# Synopsis of today’s Capital Market theory topic

Our coverage of the Capital Market Theory topic has provided the following important insights:

1. Borrowing and lending at the riskless rate of interest in combination with investing in (mean-variance efficient) risky portfolios enable investors to obtain superior risk-return trade-offs compared with investing only in mean-variance efficient risky portfolios. In the figure below (taken from page 2 of the Capital Market Theory lecture note), investors select portfolios along the Capital Market Line, which is given by the following equation: $E({r_p}) = {r_f} + \left[ {\displaystyle\frac{{E({r_m}) - {r_f}}}{{{\sigma _m}}}} \right]{\sigma _p}$.In the above figure, $\alpha$ corresponds to the optimal level of exposure to the market index which is labled as point M. When $\alpha = 0$, the investor is fully invested in the riskless asset. When $0 < \alpha < 1$, the investor is partially invested in the riskless asset and in the market index; such portfolios are referred to as “lending” portfolios. When $\alpha = 1$, the investor is fully invested in the market index. Finally, when $\alpha> 1$, the investor funds her investment in the market index with her initial wealth plus borrowed money; such portfolios are referred to as “borrowing” portfolios.
2. Given that investors select (based upon their level of tolerance for risk) portfolios that lie on the Capital Market Line, this behavior has implications for the pricing of risk for individual securities. Specifically, the Capital Market Line implies that for individual securities, the Security Market Line must hold. The equation for the Security Market Line (which is commonly referred to as the Capital Asset Pricing Model, or CAPM) is given by the following equation: $E({r_i}) = {r_f} + \left[ {E({r_m}) - {r_f}} \right]{\beta _i}$, where ${\beta _i} = {\sigma _{i,m}}/\sigma _m^2.$
3. According to the CAPM, the appropriate measure of risk for an individual stock is its beta, which indicates how much systematic risk the stock has compared with an average risk investment such as the market portfolio. Beta for security i (${\beta _i}$) is measured by dividing the covariance between i and the market (${\sigma _{i,m}}$) by market variance ($\sigma _m^2$). If the investor purchases an average risk security, then its beta is 1 and the expected return on such a security is the same as the expected return on the market. On the other hand, if the security is riskier (safer) than an average risk security, then it’s expected return is higher (lower) than the same as the expected return on the market.
4. If the expected return on a security is higher (lower) than the expected return indicated by the CAPM equation, this means that the security is under-priced (over-priced). Investors will recognize this mispricing and bid up (down) the under-priced (over-priced) security until its expected return conforms to the CAPM equation.
5. According to the CAPM, only systematic (i.e., non-diversifiable) risk is priced. Systematic risks are risks which are common to all firms (e.g., return fluctuations caused by macroeconomic factors which affect all risky assets). On the other hand, unsystematic (i.e., diversifiable) risk is not priced since its impact on a diversified asset portfolio is negligible. Diversifiable risks comprise risks that are firm-specific (e.g., the risk that a particular company will lose market share or go bankrupt).