

The security market line ("SML" or "characteristic line") graphs the systematic (or market) risk versus the return of the whole market at a certain time and shows all risky marketable securities. The SML essentially graphs the results from the capital asset pricing model (CAPM) formula. The xaxis represents the risk (beta), and the yaxis represents the expected return. The market risk premium is determined from the slope of the SML.
The security market line is a useful tool for determining whether 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 because the investor can expect a greater return for the inherent risk. A security plotted below the SML is overvalued because the investor would be accepting less return for the amount of risk assumed. Expected values for the SML are calculated with the following equation:
Where: r_{f} = the riskfree rate
B_{s} = the beta of the investment
E_{mkg} = the expected return of the market
E_{s} = the expected return of the investment
The beta is thus the sensitivity of the investment to the market or current portfolio. It is the measure of the riskiness of a project. When taken in isolation, a project may be considered more or less risky than the current risk profile of a company. By using the SML as a means to calculate a company's WACC, this risk profile would be accounted for.
Example:
When a new product line for Newco is considered, the project's beta is 1.5. Assuming the riskfree rate is 4% and the expected return on the market is 12%, compute the cost of equity for the new product line.
Answer:
Cost of equity = r_{f} + B_{s}(E_{mkt}  r_{f}) = 4% + 1.5(12%  4%) = 16%
The project's required return on retained earnings is therefore 16%, a number which should be used in our calculation of weighted average cost of capital (WACC).
Estimating Beta
In risk analysis, estimating the beta of a project is quite important. But like many estimations, it can be difficult to determine.
The two most widely used methods of estimating beta are:
1. Pureplay method
2. Accountingbeta method
1. PurePlay Method
When using the pureplay method, a company seeks out companies with a product line that is similar to the line for which the company is trying to estimate the beta. Once these companies are found, the company would then take an average of those betas to determine its project beta.
Suppose Newco would like to add beer to its existing product line of soda. Newco is quite familiar with the beta of making soda given its history. However, determining the beta for beer is not as intuitive since Newco as it has never produced it.
To determine the beta of the new beer project, Newco can take the average beta of other beer makers, such as AnheuserBusch and Molson Coors.
2. AccountingBeta Method
When using the accountingbeta method, a company would run a regression using the company's return on assets (ROA) against the ROA for market benchmark, such as the S&P 500. The accounting beta is the slope coefficient of the regression.
The typical procedure for developing a riskadjusted discount rate is as follows:
1. A company first begins with its cost of capital for the firm.
2. The cost of capital then must be adjusted for the riskiness of the project, by adjusting the company's cost of capital either up or down depending on the risk of the project relative to the firm.
For projects that are riskier, the company's WACC would be adjusted higher, and if the project is less risky, the company's WACC is adjusted lower. The main issue in this procedure is that it is subjective.
Capital Rationing
Essentially, capital rationing is the process of allocating the company's capital among projects to maximize shareholder return.
When making decisions to invest in positive netpresentvalue (NPV) projects, companies continue to invest until their marginal returns equal their marginal cost of capital. There are times, however, when a company may not have the capital to do this. As such, a company must ration its capital among the best combination of projects with the highest total NPV.
Risk Premium
At its most basic level, risk premium is the return in excess of the riskfree rate of return that an investment is expected to yield. An asset's risk premium is a form of compensation for investors who tolerate the extra risk in a given investment compared to that of a riskfree asset.
Think of a risk premium as a form of hazard pay for your investments. Just as employees who work in relatively dangerous jobs receive hazard pay as compensation for the risks they undertake, risky investments must provide an investor with the potential for larger returns to warrant taking on the additional liability.
For example, highquality corporate bonds issued by established corporations earning large profits have very little risk of default. Therefore, such bonds will pay a lower interest rate (or yield) than bonds issued by lessestablished companies with uncertain profitability and relatively higher default risk.
Market Risk Premium
Market risk premium is the difference between the expected return on a market portfolio and the riskfree rate. Market risk premium is equal to the slope of the security market line (SML). Three distinct concepts are part of market risk premium:
1) Required market risk premium is the return of a portfolio over the riskfree rate (such as that of treasury bonds) required by an investor;
2) Historical market risk premium is the historical differential return of the market over Treasury bonds; and
3) Expected market risk premium is the expected differential return of the market over Treasury bonds.
