Security Market Line Formula and Graph

Security Market Line Formula and Graph

In the capital asset pricing model, the security market line (SML) is related to the required return and the beta risk. The 2-stock portfolio having ρ>0 is similar to the security market line. There is a direct relationship between beta and required return. For every extra relative risk of stock with the market, the investor demands some extra return against it.

Formula of Security Market Line

rA = rRF + (rM ─ rRF) * βA

In the formula given above, the expected return that the investors desire by investing in that stock (rA).

• Risk-free rate of return (rRF).
• The return of the average stock in the market that an investor requires (rM).
• The stock A’s beta (βA).

(rM ─ rRF)*βA is known as a risk premium. This is the incremental return above the risk-free required rate of return. That is required by the investors against taking extra market risk of a stock.

The risk premium of a stock is based on only the market risk elements of total risk. So, the stock’s market price depends on the required return in an efficient market, which in turn depends on the risk premium. This risk premium finally depends on the market portion of the risk.

Price of Stock in Efficient Market

Efficient market is that market in which there is only one component of total risk i-e market risk. If a new investor desires to buy any new stock, then as he has no portfolio of stocks. This is his first time, so he has to bear both the company specific risk and the market risk of that stock. In order to get compensation for higher risk, he wants the price of the stock to be lower. This is the simple case of a new investor, who buys a stock for the first time.

However, the investor, who maintains a diversified portfolio of different stocks, has already eliminated the company specific risk portion of the total risk. In this case he does not base the market price of a new buying stock on the total risk but only on the market risk portion.

Numerical Example

In the light of the given data, calculate the required rate of return of a stock X.

βX = +3 ( Stock X is three times as risky as the market).

rM = 15%p.a (ROR on the average stock of the market).

rRF = 10% (risk-free rate of return e.g. T-bills).

By using the formula of Security Market Line,

rRF + (rM ─ rRF) * βX = rX

10% + (15% ─ 10%) * 3 = rX

rX = 45%.

Interpretation

From the above answer it is obvious that the investor requires the return of 45% on the stock X. On the other hand the market required rate of return is 15% but the investors ROR is much higher than it. The reason behind this fact is that the beta of the stock is +3. Basically, it means that the stock X is 3 times more risky than the market. Because the market beta is always equal to +1. So, the investor wishes for a higher ROR than the expected ROR of the market. Although, which is unfavorable for the investor to accomplish his goals. Therefore he will not invest in the stock X.

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Security Market Line Graph

 

In the graph the Security Market Line is shown in the efficient market of stocks. The required rate of return (r*) is shown on the y-axis along with the risk-free rate of return. On the x-axis market risk is shown in the form of beta risk. The relationship between required return and market risk is presented through the security market line. The SML originated from the risk-free rate of return and leads to the point of market risk. So, the market beta is 1.0 at this point of SML and the market ROR is 15 %, which is higher than the risk-free ROR.

It means that the average rational investors of the efficient stock market are requiring (15%) return on their new stocks. However, the SML passes further to the top left of the graph. Finally reaches a point where the ROR is 45% which is much higher than the average market ROR. The beta of the stock X is also much higher than the market beta, which reflects that the stock is much risky. At this last point the company specific risk is eliminated and the market risk portion remains. So, the risk premium of the stock X becomes 35 % (45%-10%).

The slope of SML is equal to (rM ─ rRF) / ( βM – 0) = (rM ─ rRF) / 1. It is used to calculate the risk taking tendency of the average investors in the market. The investors are risk averse, which means that they are not willing to take extraordinary risk for any new investment. So if the SML is steeper, then no investor in the efficient market is willing to invest in the specific project or stock.

Note:

The most important point of the SML is that all the stocks in the efficient market fall on the SML. If a stock does not fall on the SML, then it will come back on the SML by the market equilibrium.

There are also certain market forces that push any extraordinary located stock towards the SML. In other words, if a stock is located above the SML, then actually it offers the rate of return against the efficient market stocks. Almost every investor runs toward that stock, because it is offering higher return, which results in the increase of the demand of that stock. This will in turn decrease the return of the stock, which then moves on the SML. If a stock falls below SML, then investors will not buy that stock which in turn increases the demand and finally the return of the stock will increase.