The Capital Assets Pricing Model

The Capital Assets Pricing Model

The capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset or equilibrium price of assets if that asset is to be added to an already well-diversified portfolio, given that assets non-diversifiable risk.

The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial literature, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor (1961, 1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Thus this is an extension of the work of Markowitz. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field of financial economics.

Assumptions of CAPM:

1. All investors aim to maximize economic utility and they are rational and risk-averse meaning that they use the idea proposed by Markowitz.
2. Are broadly diversified across a range of investments.
3. All are price takers, i.e., they cannot influence prices.
4. Can lend and borrow unlimited amounts under the risk free rate of interest.
5. Trade without transaction or taxation costs.
6. Deal with securities that are all highly divisible into small parcels.
7. Assume all information is available at the same time to all investors.
8. Perfect Competitive Markets.

CAPM in Brief:

All investors will choose to hold a portfolio of risk assets in proportion that duplicates the market portfolio, which includes all traded assets. For simplicity we generally refer all risky assets as stocks. The proportion of each stock in the market portfolio equals the market value of the stocks. 

We consider that the market portfolio will not only be on the efficient frontier, but also in the tangency portfolio to the optimum capital allocation line [CAL] derived by each investors. As a result the CML [one of the CAL] will be the best capital allocation possible. As CML is the optimum one, therefore all investors will hold market portfolio differing only in the amount of investment.

Derivation in Simplest Form

Generally all the investors will hold Market Portfolio which is the tangency between CML and opportunity set. However, if we try to make a different strategy like: 

Market Portfolio: A market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market (with the necessary assumption that these assets are infinitely divisible).

Richard Roll's critique (1977) states that this is only a theoretical concept, as to create a market portfolio for investment purposes in practice would necessarily include every single possible available asset, including real estate, precious metals, stamp collections, jewelry, and anything with any worth, as the theoretical market being referred to would be the world market

Now, beta can be measured form the raw data as:

Period	Market HPR	Heidelberg Return
February 28, 2003	-0.084%	-0.37%
March 31, 2003	-6.950%	-7.35%
April 30, 2003	4.941%	9.33%
May 31, 2003	0.477%	0.18%
June 30, 2003	4.896%	0.72%
July 31, 2003	-3.670%	-1.98%
August 31, 2003	-0.858%	2.39%
September 30, 2003	-0.535%	0.72%
October 31, 2003	1.571%	0.89%
November 30, 2003	14.894%	20.11%
December 31, 2003	5.135%	-2.06%
January 31, 2004	-0.692%	-1.65%
February 29, 2004	-0.767%	-0.76%
March 31, 2004	2.104%	2.30%
April 30, 2004	14.202%	9.76%
May 31, 2004	6.621%	2.33%
June 30, 2004	11.223%	6.15%
July 31, 2004	-2.258%	-8.31%
August 31, 2004	17.388%	20.88%
September 30, 2004	7.912%	4.43%
October 31, 2004	4.742%	-9.58%
November 30, 2004	9.740%	4.45%
December 31, 2004	5.022%	8.76%
	Beta	0.967479052

The Value of Beta:

The value of beta can be any positive value or any negative value. However absolute value of beta has different meaning to the investors.

§  A higher beta means that the sensitivity of the security return with the market return is very high. Therefore it is mot likely to be a risky security. However if the value is positive then, the security will give higher return if the market return goes up and vice-versa. Moreover a security with higher beta will be considered as aggressive stock.

§  A lower beta [lower than 1] means that the sensitivity of the security return with the market return is very low. Therefore it is mot likely to be a less risky security. However if the value is negative then, the security return will go down if the market return goes up and vice-versa. Moreover, a security with lower beta will be considered as defensive stock.

§  The Beta of 1: This is the beta of market portfolio. Because theoretically the sensitivity of market returns with market return is 1. Therefore we consider that market beta is always 1. Alternatively since some security will be aggressive, some will be defensive, some will be more aggressive or defensive, some will be less aggressive or defensive, therefore sum of all of them in one portfolio, which is market portfolio, will be 1.

It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed. If an asset is undervalued by CAPM it should be bought and an overvalued by CAPM then it should be sold.