CML vs CAPM: Risk & Return in Capital Markets

Capital Market Line (CML) vs. Capital Asset Pricing Model (CAPM)

• The CML measures risk using the total volatility of an investment (standard deviation).
• The CML is inconsistent because investors should not be compensated for unsystematic risk that can be eliminated through diversification.
• The standard deviation includes unsystematic risk, so the CML cannot explain the risk-return trade-off for individual risky assets.
• The CAPM, developed by Sharpe, Lintner, and Mossin, helps investors evaluate the risk-return trade-off for diversified portfolios and individual securities.
• Beta is employed by the CAPM to measure a security’s systematic risk compared to the market portfolio.
• The mean-variance CAPM helps estimate the required return.

CAPM Features and Application

• The CAPM is dominant because it focuses on risk from the perspective of shareholders.
• The CAPM provides a way to adjust for risk by adjusting the required return.
• The CAPM objectively applies the principle that higher expected returns compensate for higher risk.

Security Market Line (SML)

• The SML is the graphical representation of the CAPM.
• At equilibrium, securities should offer the same expected return for the same level of risk (Beta), and lie on the SML.
• Securities below the SML are overpriced, offering less return for the same risk, and their prices should decrease, increasing the expected return.
• Securities above the SML are underpriced, offering a higher expected return for the same risk.

Beta Computation

• The time interval and number of observations vary when computing Beta.
• The use of monthly versus weekly return intervals is the major cause of Beta differences.
• The S&P 500 composite index is used as a proxy for the market portfolio to compute Beta.
• The market portfolio of all risky assets should include U.S. and non-U.S. stocks and bonds, real estate, antiques, arts, and any other marketable risky asset.

CAPM Assumptions

• All investors are single-period decision-makers who want to maximize their terminal wealth.
• All investors agree on the expected returns and standard deviations of all assets, and covariances of returns between all pairs of assets.
• All investors can borrow and lend unlimited amounts of money at the risk-free rate.
• No taxes exist.
• All investments are completely divisible and can be bought and sold with no transaction costs.
• No investor holds a portfolio large enough to affect prices.
• The quantities of all investments are fixed.
• All investors agree about risk and expected return, perceive the same efficient frontier, and choose the same risky asset portfolio (the market portfolio).
• The market portfolio contains all investments in proportions such that no investment is left over.
• Each investor acquires the market portfolio and lends/borrows at the risk-free rate, moving along the CML based on their risk aversion.

Security Market Line (SML) and Required Return

• The CAPM relationship is given by the security market line (SML).
• The required return on an investment depends on the risk-free rate, the expected returns on the market portfolio, and the investment's sensitivity to factors affecting the market.

Relaxing CAPM Assumptions: Differential Borrowing and Lending Rates

• It is unrealistic to assume investors can borrow unlimited amounts at the risk-free rate; the borrowing rate is higher than the risk-free lending rate.
• Two different rates affect the Markowitz efficient frontier.
• If investors can borrow at a higher rate, the CML is fatter beyond the risky portfolio.
• Investors can engage in a margin position, investing borrowed money in a risky portfolio with a higher standard deviation and lower reward to volatility ratio.

Relaxing CAPM Assumptions: Transaction Costs

• The CAPM assumes no transaction costs, allowing investors to buy and sell mispriced securities until they are on the SML.
• Transaction costs prevent investors from correcting all mispricing; the cost of selling and buying slightly mispriced securities exceeds potential excess returns.
• Securities will plot close to the SML, but not exactly on it, making the SML a band rather than a single line.
• Lower transaction costs narrow the band.
• Transaction costs affect the number of securities in a portfolio for diversification, where the costs of adding securities may exceed their benefits.

Relaxing CAPM Assumptions: Heterogeneous Expectations and Planning Periods

• If investors have different expectations about risk and return, each would have a unique CML and SML.
• The SML would be a group of lines that are narrower when the divergence of expectations is smaller.
• The SML and CML would differ when the planning period is different.

Relaxing CAPM Assumptions: Taxes

• Individuals and institutions may face different after-tax returns.
• This is worsened by tax-differed investments and different tax rates for long-term and short-term returns.
• The tax burden could cause major differences in the CML and SML among investors.

