What Is Market Risk Premium?
The market risk premium is the premium return an investor must obtain to ensure they may invest in a stock, bond, or portfolio instead of risk-free assets.
It is computed by subtracting the expected return of the market and the risk-free rate. This formula originates from the risk premium formula:
Risk Premium = E(R) – Risk-Free Rate
Where E(R) is the anticipated return of a particular stock, market expectations will be considered when it comes to the whole market.
Moreover, it is the higher return on the portfolio due to the additional risk involved in the portfolio, such as the higher return on the portfolio due to the additional risk involved in the portfolio.
This idea is based on the capital asset portfolio model (CAPM) model, which measures how closely risk and necessary return are related in a healthy market. It can be determined by finding the slope of the security market line (SML) that represents the graphical aspect of the CAPM model.
Concepts Used to Determine Market Risk Premium
The correlation between returns from a portfolio of assets and the yields on treasury bonds is known as the market risk premium. This premium reflects the required, historical, and expected returns.
- Required risk premium: The minimum that investors should consent to. Investors will not make investments if the rate of return is less than the needed rate of return. Another name for it is the hurdle rate of return.
- Historical risk premium: A figure derived from an investment instrument. That figure calculates the premium representing the return's historical performance as an investor. All investors will receive the same return from the historical premium because the value is determined by previous performance.
- Expected market risk premium: Depends on the anticipated investment return.
All investors will experience the same historical market risk premium because the value is based on actual events. However, depending on risk tolerance and investment styles, the necessary and projected market premium will vary from investor to investor.
Investors need reimbursement for opportunity cost and risk. The risk-free rate is the theoretical interest rate that would be paid on long-term, risk-free investments in U.S. government bonds. Due to the minimal default risk, Treasuries have historically been used as a stand-in for the risk-free rate.
Because of this underlying stability, Treasuries have generally maintained very modest yields. Equity market returns are based on anticipated returns on a broad benchmark index, such as the Dow Jones Industrial Average's Standard & Poor's 500 indexes (DJIA).
Real equity returns vary with the success of the underlying company, and this fact is reflected in the market pricing for these assets. While historical return rates have varied over time as the economy has developed and gone through cycles, common wisdom has typically predicted a long-term potential of around 8% yearly.
Because their capital is more at risk, investors seek a premium on the return on their equity investments compared to lower-risk options, which causes the equity risk premium.
Market Risk Premium Formula & Calculation
The premium is a part of several models, such as the capital asset pricing model and the security market line, where MRP consists of the slope of the line.
However, it can be used on its own through its formula:
Market risk Premium = E(RM) – Rf
E(RM) is the market's expected return, and Rf is the risk-free rate.
For example, assume that XYZ had a return of 12% over the past year and a risk-free rate of 5.3%. The market risk premium becomes
Market risk Premium = E(RM) – Rf = 12% - 5.3% = 6.7%
Market Risk Premium and Security Market Line
Security Market Line (SML): Since the market risk premium has an important use in the CAPM model, which requires further elaboration.
In the CAPM, an asset's return is calculated by multiplying its beta by the risk-free rate plus the premium. The beta is a metric used to evaluate an asset's level of risk to the market as a whole.
An asset with a beta of 0.50 has half the systematic risk of an ordinary asset. Whereas an asset with a beta of 2.0 has twice the systematic risk. Not to mention an asset with a beta of 1.0 is average. The premium is modified to reflect the asset's risk.
A positively sloping, straight line known as the securities market line (SML) shows the link between expected return and beta. Consider a market portfolio, which is a collection of all marketable securities, whose anticipated return is represented by E(RM)
A market portfolio must consist of these assets since every asset in the market must be plotted on the SML. The market portfolio must have average systematic risk since it represents all assets on the market, meaning a beta of 1.
We could express the slope of the SML as
SML Slope = [E(RM) - Rf]/ βM = [E(RM) - Rf]/ 1 = [E(RM) - Rf]
The premium is the slope of the SML, the term E(RM) - Rf
Application of CAPM
The equation of the SML that depicts the link between anticipated return and beta is called the capital asset pricing model (CAPM).
Let E(Ri) and βi stand for the expected return and beta, respectively, on any asset in the market, and the following equation is the CAPM:
E(Ri) = Rf + [E(RM) - Rf ] x βi
Where
- E(Ri): the expected return of investment
- E(RM): the market’s expected return
- Rf: risk-free rate
- βi: beta of the investment
- E(RM) - Rf: market risk premium,
For instance, consider the risk-free rate is 3.4%, the beta of stock A is 1.23, and the market risk premium is 7.9%. What is the expected return of stock A and the expected return of the market?
- Rf= 3.4%
- E(RM) - Rf= 7.9%
- βA = 1.23
E(RA) = Rf + [E(RM) - Rf ] x βA
= 3.4 + (7.9) x (1.23) = 3.4 + 9.717 = 13.117%
E(RM) - Rf = 7.9%
E(RM) = 7.9% + Rf = 7.9 + 3.4 = 11.3%
Moving along, Suppose firm A has a beta of 1.24 and an expected return of 0.111, and firm B has a beta of 0.91 and an expected return of 0.086. Find the expected return of the market and the risk-free rate.
First, we need to use the SML equation to find the risk-free rate since we do not have the market risk premium nor the expected market rate.
[E(RA) - Rf ] / βA = [E(RB) - Rf ] / βB
(0.111 – Rf) / 1.24 = (0.086 – Rf) / 0.91
0.91 x (0.111 – Rf) = 1.24 x (0.086 – Rf)
0.10101 – 0.91 Rf = 0.10664 – 1.24 Rf
0.33 Rf = 0.00563
Rf = 0.00563 / 0.33
Rf = 0.017 = 0.017 x 100 = 1.7%
Now using CAPM, we can find the expected return of the market:
E(RA) = Rf + [E(RM) - Rf ] x βA
0.111 = 0.017 + 1.24(E(RM) – 0.017)
1.24 E(RM) = 0.111 - 0.017 + 0.021
1.24 E(RM) = 0.115
E(RM) = 0.115 / 1.24 = 0.0927 = 0.0927 x 100 = 9.27%
The CAPM demonstrates that the projected return for a particular asset relies on three factors:
- Purely time-valued currency: The risk-free rate determines the reward for delaying receiving your money without taking any risks.
- Reward for systematically taking a risk: This is the compensation paid for assuming an average level of systematic risk in addition to waiting, as assessed by the market risk premium.
- Systematic risk amount: This is the amount of systematic risk contained in a specific asset or portfolio relative to an average asset, as determined by the asset's beta.
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