the birth of the Capital Asset Pricing Model (CAPM), enormous efforts have been

devoted to studies evaluating the validity of this model, a unique breakthrough and valuable contribution to the world of financial economics. Some empirical studies conducted, have appeared to be in harmony with the principles of CAPM while others contradict the model. One of the significant contributions to the theory of financial economics occurred during the 1960s, when a number of researchers, among whom William Sharpe was the leading figure, used Markowitz’s portfolio theory as a basis for developing a theory of price formation for financial assets, the so-called Capital Asset Pricing Model (CAPM). Markowitz’s portfolio theory analyses how wealth can be optimally invested in assets, which differ in regard to their expected return and risk, and thereby also how risks can be reduced. The foundation of the CAPM is that an investor can choose to expose himself to a considerable amount of risk through a combination of lending-borrowing and a correctly composed portfolio of risky securities. The model emphasizes that the composition of this optimal risk portfolio depends entirely on the investor’s evaluation of the future prospects of different securities, and not on the investors’ own attitudes towards risk. The latter is reflected

exclusively in the choice of a combination of a risky portfolio and risk-free investment or borrowing. In the case of an investor who does not have any special information, that is better information than other investors, there is no reason to hold a different portfolio of shares than other investors, which can be described as the market portfolio of shares. The Capital Asset Pricing Model (CAPM) incorporates a factor that is known as the “beta value” of a share. The beta of a share designates its marginal contribution to the risk of the entire market portfolio of risky securities. This implies that shares designated with high beta coefficient above 1 is expected to have over-average effect on the risk of the total portfolio while shares with a low beta coefficient less than 1 are expected to have an under-average effect on the aggregate portfolio. In efficient market according to CAPM, the risk premium and the expected return on an asset will vary in direct proportion to the beta value. The equilibrium price formation on efficient capital market generates these relations.

Thanks for your insight on CAPM. Can the CAPM beta be adjusted to reflect the effect of financial risk? This may be the connection to the financial risk emphasize in the M&M proposition two. Clarification are welcome.

Is the Differenciation between the "levered beta" and the "asset beta" what you are looking for? Simply insert CAPM-Formula into MM-Leverage... http://www.investopedia.com/terms/u/unleveredbeta.asp

Yes, that is the connection that I am talking about. Thank you for the information, it helps to clarify my thoughts.

MM showed that the capital structure of the firm shouldn't matter in a "pure" World. So the WACC should remain unchanged when the leverage changes. Leaving the cost of debt (kd) untouched, this implicitly means that the cost of equity (ke) should adapt to keep the WACC at the same level, i.e. ke=ka+(ka-kd)*D/E. This provides an equation for ke as a function of the cost of assets (ka). Since the CAPM proposes ke as a linear combination of risk-free rate and the market premium with Beta (Be) as the key variable, the same relationship should hold for betas, i.e. Be=Ba+(Ba-Bd)*D/E. With Hamada's simplification of Bd=0, that leaves you with the well known equation for BaBe.

Hugues, thank you for further explanation on the connection between M&M and CAPM.

the beta can be adjusted by incorporating various factors such as GDP, Interest rate, inflation etc. there are example like the Fama French 3 factor model and the Ghosh approach also. incorporate the same.

Adaoui and Agnihotri, I appreciate your inputs on the connection between CAPM and M&M.

MM's Propositions are independent of the valuation framework. Suppose V( ) is a valuation operation. Given some cash flow at time t, CF(t), V(CF(t)) finds the correct present value of that cash flow. MM's Proposition can be demonstrated to be true under that general valuation framework given all the assumptions inherent in MM (no taxes, no bankruptcy costs, no informational asymmetries). A specific instance of V( ) is the CAPM. Therefore, yes MM's Proposition can be proven under the CAPM (also if the APT is the correct valuation framework --- there could be others too).

Thank you for the explanation on the CAPM and MM connections.

Conection between levered and unlevered betas is derived assuming that both MM and CAPM are true. MM and CAPM are perfectly consistent.

Yes, the connection holds if both the MM and CAPM are correct. Thank you for your contribution.

i wrote a paper on this some years ago in the vein of capital structure and the Hamada equation. i will post it here. give me 24 hours to find it.