- As the size of a portfolio increases, the portfolio’s variance is dependent more on the covariances among the securities in the portfolio than on the variances of the individual securities. This happens because as the portfolio size increases, the number of covariance terms increases exponentially while the number of variance terms increases linearly. Therefore the variance term in calculating the variance of a portfolio approaches zero.
- The components of an asset’s total risk are (1) undiversifiable risk (covariance risk) and (2) diversifiable risk (remaining risk in the portfolio). Diversifiable risks are unique to a particular asset (or company) and can be “washed out” by investing in a portfolio of assets with different types of unique risk characteristics. This is also known as non-systematic risk. Undiversifiable risk is also known as market risk or systematic risk and cannot be diversified away. It relates to economic and other factors that are outside the control of the asset (or company).
- Market risk is systematic because it is systematically dependent on the vagaries of the US economy
- The limit of diversification is reached when the risk of the portfolio can be reduced no further by additional diversification. This risk level is the average covariance risk of the portfolio, which indicates that the variance risk of the portfolio has been eliminated.
- Relevant risk is the non-diversifiable portion of an asset’s risk. This is sometimes called systematic, or market risk. It is relevant because investors can diversify away non-systematic risk, leaving only systematic risk “relevant.” It is also relevant in that it is the systematic risk that determines the supply and demand for an asset and hence its equilibrium price.
- The relevant risk would decline if you invest internationally because the international markets have economic factors that differ from the US market. These differing factors would serve to offset systematic risk (relevant risk) to a certain degree, in the same way that diversification offsets non-systematic risk domestically. However, this reduction in relevant risk has a floor as well.
- Beta is a statistical measure that relates the sensitivity of a security’s returns to changes in the returns on the market. It relates market risk to asset risk.
- Beta is a leverage measure of market returns because an assets beta will indicate the expected return on an asset given a certain return on the market; levered up or down (i.e. above or below 1).
- Beta is calculated using the characteristic line approach, mathematical formulas, or is published by investment houses.
- Portfolio betas are the betas for an entire portfolio of assets and indicate the responsiveness of a portfolio’s value to changes in the market. The are calculated as the weighted average sum of the betas of each security in the portfolio.
- The second term in the CAPM model is the market risk premium term, and is a measure of the spread between the expected return on the market and the risk free rate of return. The first term is beta, and indicates the “number of risk premiums” associated with the asset. In other words, the second term is the expected risk in the market, and the first term is that risk amplified by the assets relationship to the market.
- The five testable implications of CAPM are:
- A security’s return should increase with its relevant risk
- The relationship between return and risk should be linear
- Nonsystematic risk should not affect returns
- On average, the slope of the CAPM should equal the risk premium
- On average, the intercept should equal the risk-free rate
- Empirical evidence has shown that 1-3 are clearly accurate, and that the slope of the CAPM is actually flatter than the above indicate. This merely states that the model is not perfect, but is a good estimate. Other research says that CAPM is bogus and that no relationship exists, but CAPM keeps cropping up again and again as a pretty good model.
- CAPM’s strengths are its intuitiveness and ease of use, while its weaknesses are its broad and general assumptions.
- The APT is a pricing theory that assumes no arbitrage can exist in the market and that prices are affected by more than one factor. In other words, an asset can be affected my several betas, called factor betas, and have multiple relationships with multiple factors.
- CAPM and APT are similar in that APT is an extension of the beta/ risk premium format of the CAPM model. APT however is based on much more simplified assumptions and is therefore often more appealing. CAPM implies a single beta with the market. APT implies multiple relationships with as many factors as are relevant. Both allow for the elimination of non-systematic, or idiosyncratic, risk through diversification.

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