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10. The Capital Asset Pricing Model and the security market line

Keith holds a portfolio that is invested equally in three stocks (wDwD = wAwA = wIwI = 1/3). Each stock is described in the following table:

Stock	Beta	Standard Deviation	Expected Return
DET	0.7	25%	8.0%
AIL	1.0	38%	10.0%
INO	1.6	34%	13.5%

An analyst has used market- and firm-specific information to make expected return estimates for each stock. The analysts expected return estimates may or may not equal the stocks required returns.

The risk-free rate [rRFrRF] is 6%, and the market risk premium [RPMRPM] is 4%. Use the following graph with the security market line (SML) to plot each stocks beta and expected return. (Note: Click on the points on the graph to see their coordinates.)

Your AnswerStock DETStock AILStock INO00.20.40.60.81.01.21.41.61.82.020181614121086420RATE OF RETURN (Percent)RISK (Beta)

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The SML graphs the relationship between an assets beta and its required return. The risk-free rate [rRFrRF] is the vertical intercept of the SML, and the market risk premium [RPMRPM] is the slope of the SML. You can plot the SML on the graph by using this information. The risk-free rate is 6%, so the vertical intercept of the SML is (0, 6). The market risk premium is 4%, so the slope of the SML must be 4. You can solve for another point on the SML by using the Capital Asset Pricing Model (CAPM) equation and solving for the required return when the beta equals 1.0, as follows:

riri	= =	rRF + bi(RPM)rRF + bi(RPM)
	= =	6.0% + 1.0(4.0%)6.0% + 1.0(4.0%)
	= =	10.0%10.0%

So another point on the SML is (1, 10), which is interpreted to mean that a stock with a beta equal to 1.0 will have a required return of 10%.

To plot the stock on the graph, drag each stocks marker onto the graph and place it at the point that corresponds to the stocks indicated beta and expected return. For instance, stock DETs marker (orange square) is placed at (0.7, 8.0), stock AILs marker (green triangle) is placed at (1.0, 10.0), and stock INOs marker (purple diamond) is placed at (1.6, 13.5).

A stock is in equilibrium if its required returnequals its expected return. In general, assume that markets and stocks are in equilibrium (or fairly valued), but sometimes investors have different opinions about a stocks prospects and may think that a stock is out of equilibrium (either undervalued or overvalued). Based on the analysts expected return estimates, stock INO isin equilibrium , stock AIL is in equilibrium, and stock DET isundervalued .

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Stock INOs expected return is 13.5%. Use the CAPM to find its required return as follows:

riri	= =	rRF + bi(RPM)rRF + bi(RPM)
	= =	6.0% + 1.6(4.0%)6.0% + 1.6(4.0%)
	= =	12.4%12.4%

Here is one way to think about the issue: Investors in the market require a return of 12.4% for holding stock INO, but this analyst believes that the stock actually will return 13.5%. By the analysts estimate, it sounds as if the stock is quite a bargain. You require only a 12.4% return, but you expect to get a 13.5% return instead; it sounds as if the stock is undervalued. You can see this on the graph, because at a beta of 1.6, the expected return (13.5%) is greater than the required return (shown by the SML). In fact, any asset that plots on this graph above the SML is thought to be undervalued, whereas assets below the SML are thought to be overvalued. An asset lying directly on the SML is said to be in equilibrium.

Stock AILs required return can be calculated as follows:

rArA	= =	6.0% + 1.0(4.0%)6.0% + 1.0(4.0%)
	= =	6.0% + 4.0% = 10.0%6.0% + 4.0% = 10.0%

Stock DETs required return can be calculated as follows:

rDrD	= =	6.0% + 0.7(4.0%)6.0% + 0.7(4.0%)
	= =	6.0% + 2.8% = 8.8%6.0% + 2.8% = 8.8%

Compare the stocks required returns with their expected returns. Stock AIL is fairly valued, because its required and expected returns are equal (10.0%). Stock DET is overvalued, because its required return (8.8%) is greater than its expected return (8.0%). The graph verifies these conclusions. Stock AIL lies on the SML, stock INO lies above the SML, and stock DET lies below it.

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