Home > Capital asset pricing model
5 The efficient (Markowitz) frontier
The CAPM assumes that the risk-return profile of a portfolio can be optimized - an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e. one for each level of return, comprise the efficient (Markowitz) frontier.
6 The market portfolio
An investor might choose to invest a proportion of her wealth in a portfolio of risky assets with the remainder in cash - earning interest at the risk free rate (or indeed may borrow money to fund her purchase of risky assets in which case there is a negative cash weighting). Here, the ratio of risky assets to risk free asset determines overall return - this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways:
- By investing all of one’s wealth in a risky portfolio,
- or by investing a proportion in a second portfolio and the remainder in cash (either borrowed or invested).
For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2) will generally have the lower variance and hence be the more efficient of the two.
This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal portfolio which can be combined with cash to achieve the lowest level of risk for any possible return. This is the market portfolio .
7 Shortcomings of CAPM
- The model does not appear to adequately explain the variation in stock returns. Empirical studies realized in the past 15 years show that low beta stocks may offer higher returns.
- What is the "market portfolio"? Does it include the bond market? Real estate? Commodities? Private placements?
- The market portfolio, and hence its return, are not observable and have to be estimated.
- The model assumes that all investors are risk averse. Some investors (e.g., some day traders), however, can not be considered to be risk averse.
- The model assumes that all investors create mean-variance optimized portfolios. However, there are many investors who don't know what a mean-variance optimized portfolio is.
8 Finding related topics
9 References
- Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47
- Markowitz, Harry M. (1999). The early history of portfolio theory: 1600-1960, Financial Analysts Journal, 55 (4)
- Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3)
- Tobin, James (1958). Liquidity preference as behavior towards risk, The Review of Economic Studies, 25
10 External links
Economics Finance Financial mathematics
