Comparing Securities with the Security Market Line

Comparing an Asset with Its CAPM Benchmark

The security market line (SML) gives the CAPM-required expected return for each level of systematic risk, measured by beta. Comparing an asset with that line is a way to ask whether its expected return appears sufficient for its beta. The key is to compare the asset’s expected return with the CAPM return at the same beta, not with the market return or with another asset’s required return.

This comparison gives a relative-pricing signal under the CAPM framework. An asset whose expected return is above the SML offers more expected return than the model requires for its beta; an asset below the line offers less. That signal depends on the inputs and model assumptions. It is not a guarantee about future performance or a conclusion that holds under every valuation model.

Definition: For a risk-free rate $r_f$, expected market return $E[R_M]$, and asset beta $\beta_j$, the CAPM-required return on asset $j$ is $$ r_j^{\mathrm{CAPM}} = r_f + \beta_j\bigl(E[R_M]-r_f\bigr). $$ The asset’s SML return gap is its estimated expected return minus this CAPM-required return: $$ G_j = E[R_j] - r_j^{\mathrm{CAPM}}. $$ A positive gap places the asset above the SML; a negative gap places it below; a zero gap places it on the line.

The model uses the risk-free rate and the expected return on the market for the same period and in consistent units. The market risk premium is $E[R_M]-r_f$, not $E[R_M]$ by itself. Beta measures sensitivity to market risk: it determines how much of that premium the asset’s CAPM-required return includes. The SML is therefore a graph of CAPM-required expected return against beta, with intercept $r_f$ and slope equal to the market risk premium.

To interpret a comparison, first calculate the required return at the asset’s beta. Then subtract that benchmark from the asset’s own expected return. Keeping this order explicit prevents sign errors: expected return minus required return is positive above the line and negative below it.

How Position on the SML Signals Relative Pricing

In the CAPM equilibrium interpretation, an asset on the SML offers the return required for its systematic risk. An asset above the line offers a higher expected return than required at that beta. If the expected cash flows and beta estimate are reliable, investors may view it as relatively underpriced: demand for it can push its price up, reducing the return available to a new investor. An asset below the line offers less than its CAPM benchmark and may be viewed as relatively overpriced; a lower price would raise its expected return.

These terms are relative to the CAPM benchmark. “Underpriced” does not mean that an asset must rise in price, and “overpriced” does not mean that it must fall. The market may revise its expectations, the beta estimate may be wrong, or the CAPM may not describe the asset’s required return well. The comparison is a model-based assessment, not a certain forecast.

Position	Return comparison	CAPM relative-pricing interpretation
Above the SML	$E[R_j] > r_j^{\mathrm{CAPM}}$, so $G_j > 0$	Relatively underpriced, if the inputs and CAPM benchmark are appropriate
On the SML	$E[R_j] = r_j^{\mathrm{CAPM}}$, so $G_j = 0$	Consistent with CAPM pricing at that beta
Below the SML	$E[R_j] < r_j^{\mathrm{CAPM}}$, so $G_j < 0$	Relatively overpriced, if the inputs and CAPM benchmark are appropriate

Why a Higher Price Reduces the Expected Return

The price interpretation follows from the relationship between the price paid now and the cash flows expected over the holding period. Consider a one-period investment with current price $P_0$, expected end-of-period distribution $E[D_1]$, and expected end-of-period price $E[P_1]$. Assume the expected cash flows are fixed and $P_0$ is positive. The expected holding-period return is

E[R] = \frac{E[D_1]+E[P_1]-P_0}{P_0} = \frac{E[D_1]+E[P_1]}{P_0}-1.

Writing $K=E[D_1]+E[P_1]$, the expected return is $K/P_0-1$. If $K>0$, its sensitivity to the current price is

\frac{\partial E[R]}{\partial P_0} = -\frac{K}{P_0^2} < 0.

Thus, with expected cash flows held fixed, a higher purchase price reduces the expected return, while a lower purchase price raises it. This explains the direction of the usual SML pricing interpretation. It does not establish that the price will adjust as predicted: the expected cash flows, beta, or market inputs could change instead. This relationship also should not be applied without qualification when the cash-flow assumptions or investment structure differ.

Worked Comparisons

Worked Example: An Asset Above the SML

A hypothetical infrastructure fund has beta $1.20$ and an estimated expected annual return of $11.40\%$. For the same annual horizon, assume a risk-free rate of $3.40\%$ and an expected market return of $9.40\%$. Determine its CAPM-required return, its position relative to the SML, and the relative-pricing interpretation. Use the same return basis for all rates.

Method. Calculate the market risk premium, apply CAPM at the fund’s beta, and subtract the required return from the estimated expected return.