The historical market risk premium will be the same for all investors since the value is based on what actually happened. The required and expected market premiums, however, will differ from investor to investor based on risk tolerance and investing styles. The market risk premium can be calculated as follows:
Market Risk Premium = Expected Return of the Market – RiskFree Rate
The expected return of the market can be based on the S&P 500, for example, while the riskfree rate is often based on the current returns of treasury bonds.
The Equity Risk Premium: More Risk for Higher Returns
In theory, stocks should provide a greater return than safe investments like Treasury bonds. The difference is called the equity risk premium: the excess return that you can expect from the overall market above a riskfree return. There is vigorous debate among experts about the method employed to calculate the equity premium and, of course, the resulting answer. In this section, we take a look at these methods  particularly the popular supplyside model  and the debates surrounding equity premium estimates.
Why Does It Matter?
The equity premium helps to set portfolio return expectations and determine asset allocation policy. A higher premium, for instance, implies that you would invest a greater share of your portfolio into stocks. Also, the capital asset pricing relates a stock's expected return to the equity premium; a stock that is riskier than the market  as measured by its beta  should offer excess return above the equity premium.
Greater Expectations
Compared to bonds, we expect extra return from stocks due to the following risks:
But history is one thing, and what we really want to know is tomorrow's equity premium. Specifically, how much of a premium above a safe investment should we expect for the stock market going forward? Academic studies tend to arrive at lower equity risk premium estimations  in the neighborhood of 23%, or even lower! Later in this article, we'll explain why this is always the conclusion of an academic study, whereas money managers often point to recent history and arrive at higher estimations of premiums.
Getting at the Premium
Here are the four ways to estimate the future equity risk premium:
What a range of outcomes! Opinion surveys naturally produce optimistic estimates, as do extrapolations of recent market returns. But extrapolation is a dangerous business: first, it depends on the time horizon selected, and second, we cannot know that history will repeat itself. Professor William Goetzmann of Yale has cautioned, "History, after all, is a series of accidents; the existence of the time series since 1926 might itself be an accident." For example, one widely accepted historical accident concerns the abnormally low longterm returns to bondholders that started right after World War II (and subsequently low bond returns increased the observed equity premium). Bond returns were low in part because bond buyers in the 1940s and 1950s  misunderstanding government monetary policy  clearly did not anticipate inflation.
Building A SupplySide Model
The security market line is a useful tool for determining whether 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 because the investor can expect a greater return for the inherent risk. A security plotted below the SML is overvalued because the investor would be accepting less return for the amount of risk assumed. Expected values for the SML are calculated with the following equation:
E_{s} = r_{f} + B_{s}(E_{mkt}  r_{f}) 
Where: r_{f} = the riskfree rate
B_{s} = the beta of the investment
E_{mkg} = the expected return of the market
E_{s} = the expected return of the investment
The beta is thus the sensitivity of the investment to the market or current portfolio. It is the measure of the riskiness of a project. When taken in isolation, a project may be considered more or less risky than the current risk profile of a company. By using the SML as a means to calculate a company's WACC, this risk profile would be accounted for.
Example:
When a new product line for Newco is considered, the project's beta is 1.5. Assuming the riskfree rate is 4% and the expected return on the market is 12%, compute the cost of equity for the new product line.
Answer:
Cost of equity = r_{f} + B_{s}(E_{mkt}  r_{f}) = 4% + 1.5(12%  4%) = 16%
The project's required return on retained earnings is therefore 16%, a number which should be used in our calculation of weighted average cost of capital (WACC).
Estimating Beta
In risk analysis, estimating the beta of a project is quite important. But like many estimations, it can be difficult to determine.
The two most widely used methods of estimating beta are:
1. Pureplay method
2. Accountingbeta method
1. PurePlay Method
When using the pureplay method, a company seeks out companies with a product line that is similar to the line for which the company is trying to estimate the beta. Once these companies are found, the company would then take an average of those betas to determine its project beta.
Suppose Newco would like to add beer to its existing product line of soda. Newco is quite familiar with the beta of making soda given its history. However, determining the beta for beer is not as intuitive since Newco as it has never produced it.
