Which one of the following is represented by the slope of the security market line
options:
a. market standard deviation
b. beta coefficient
c. risk-free interest rate
d. market risk premium
The correct answer and explanation is:
The correct answer is d. market risk premium.
The Security Market Line (SML) is a graphical representation of the Capital Asset Pricing Model (CAPM), which illustrates the relationship between the expected return of an asset and its risk (measured by beta). The SML shows how much return an investor can expect for taking on a particular amount of risk, with risk measured by beta, which represents the sensitivity of an asset’s returns to the overall market returns.
The slope of the Security Market Line is the market risk premium. This is the difference between the expected return on the market (Rm) and the risk-free rate (Rf). The market risk premium represents the additional return an investor expects to earn for taking on the risk of investing in the market, as opposed to investing in a risk-free asset. Mathematically, the market risk premium is expressed as: Market Risk Premium=Rm−Rf\text{Market Risk Premium} = R_m – R_f
The slope of the SML reflects how much additional return an investor expects for each unit of market risk (beta). A steeper slope indicates that the market is offering higher returns for additional risk, and a flatter slope suggests lower returns for additional risk.
In the context of the CAPM, the formula for the expected return of an asset is: Ri=Rf+βi(Rm−Rf)R_i = R_f + \beta_i (R_m – R_f)
Where:
- Ri is the expected return of the asset.
- Rf is the risk-free rate.
- βi is the beta of the asset.
- Rm is the expected return of the market.
In this formula, the market risk premium (Rm – Rf) is the amount by which the return on the market exceeds the risk-free rate, and the slope of the SML corresponds to this premium.