First, the market risk premium is $9.40\%-3.40\%=6.00\%$. The CAPM-required return is therefore

r_j^{\mathrm{CAPM}} =3.40\%+1.20(6.00\%) =3.40\%+7.20\% =10.60\%.

The fund’s SML return gap is $11.40\%-10.60\%=0.80$ percentage points. The gap is positive, so the fund is above the SML at beta $1.20$. Under the CAPM interpretation, it offers $0.80$ percentage points more expected return than required for its systematic risk and appears relatively underpriced, conditional on the estimates and model being suitable.

Check. Substituting beta $1.20$ into the SML gives $10.60\%$; the stated expected return of $11.40\%$ is higher by exactly $0.80$ percentage points. The comparison is at the same beta, as required.

Common mistake avoided. Do not treat $11.40\%$ as a guaranteed future return. It is the stated expected-return estimate being compared with a model-required benchmark.

Worked Example: Comparing Two Securities with Equal Beta

An analyst evaluates two hypothetical renewable-energy securities, A and B. Each has beta $0.75$. Their estimated expected annual returns are $10.00\%$ for A and $7.50\%$ for B. Assume $r_f=4.00\%$ and $E[R_M]=10.00\%$ for the same annual horizon. Calculate the benchmark and gap for each security, then compare their relative-pricing signals.

Method. Because the securities have equal beta, calculate their shared CAPM-required return once. Then compare each expected return with that common benchmark.

The market risk premium is $10.00\%-4.00\%=6.00\%$. For either security,

r^{\mathrm{CAPM}} =4.00\%+0.75(6.00\%) =4.00\%+4.50\% =8.50\%.

For A, the gap is $10.00\%-8.50\%=+1.50$ percentage points. A is above the SML and has the stronger positive relative-pricing signal. For B, the gap is $7.50\%-8.50\%=-1.00$ percentage point. B is below the SML and has a negative relative-pricing signal. Both calculations use the same beta-specific benchmark; comparing either security directly with the market return of $10.00\%$ would answer a different question.

Check. A’s expected return exceeds the common benchmark by $1.50$ percentage points, while B’s falls short by $1.00$ percentage point. The difference between their expected returns is $10.00\%-7.50\%=2.50$ percentage points, which also equals the difference between their gaps because their required returns are equal.

Common mistake avoided. Equal beta means equal CAPM-required returns when the same $r_f$ and market risk premium apply. It does not mean the two securities have equal expected returns or equal pricing signals.

Worked Example: Comparing Assets on Opposite Sides of the SML

A hypothetical insurer is reviewing two investment candidates. Asset C has beta $1.50$ and an estimated expected annual return of $10.20\%$. Asset D has beta $-0.25$ and an estimated expected annual return of $2.00\%$. Assume an annual risk-free rate of $2.00\%$ and an expected annual market return of $8.00\%$. Determine each CAPM-required return and position. Which asset has the larger positive gap?

Method. Calculate the common market risk premium, apply the SML separately at each beta, and compare each estimated expected return with its own required return.

The market risk premium is $8.00\%-2.00\%=6.00\%$. For C,

r_C^{\mathrm{CAPM}} =2.00\%+1.50(6.00\%) =2.00\%+9.00\% =11.00\%.

C’s gap is $10.20\%-11.00\%=-0.80$ percentage points, so C is below the SML. For D,

r_D^{\mathrm{CAPM}} =2.00\%+(-0.25)(6.00\%) =2.00\%-1.50\% =0.50\%.

D’s gap is $2.00\%-0.50\%=+1.50$ percentage points, so D is above the SML. D has the larger positive gap; C’s gap is negative. A negative beta gives a CAPM-required return below the risk-free rate when the market risk premium is positive. That result follows from the SML equation and does not, by itself, imply a calculation error.

Check. The estimated return for C is $0.80$ percentage points below its $11.00\%$ benchmark; D’s is $1.50$ percentage points above its $0.50\%$ benchmark. The two assets must be assessed at their own betas, not against one another’s required returns.

Common mistake avoided. Do not replace the negative beta with its absolute value. Doing so would change D’s required return from $0.50\%$ to $3.50\%$ and reverse the comparison.

A Reliable Comparison Procedure

A compact procedure helps keep the benchmark, sign, and interpretation aligned. Use it when several securities have different betas or when a problem gives percentages in different forms.

Check the inputs.
Confirm that the risk-free rate and expected market return refer to the same period and use consistent units. Identify each asset’s beta and estimated expected return.

Find the market risk premium.
Subtract the risk-free rate from the expected market return: $E[R_M]-r_f$. Do not use the market return alone as the premium.

