the expected returns of both the stocks are similar to the average historical returns. Thus, it is assumed that the historical returns are representative to estimate the future returns, or in other words, the future returns can be reasonable predicted by historical returns. In the same way, it is also assumed that the relevant risks faced by investors are the volatility of stock prices. Then, it is also assumed that the stock returns are normally distributed.