Empirical Tests of the CAPM

• Empirical studies examine the stability of Beta as a measure of systematic risk and the positive linear relationship between Beta and the rate of return.
• Beta as a risk measure is not stable over time for individual stocks, but it is stable for portfolios of stocks.
• A positive relationship was found between risk and return, but it was not completely linear.
• CAPM appears to underprice low-beta stocks and overprice high-beta stocks.
• P/E (price to earnings ratio) and firm size have an inverse impact on returns after considering the CAPM, showing that they need to be considered along with Beta.
• Stocks with low P/E ratios outperformed high P/E stocks; value stocks outperformed growth stocks.
• Size is important and the high book to market ratio affects P/E ratio.
• There are extensive studies that tested for the CAPM and the general conclusion is that CAPM does explain differences in return between assets with different risk levels, but it does not explain all differences.
• The CAPM is not a complete model in explaining the relationship between risk and return because beta does not explain a very high percentage of the variance in returns among securities.
• Some other factors in addition to beta do explain securities’ returns.

Issues in Empirical Tests of the CAPM

• Studies substitute historical results for expectations, assuming that historical results will equal expected results in the long run.
• Richard Roll explained that failure to find the risk-return relationship may result from selecting an inefficient market index to represent the market portfolio.
• A theoretically correct index would incorporate every security or investment, making a valid test of the CAPM impossible.
• Deviation from CAPM predictions may result from inaccuracy of the model and inaccuracy of the tests, called Benchmark error.
• The CAPM has gained popularity due to its simplicity, and because no improved model exists, the CAPM is still the model of choice in practice.

Beta Estimation

• Beta based on historical returns: beta is the slope coefficient of the return for the security regressed on return for the market portfolio.
• Beta changes over time due to changes in financial leverage or changes in the nature of the business.
• Beta for comparable companies: if historical data in unavailable or inapplicable because of drastic changes in the company business, the beta can be estimated by reference to other companies.
• Companies should be similar in products, market positions, and leverage.
• If financial leverage is different when using betas for other companies, the estimate of beta may be affected by this difference in financial leverage.

Risk-Adjusted Required Return for Projects

• The risk-adjusted required return for the company is appropriate for projects of average risk.
• Decision-making will be improved if adjustment is made for proposed investments with above or below average risk.
• One way to do this is to decide that all projects in a particular business category or division have similar risk characteristics.
• The required return for a division can be estimated by treating the division as if it were a separate company.
• This approach is referred to as the pure play approach. The required steps are as follow: Identify a company or companies similar to the division, compute the average unleveraged beta for the companies similar to the division, compute a leveraged beta for the division, based on the average unleveraged betas for similar companies, compute the division cost of equity using the leveraged beta and then the WACC.
• A division debt ratio is needed to compute a division weighted average cost of capital.
• This can be done by allocating debt and equity of the company among the divisions in a way that approximates the amount of debt and equity the divisions would carry as independent companies.

CAPM Deficiencies and Additional Risk Measures

• The empirical testing of the CAPM proved some deficiencies in how the model explain the relation between risk and return.
• From the absence of market portfolio to the non-linear relation between risk and return, recent models have indicated the need to consider additional risk measures.

Arbitrage Pricing Theory (APT)

• Ross developed the APT, requiring limited assumptions and allowing for multiple dimensions of investment risk.
• The APT model three major assumptions are: Capital market are perfectly competitive, Investors always prefer more wealth to less wealth, The stochastic process generating asset returns is a linear function of a set of risk factors.
• Several empirical tests focused on the APT, but the model does not specify the factors.
• The nature and number of these factors change over time and between economies.
• Information on these variables should be timely and accurate, The relationship should be theoretically justifiable on economic grounds, Factors should be non-diversifiable, macroeconomic rather than firm specific, Their impact on asset prices manifests in their unexpected movements.
• Roll and Ross found that the maximum reasonable number of factors was five using 42 portfolios of 30 stocks each.
• The importance and the number of the factors might differ among portfolios.
• Support for the validity of the APT model came from the fact that two, three or more factors are required to explain the returns; which is an improvement of the single factor CAPM.
• The challenge in implementing a test for the CAPM is to specify the market portfolio, which cannot be observed.
• The primary practical problem associated with implementing the APT is that neither the identity nor the exact number of the underlying risk factors are developed by the theory.

Empirical Factor Specifications for APT

• Risk factors can be macro-economic in nature or viewed at a micro-economic level.
• The micro economic level focuses on relevant characteristics of the securities themselves, such as the firm’s financial ratios.

Fama and French Model

• The Fama and French model tries to improve the measure of market return.
• Fama and French found that within the CAPM framework, value stocks outperform growth stocks and small cap stocks tend to outperform large cap stocks.
• The Fama and French three factor model adjusts for these anomalies. The three factors are: Company size as measured by small cap minus large cap (SMB), Price-to-Book ratio as measured by High book-to-market ratio minus low (HML), Market risk premium (similar to CAPM).
• The Fama-French three factor model explains over 90% of the diversified portfolios returns, average of 70% for the CAPM.