Calculate the asset’s SML return.
Use $r_j^{\mathrm{CAPM}}=r_f+\beta_j(E[R_M]-r_f)$ with that asset’s own beta.

Calculate and interpret the gap.
Subtract the required return from the estimated expected return. A positive result is above the line, a negative result is below, and zero is on it.

State the qualification.
Describe the result as a CAPM-based relative-pricing signal, conditional on the estimates and model assumptions, rather than a certain prediction.

Common Traps and Model Limits

A frequent error is to multiply beta by the expected market return rather than by the market risk premium. For example, with $r_f=3.00\%$, $E[R_M]=9.00\%$, and $\beta=1.20$, the incorrect calculation $1.20(9.00\%)=10.80\%$ treats the full market return as compensation for systematic risk. CAPM instead gives

r_j^{\mathrm{CAPM}} =3.00\%+1.20(9.00\%-3.00\%) =3.00\%+7.20\% =10.20\%.

If the estimated expected return were $10.50\%$, the incorrect benchmark would produce a gap of $10.50\%-10.80\%=-0.30$ percentage points and incorrectly place the asset below the SML. The correct gap is $10.50\%-10.20\%=+0.30$ percentage points, placing it above. The risk-free return is the SML intercept; beta scales the market risk premium, not the entire expected market return.

Mixing return periods. An annual market return cannot be combined directly with a monthly risk-free rate without converting to a consistent basis.
Reversing the subtraction. The defined gap is expected return minus CAPM-required return. Reversing it reverses the above-or-below interpretation.
Comparing with the wrong benchmark. The market return is the SML return only at beta $1$. For another beta, calculate the required return at that beta.
Overstating the conclusion. A positive or negative gap is conditional on the estimated expected return, beta, market premium, and CAPM being appropriate. It does not guarantee a price change.

The SML comparison is useful for organizing a valuation judgment, comparing candidate investments, and identifying which assumption drives a conclusion. The calculation is only as dependable as its inputs: changes in beta or the market risk premium change the required return, while revisions to expected cash flows can change the asset’s estimated expected return. When either estimate is uncertain, the apparent distance from the line should be interpreted cautiously.

Key takeaway: Calculate the CAPM-required return at the asset’s own beta, then subtract that benchmark from the asset’s estimated expected return. A positive gap is above the SML, a negative gap is below it, and either pricing interpretation is conditional on the CAPM inputs and assumptions.

Check Your Understanding

For each problem, use the supplied CAPM inputs and compare the estimated expected return with the required return at the same beta.

A hypothetical asset has beta $0.50$, an estimated expected annual return of $7.40\%$, a risk-free rate of $3.00\%$, and an expected market return of $9.00\%$. Calculate its required return and identify its position relative to the SML. (Answer: Required return $6.00\%$; gap $+1.40$ percentage points; above the SML.)
A security has beta $1.10$ and an estimated expected annual return of $10.80\%$. The annual risk-free rate is $4.50\%$, and the expected market return is $10.50\%$. Determine its required return and relative-pricing signal. (Answer: Required return $11.10\%$; gap $-0.30$ percentage points; below the SML.)
Two hypothetical assets each have beta $0.80$. Their expected annual returns are $8.40\%$ and $6.90\%$. If $r_f=2.00\%$ and $E[R_M]=8.00\%$, calculate the common required return and both gaps. (Answer: Required return $6.80\%$; gaps $+1.60$ and $+0.10$ percentage points; both are above the SML.)
An asset has beta $-0.50$ and an estimated expected annual return of $4.20\%$. Given $r_f=5.00\%$ and $E[R_M]=8.00\%$, calculate its required return and gap. (Answer: Required return $3.50\%$; gap $+0.70$ percentage points; above the SML.)
Asset E has beta $0.60$ and an estimated expected annual return of $6.10\%$. Asset F has beta $1.40$ and an estimated expected annual return of $10.00\%$. If $r_f=2.50\%$ and $E[R_M]=8.50\%$, calculate each benchmark and state which asset is on the line. (Answer: E’s required return is $6.10\%$, so E is on the SML; F’s required return is $10.90\%$, so F has a $-0.90$-percentage-point gap and is below it.)

Position	Return comparison	CAPM relative-pricing interpretation
Above the SML	\(E[R_j] > r_j^{\mathrm{CAPM}}\), so \(G_j > 0\)	Relatively underpriced, if the inputs and CAPM benchmark are appropriate
On the SML	\(E[R_j] = r_j^{\mathrm{CAPM}}\), so \(G_j = 0\)	Consistent with CAPM pricing at that beta
Below the SML	\(E[R_j] < r_j^{\mathrm{CAPM}}\), so \(G_j < 0\)	Relatively overpriced, if the inputs and CAPM benchmark are appropriate

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