## Friday, February 26, 2010

### Refining The Capital Asset Pricing Model for Practical Investment Use

The capital asset pricing model is a great display of academic prowess in financial theory. However, it does have its limitations. Mainly, the criticism it receives is that it makes a number of assumptions that do not necessarily hold true in market conditions. The biggest one I feel is is the beta coefficient, or β.

To break it down the capital asset pricing model (CAPM) is a way of determining the cost of equity for a company. This is often also referred to as the investor's expected rate of return for investing in a security. The formula is as follows:

$E(R_i) = R_f + \beta_{i}(E(R_m) - R_f)\,$
where:

E (Ri) = expected rate of return of investment i
Rf = the risk free rate of return (usually the 10-year bond return)
βi = beta coefficient of investment i (the individual price volatility of the investment relative to the market as a whole).
E(Rm) = expected return of the market as a whole

The biggest concern is with β. The capital asset pricing model as it stands alone assumes that the riskiness of an investment is based upon the past price volatility of the investment. This is HUGE assumption, because future prices cannot be accurately extrapolated from the past prices. Market prices of a security are determined not only by supply and demand from investors, but also the profitability and growth prospects of a security. The beta coefficient is assuming that market prices are efficient and that all information is known to all investors.

However, we know that not all information is known to all investors, and not all information is important to all investors. Also time horizons for investors differ (another huge assumption of the model), therefore even if all information was known, some information may disregarded by short term investors if it does not serve their time horizon. The information that a trader will be looking at may affect his view of the price, while a long term value investor may see information that reflects his view of the price.

In present circumstances, the current market prices are the averages of investor perceptions. Therefore, if most investors are arguably short term oriented, the price of that stock will more favorably reflect short term prospects. For example, if Ford stock has low upwards movement prospects in the short term because Ford is taking non-cash charges (thus reducing current earnings) , the majority of investors may be uninterested in that stock, and the price of the stock will reflect there lack of demand for it.

This is why it is important to have a somewhat longer investment horizon. You want to account for short term prospects and long term prospects. Yeah, Ford may be taking short-term non-cash charges and reducing their earnings, but is a non-cash charge really a reflection of a change in business value, especially if the company is still making adequate capital expenditures to improve the business for the long term?

The market is not perfectly efficient, which gives the individual investor an edge if they are willing to resist the temptation of short term sentiments.

So how do we adapt CAPM for reliably determining the cost of equity? Simplistically, an investor can expect the market to return 11% on average over time. Therefore, it is reasonable to say that an investor should expect no more than an 11% return on average from their portfolio (this is supported by the latest indexing fad).

Even though the expected return may fall short of what an investor's actual return may be, it is fair to say that a prudent and rational investor should expect no more than what the market will return (unless of course the risk free rate were to exceed that, in which case the last thing anybody would be concerned about is their return on investment when the whole market is collapsing!).

With the cost of equity set to be at a value of 11%, the discount rate for a security can thus be figured out by the company's weighted cost of capital, utilizing the borrowing rates of a company after taxes and our constant cost of equity. Thus we have a maximum discount rate for a public company to be no more than 11%* (if the company is 100% equity financed).

This figure to me seems fair, considering Warren Buffet discounts utilizing only the risk free rate.

*This discount rate only can be comfortably applied to non-controlling shares of publicly traded companies of a reasonable size (excluding micro caps) without getting into liquidity discounts, size discounts, and control premiums.