To determine the beta of the new beer project, Newco can take the average beta of other beer makers, such as AnheuserBusch and Molson Coors.
2. AccountingBeta Method
When using the accountingbeta method, a company would run a regression using the company's return on assets (ROA) against the ROA for market benchmark, such as the S&P 500. The accounting beta is the slope coefficient of the regression.
The typical procedure for developing a riskadjusted discount rate is as follows:
1. A company first begins with its cost of capital for the firm.
2. The cost of capital then must be adjusted for the riskiness of the project, by adjusting the company's cost of capital either up or down depending on the risk of the project relative to the firm.
For projects that are riskier, the company's WACC would be adjusted higher, and if the project is less risky, the company's WACC is adjusted lower. The main issue in this procedure is that it is subjective.
Capital Rationing
Essentially, capital rationing is the process of allocating the company's capital among projects to maximize shareholder return.
When making decisions to invest in positive netpresentvalue (NPV) projects, companies continue to invest until their marginal returns equal their marginal cost of capital. There are times, however, when a company may not have the capital to do this. As such, a company must ration its capital among the best combination of projects with the highest total NPV.
Risk Premium
At its most basic level, risk premium is the return in excess of the riskfree rate of return that an investment is expected to yield. An asset's risk premium is a form of compensation for investors who tolerate the extra risk in a given investment compared to that of a riskfree asset.
Think of a risk premium as a form of hazard pay for your investments. Just as employees who work in relatively dangerous jobs receive hazard pay as compensation for the risks they undertake, risky investments must provide an investor with the potential for larger returns to warrant taking on the additional liability.
For example, highquality corporate bonds issued by established corporations earning large profits have very little risk of default. Therefore, such bonds will pay a lower interest rate (or yield) than bonds issued by lessestablished companies with uncertain profitability and relatively higher default risk.
Market Risk Premium
Market risk premium is the difference between the expected return on a market portfolio and the riskfree rate. Market risk premium is equal to the slope of the security market line (SML). Three distinct concepts are part of market risk premium:
1) Required market risk premium is the return of a portfolio over the riskfree rate (such as that of treasury bonds) required by an investor;
2) Historical market risk premium is the historical differential return of the market over Treasury bonds; and
3) Expected market risk premium is the expected differential return of the market over Treasury bonds.
The historical market risk premium will be the same for all investors since the value is based on what actually happened. The required and expected market premiums, however, will differ from investor to investor based on risk tolerance and investing styles. The market risk premium can be calculated as follows:
Market Risk Premium = Expected Return of the Market – RiskFree Rate
The expected return of the market can be based on the S&P 500, for example, while the riskfree rate is often based on the current returns of treasury bonds.
The Equity Risk Premium: More Risk for Higher Returns
In theory, stocks should provide a greater return than safe investments like Treasury bonds. The difference is called the equity risk premium: the excess return that you can expect from the overall market above a riskfree return. There is vigorous debate among experts about the method employed to calculate the equity premium and, of course, the resulting answer. In this section, we take a look at these methods  particularly the popular supplyside model  and the debates surrounding equity premium estimates.
Why Does It Matter?
The equity premium helps to set portfolio return expectations and determine asset allocation policy. A higher premium, for instance, implies that you would invest a greater share of your portfolio into stocks. Also, the capital asset pricing relates a stock's expected return to the equity premium; a stock that is riskier than the market  as measured by its beta  should offer excess return above the equity premium.
Greater Expectations
Compared to bonds, we expect extra return from stocks due to the following risks:
 Dividends can fluctuate, unlike predictable bond coupon payments.
 When it comes to corporate earnings, bond holders have a prior claim while common stock holders have a residual claim.
 Stock returns tend to be more volatile (although this is less true the longer the holding period).
But history is one thing, and what we really want to know is tomorrow's equity premium. Specifically, how much of a premium above a safe investment should we expect for the stock market going forward? Academic studies tend to arrive at lower equity risk premium estimations  in the neighborhood of 23%, or even lower! Later in this article, we'll explain why this is always the conclusion of an academic study, whereas money managers often point to recent history and arrive at higher estimations of premiums.
Getting at the Premium
Here are the four ways to estimate the future equity risk premium:
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