Finance Any Asset Pricing Theory forms the basic foundation of finance theory, in that it deals with the value of any asset under unknown or uncertain circumstances. The relationship between an asset and its price is the mainstay of the asset pricing theory: the lower the price, the poorer the expected performance. The Arbitrage Pricing Theory derives from this theory. The basic idea in the APT theory is that any sort of risk in asset returns must not affect the pricing of the asset in any way; it must depend on the covariance of assets with the risk factors. (Bayesian Approach of the Arbitrage Pricing Theory) The APT originated from Stephen Ross, 1976-1978. Ross had used a statistical procedure for assets returns, with the belief that there are in existence no arbitrage probabilities. The APT must of necessity involve a lot of risk taking processes, (Definition of Arbitrage Pricing Theory.)

While CAPM, which in other words means Capital Asset Pricing Model, and is an alternative to the APT, is an economic theory that values 'stocks' that are nothing but something that denote ownership or proprietary rights on the particular company's assets and lay claims on a fair share of the profits. The CAPM is responsible for relating risks taken by the investor with 'expected returns' which is, in other words, a calculation on the investment made by the investor, including any additional costs and dividends, and valuing the stocks accordingly. (Capital Asset Pricing Model)

How do these two theories work and which theory seems to work better for an investor? An in-depth comparison is necessary to come to any conclusion. Let us analyze the CAPM first. In the CAPM, a risk is defined with the help of the beta concept. Beta is the movement of individual stocks as against the movement of the overall stock market, or as against the proxy like the S&P 500 index. The calculations off the amount of risk are done on a data that has been accumulated over a day or a week or a month, over a period of one year. The figure that arrives is called the beta, and it serves as an accurate predictor of market behavior for the future. Whenever there is a change in the stock market, as when the stocks go up or down by a particular percentage, the result is that the stocks go up or down correspondingly, by the same percentage, multiplied by beta.

Therefore, according to the CAPM theory, stocks with a beta value of more than 1 are considered to be more at risk than the stocks that those with a negative beta, for whom stocks tend to move in the direction opposite to that of the market. The formula that is employed in the calculation of CAPM is E (R) = r + ERP multiplied by beta. E (R) is nothing but the expected rate of return on a stock, while r is the risk free interest rate, and ERP is the equity risk premium for the overall market. The innovators of CAPM, Sharpe, Lintner, and Mossin developed it as a logical sequence of the 'mean- variance theory'. The risk free interest rate is generally based on the government's treasury. For example, if the risk free interest rate were taken as being 5% and the ERP is taken to be 5.5%, and the company Gillette has a beta of 1.37. (Free Money and the CAPM)

The formula for the calculation of CAPM says that the expected returns from a purchase of Gillette can be calculated as 5+5.5 * 1.37 = 12.54%. In another example, if a stock from Charles Schwab with a beta of 1.85 were to be taken, the expected returns would be 5+5.5 * 1.85. The result would be 15.17%. Now the investor gets his share of free money. Therefore, it is better to invest in a company with a higher beta rather than with a lower one, since, in the long run, the wait would be worth it. The problem is, is CAPM a true calculation that actually helps an investor in a practical manner? The first problem in CAPM is that nothing is said about the company in which one would want to invest. The beta could be similar for entirely different companies, and CAPM would state that one company is as good as the other one, even if it is not. (Free Money and the CAPM)

The problem is that CAPM is written taking into consideration simple facts such as historical data of the...

The second problem in a CAPM theory is that the investor is not aware of the price that he has to pay for the stock. CAPM does not actually take into consideration current stock prices, although it may play a minor part in the beta calculations. This happens basically due to the reason that CAPM makes the assumption that the market is efficient, and this serves to simplify things. Though there are quite a few versions of the same, the basic result is that they all end at the same point, and whatever be the price of stock; this is the price at which you must buy or sell it for.
Whatever be the strategy, this is what will happen at the end, confirms the EMH or the 'efficient market hypothesis'. The EMH argues that the very same information is made available to almost anybody who wants to avail of it, and just because an individual uses this in his transactions, it does not necessarily entail or even ensure his success. So the CAPM basically proves to be an ineffective tool. The third problem in a CAPM is that it sometimes delivers bizarre results. For example, if the company Gillette were to close on March 31 at 50 instead of at 59.4375, its beta would have been at 1.31. If it had closed at 70, its beta would have been at 1.44. What the figures mean is that if the price of stock is higher, the higher the beta. If you want a portfolio with a higher beta, then you would have to buy stock at a higher price! As compared to S&P500, which, assuming it had closed at 1230 instead of at 1286.37 on March 31, the beta goes down from 1.37 to 1. 19. (Free Money and the CAPM.)

Arbitrage actually means the idea of getting something for nothing, at no risk of loss. For example, assume a portfolio would have to be made wherein there would have to be no investment and a long and a short portfolio in assets could be formed. This investment- less portfolio would, maybe have a positive impact, but, never a negative one. This is what is meant by an arbitrage. When you start from a position of zero and move on to making a nominal profit but never a loss, then this is arbitrage. If there is a risk-less profit achieved, this is a special case of arbitrage. If this profit or, in other words, return, is positive, an arbitrage is the buying of the portfolio and thereby gain a risk free profit. In the same way, if the return were negative, then the profit would be achieved in selling off the portfolio, a certainly risk-free proposition. If, by chance the returns were actually zero, then there would be no arbitrage. Another method of creating an opportunity for arbitrage would be when a non-zero investment is made up so that a minimal return is earned; this return would have to be equal that of the current market rate of risk free return interest rates. (Finance 500, APT)

If this were not done, then arbitrage would be necessary. Generally, it is not very common to find easy profits arising from arbitrage opportunities in a real asset market. If there were an arbitrage opportunity present, investors would move to make a profit, and this in turn would move the asset prices towards a non- arbitrage situation. For example, when there is a profit produced by a zero-investment portfolio, and investors purchase this portfolio, the prices of the assets in this portfolio would rise, as they would be 'bid' up. Then the cost of the portfolio would not be zero, and the cost would go up until the present value of the portfolio is reached. The arbitrage opportunity is therefore lost. It can be stated that in an asset market where there is competition, and prices are at an equilibrium, then no opportunity for arbitrage will actually exist. Therefore, when there is no arbitrage present, there will be achieved powerful asset pricing. (Finance 500, APT)

The principle of 'covered interest parity condition' was among the first few users of the arbitrage principle, primarily in foreign markets. (Finance 500, APT) The APT, in short, divides the risks that are present into smaller risks. The four-factor version of the APT that is these: one must assume that there is a certain amount of systematic risks that drive the security risks in a strong and solid line, there…