Capital asset pricing model (CAPM) and arbitrage pricing theory (APT) are both methods of assessing an investment's risk in relation to its potential reward and whether the potential investment yield is worthwhile.
CAPM developed by Sharpe 1964. The basic theory behind this model is that investor needs to be compensated for Time Value of Money and the risk that they are taking.
The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk. This is calculated by taking a risk measure of the market (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).
APT developed by Ross 1978. The basic theory of arbitrage pricing theory is the idea that the price of a security is driven by a number of factors such as macro factors, and company specific factors.
r = rf + β1f1 + β2f2 + β3f3 + ⋅⋅
Where r is the expected return on the security,
rf is the risk free rate,
Each f is a separate factor and
each β is a measure of the relationship between the security price and that factor.
The CAPM bases the price of stock on the time value of money (risk-free rate of interest (rf)) and the stock's risk, or beta (b) and (rm) which is the overall stock market risk. APT does not regard market performance when it is calculated. Instead, it relates the expected return to fundamental factors. APT is more complicated to calculate compared to CAPM because more factors are involved. CAPM uses the formula: expected rate of return (r) = rf +b (rm - rf). The formula for APT is: expected return = rf + b1 (factor 1) + b2 (factor 2) + b3 (factor 3). APT uses a beta (b) for each particular factor regarding the sensitivity of the stock price.