13. Capital Asset Pricing Model and Other Risk Premium Models
The Capital Asset Pricing Model is a risk premium approach to gauging a firm's cost of equity capital.43
The yield on long-term Treasury securities is normally used as Rf. Risk premiums are measured in different ways. The Capital Asset Pricing Model is a theory of the risk and expected returns of common stocks. In the Capital Asset Pricing Model, two types of risk are associated with a stock: firm-specific risk or unsystematic risk, and market or systematic risk, which is measured by a firm's beta. The only risk that investors receive a return for bearing is systematic risk.
According to the Capital Asset Pricing Model, the expected return on a company's stock, which is also the equity cost rate (K), is equal to:
K = (Rf) + ß * [E(Rm) - (Rf)]
Where:
K = the estimated rate of return on the stock;
E(Rm) = the expected return on the overall stock market (Often the Standard & Poor's 500);
(Rf) =the risk-free rate of interest (Usually Long-term U.S. Treasury Notes);
[E(Rm) - (Rf)] = the expected equity or market risk premium-the excess return that an investor expects to receive above the risk-free rate for investing in risky stocks; and
Beta (ß) = the systematic risk of an asset.
To estimate the required return or cost of equity using the Capital Asset Pricing Model requires three inputs: the risk-free rate of interest (Rf), the beta (ß), and the expected equity or market risk premium [E(Rm) - (Rf)]. Rf is the easiest of the inputs to measure-it is the yield on long-term Treasury bonds. Beta, the measure of systematic risk, is a little more difficult to measure because there are different opinions about what adjustments, if any, should be made to historical betas due to their tendency to regress to 1.0 over time. And finally, an even more difficult input to measure is the expected equity or market risk premium (E(Rm) - (Rf)).
Exhibit DRA-1, Attachment JRW-11 provides DRA's Capital Asset Pricing Model study results.
13.1. The Risk-Free Interest Rate
The yield on long-term U.S. Treasury bonds has usually been viewed as the risk-free rate of interest in the Capital Asset Pricing Model44 in response to a strong economy and increases in energy, commodity, and consumer prices.
According to DRA, in late 2006, long-term interest rates declined to 4.5% as commodity and energy prices declined and inflationary pressures subsided. These rates rebounded to the 5.0% level in the first half of 2007. Ten-year Treasury yields began to decline in mid-2007 at the beginning of the financial crisis, and fell below 3.0% as the housing and sub-prime mortgage crises led to an overall credit crisis and economic recession. These rates bottomed out in December of 2008 and have increased steadily since that time as prospects for an economic recovery have increased.
13.2. DRA's Capital Asset Pricing Model Risk-Free Interest Rate
The U.S. Treasury began to issue the 30-year bond in the early 2000s as the U.S. budget deficit increased. As such, the market has once again focused on its yield as the benchmark for long-term capital costs in the United States. As of June 9, 2009, as shown in Exhibit DRA-1, Page 2 of Attachment JRW-11, the rates on 10- and 30-year U.S. Treasury Bonds were 3.83% and 4.61%, respectively. Given this recent trend of increasing 30-year Treasury yields, DRA asserts that a long-term Treasury rate of 4.75% is reasonable for the future and thus it is its risk-free rate, or Rf, for the Capital Asset Pricing Model.
13.3. Capital Asset Pricing Model Betas
Beta is a measure of the systematic risk of a stock. The market, usually taken to be the Standard & Poor's 500, has a beta of 1.0. A stock with the same price movement as the market also has a beta of 1.0.45 A stock's beta is calculated by a linear regression of a stock's return compared to the market's return.
In estimating an equity cost rate for the proxy group, DRA used the betas from the Value Line Investment Survey. Exhibit DRA-1, Page 3 of Attachment JRW-11 shows that the average beta for the companies in Water and Gas Proxy Groups is 0.78 and 0.67, respectively.
13.4. Alternative Views on Equity Risk Premium
The equity or market risk premium-(E(Rm) - (Rf))-is equal to the expected return on the stock market (e.g., the expected return on the Standard & Poor's 500 (E(Rm)) minus the risk-free rate of interest (Rf). The equity premium is the difference in the expected total return between investing in equities and investing in "safe" fixed-income assets, such as long-term government bonds. However, while the equity risk premium is easy to define conceptually, it is difficult to measure because it requires an estimate of the expected return on the market. None of the Applicants or DRA derived a "risk premium" in the same manner.
DRA argues that its ex ante equity risk premium is appropriate because it is consistent with the expectations of chief financial officers (CFO) as found in a June 2009 CFO survey conducted by CFO Magazine and Duke University, where the expected 10-year equity risk premium was 4.11%. DRA argues its equity risk premium is also consistent with professional forecasters and leading consulting firms, such as McKinsey. (Exhibit DRA-1 at 46-47.)
13.5. DRA's Capital Asset Pricing Models Results
The results of DRA's Capital Asset Pricing Model study46 are:
K = (Rf) + ß * [E(Rm) - (Rf)]
Risk-Free Rate |
Beta |
Equity Risk Premium |
Equity Cost Rate | |
Water Proxy Group |
4.75% |
0.78 |
4.33% |
8.13% |
Gas Proxy Group |
4.75% |
0.67 |
4.33% |
7.65% |
43 In the risk premium model, the cost of equity is the sum of the interest rate on a risk-free bond (Rf) and a risk premium (RP): K = Rf + RP.
44 The 10-year U.S. Treasury yields over the past five years are in Exhibit DRA-1, Page 2 of Attachment JRW-11. These rates hit a 60-year low in the summer of 2003 at 3.33%. They increased with the rebounding economy and fluctuated in the 4.0-4.50 percent range in recent years until advancing to 5.0% in early 2006.
45 A stock whose price movement is greater than that of the market, such as a technology stock, is riskier than the market and has a beta greater than 1.0. A stock with below average price movement, such as that of a regulated public utility, is less risky than the market and has a beta less than 1.0.
46 Exhibit DRA-1, Page 1 of Attachment JRW-11.
