# the slope of the capm is beta or risk premium?

Page 223 book 5 says that the slope of the CML is the sharpe ratio and the slope of the SML is the market risk premium. I always thought that the slope of the SML is the beta. E® = rfr + b[E(Rm) - rfr] ---- can anyone confirm that the slope is the market risk premium and not beta? I am doubtful because in quant we learned that the coefficient of the indendepent variable = slope = beta (You can see Schweser Exam 2 #13 where they calculate the CAPM by using the coefficient of the independent variable Rm as the beta). This would make beta the slope. Unless I am mixing up topics.

SML: The independent variable is beta and the slope is rm-rf, intercept is rf.

cpk, would you mind taking a look at #13 in exam 2. the Q asks to calculate the required return and the answer says “the beta of 1.04 is estimated from the slope coefficient on the independent variable from the regression.” they are using the SLOPE coefficient of 1.04 as the beta in the capm. or is this slope coefficent not really a slope in the sense of a line on a graph

schweser exam 2 AM in Book 1?

slope of SML is mkt risk premium (systematic risk only) slope of CML/CAL is sharpe ratio (systematic+unsystematic risk)

yes sir. page 78.

Remember you estimate beta based on regression done on market risk premium. so I’d think the slope is Beta. However I’ve noticed PM is just not worth the time. lol.

chowder, what u say agrees completey with the chart that schweser puts in PM. but like i said before, the quant section and particularly that exam Q tells us that the slope coefficient of the independent variable is the slope of the single regression equation. that would make the slope = beta

This regression is the market model - not the CAPM. and yes - market model slope is the Beta - and RM is the independent variable.

regarding the market model Rm is it equity risk premium or not? because Treynor black formula is almost exactly the same if it is… thanks

RM is not Market Risk Premium, it is the Return on the Market.

the exam question says “The required return on equity (according to the CAPM) for O’Connor is closest to:” it is referring to CAPM. it then goes into the ANOVA table, pulls out the coefficient for the independent variable Rm, and tells us in the answer that this is the beta.

that is correct. Market Model: is ri = alphai + betai * RMarket this is a linear regression with alphai being the intercept, betai the slope, rMarket the independent variable and ri the dependent. that is what they used on the quant model they provided you. S&P 500 is your proxy for the Market. – read the passage at the bottom of pg 76 which lays this all out for you.

ahh just caught that on the bottom of 76 where they actually write out the market model. thank you for the help. so two quick followups. 1. they are using the anova table to find the beta for the market model (in which the beta is the slope) but then they are using that same beta to find the capm reuired return (the beta is not the slope in this model but it can still be used). correct? 2. what is exactly meant by the alpha intercept? i saw it in the fundamental model as well. i know its the value of the return when the RMarket is zero, but is there anything you can add to make it more intutive? thanks again.

SML and CML and CAPM are all a little confusing. Here’s some help. SML is used for finding E® of individual assets based on the level of systematic risk (i.e. risk that is correlated with market movements). The line is defined by the RFR return on the y-axis and the return on the market at Beta=1 (because the market has a beta of 1 relative to itself). That means the slope of the SML is (R_mkt - RFR) / (1-0) = (R_mkt - RFR) = Market Risk Premium. The CML is the set of optimal portfolios that you conclude from CAPM’s assumptions. It is easy to confuse with the SML because it also goes through the RFR return on the y-axis and the market portfolio on the chart. However, the x-axis is measured in terms of risk (typically total portfolio SD), so the slope is (R_mkt - RFR) / (SD(mkt) - 0) = (R_mkt - RFR) / SD(mkt) = Sharpe Ratio of the market portfolio. The chart containing the CML represents the risk and return of PORTFOLIOS of assets, and concludes that the only portfolios worth holding are combinations of the RFR and the market portfolio, and those are all portfolios that fall along the CML. Other portfolios can be plotted on the chart, but they all lie below the CML if CAPM’s assumptions hold. It is possible to hold portfolios with just one asset in them, so you can plot individual assets on the same chart, and it is common to do that. However, doing so makes it easy to forget that the chart is about portfolio returns, and not really about the returns on single assets. One reason why CAPM is easy to confuse with the CML is because the CBOK has been busy telling you that you use CAPM to estimate required returns on equity, when in fact you are really using the SML to do it. Technically, they’re not lying because CAPM is the set of assumptions that implies that you can use the SML to get K_e, but the formula that you use is in fact the SML, when you’re computing cost of equity. If you can separate CAPM the theory about optimal portfolios to hold vs. CAPM the set of assumptions that tell you you can use the SML to estimate required returns, it may be easier to absorb that part of portfolio management.

>That means the slope of the SML is (R_mkt - RFR) / (1-0) = (R_mkt - RFR) = Market Risk Premium. yes, that was what I was about to reply to as the source of the confusion above, not that I’m not confused about a ton of things in the SS.

so both sml and cml rely on capm theory, but sml uses capm assumptions for the plot?