Security Market Line

CAPM says an asset should earn the risk-free rate plus a reward for its systematic risk, measured by beta. Draw that relationship as a line and you have the Security Market Line.

The workbook calls it the graphical representation of CAPM: it depicts the relationship between systematic risk and expected rate of return on an asset traded in the capital market.

Its use is practical. Find a security's beta on the horizontal axis, go straight up to the line, and read off the return the security should offer. Then compare that with what the analyst actually expects it to return. If the forecast is higher than the line, the security is cheap. If lower, it is expensive.

The equation is CAPM:

E(Ri) = Rf + βi × (E(Rm) − Rf)

The workbook's first example. Where the average risk-free rate is 6% and the market portfolio has returned 20%, the market's excess return is 20 − 6 = 14%. With an ongoing risk-free rate of 8% and a beta of 1.5:

8% + (1.5 × 14%) = 29%

— the expected return under perfect market and equilibrium conditions.

Spotting mispricing. Theoretically, under market equilibrium, all assets and all portfolios should plot on the SML. So:

• a security whose estimated return plots above the SML is undervalued — it offers more than its systematic risk warrants;
• one that plots below is overvalued.

The workbook's second example: beta 1.2, Rf 8%, Rm − Rf 14% gives a required 24.8%. If the stock is expected to generate 26%, it plots above the line and is undervalued.

SML versus CML. The CML plots standard deviation and holds only efficient portfolios. The SML plots beta and holds every security and portfolio, efficient or not — because under CAPM only systematic risk is priced.

E(Ri) = Rf + βi × (E(Rm) − Rf)

βi = Cov(i,m) ÷ σ²m

Alpha (distance from the line) = Forecast return − E(Ri)

A Category III AIF analyst has Rs 25 lakh to place in one of two stocks, using the workbook's market inputs — Rf = 8%, Rm − Rf = 14%:

Stock C's beta and 26% forecast are the workbook's; Stock D's figures are illustrative.

In rupees, on Rs 25 lakh for a year:

Stock C: required Rs 6.20 lakh, forecast Rs 6.50 lakh  → Rs 30,000 above what its risk warrants
Stock D: required Rs 4.80 lakh, forecast Rs 4.25 lakh  → Rs 55,000 short of what its risk warrants

D has the lower beta and the lower forecast, which is fine — lower risk should earn less. The problem is that it earns less than even its lower risk warrants. C is the buy; D is a candidate to avoid or short.

Note what the SML does not tell you: whether C is a good stand-alone holding. Its total risk might be high. The SML only prices the market-related part.

Chapter 3, section 3.14, defines the SML with the 29% and 24.8% worked examples, and Exhibit 3.7 shows securities C (undervalued, above) and D (overvalued, below). Section 3.12.1 warns that a wrong market proxy shifts the position and slope of the SML. Expect a CAPM calculation, an above/below-the-line judgement, and the SML-versus-CML distinction.

• Above the SML = undervalued. Below = overvalued. The instinct to read "above the line" as "too high a price" is backwards — it means too high a return for the risk, so the price is too low.
• SML uses beta (systematic risk); CML uses standard deviation (total risk).
• All securities and portfolios plot on the SML in equilibrium, not only efficient portfolios.
• The market portfolio sits at beta 1 on the SML, earning Rm.
• Workbook arithmetic slip: section 3.13 says a beta of 0.80 means a 10% fall in the market leads to a 15% decline in the stock. At beta 0.80 it is an 8% decline; 15% is the beta-1.50 figure from the sentence before. Use beta × market move.
• The SML's position depends on the market proxy. A different index can move a stock from above to below the line.