Capital asset pricing model formula (CAPM formula):
Sharp found that the expected return formula of a single risky asset or its combination is as follows:
Expected return = risk-free return+beta coefficient of securities * (market expected return-risk-free return)
The following answers your questions in turn:
Question 1: Based on CAPM, assuming the risk-free discount rate is 5%, the expected return of market portfolio is 14%, and β= 1.5, what is the required recovery rate of a single risky asset?
Solution: The required recovery rate of a single risky asset (i.e. expected rate of return) = 5%+1.5 * (14%-5%) =18.5%.
Question 2: The capital asset pricing model only presents systematic risks (that is, inevitable risks) to investors. Is this view right or wrong? Please explain.
A: Correct.
Systematic risk: refers to the risk that cannot be eliminated by decentralization in the market. For example, interest rates, economic recession and war are all risks that cannot be eliminated through diversification.
Non-systematic risk: also known as unique risk or idiosyncratic risk, this is the risk of individual stocks, and investors can eliminate it by changing the stock portfolio. From a technical point of view, the return of non-systematic risk is an integral part of stock return, but the risks it brings do not change with the changes of the market.
Modern portfolio theory points out that special risks can be eliminated through diversification. Even if the portfolio includes stocks in all markets, diversification will not eliminate systemic risks.
CAPM considers the influence of non-dispersible risk (market risk) on the required rate of return of securities. It has been assumed that investors can disperse the risk of diversification (company-specific risk) by fully diversifying their investments, so only the risk of non-diversification is the risk that investors are concerned about at this time, so only these risks can get the risk premium.
Supplement: (This is to show that the initial formula of CAPM model is not comprehensive)
CAPM's basic view: Risk premium is related to a wide range of systemic risk factors that affect most people.
That's true, but since the historical rate of return of American common stock proved that CAPM model was effective in the early 1970s, researchers found that CAPM model was not completely consistent with the data and could not fully explain the structure of expected return on assets. Now that * * * knowledge has been formed, the original simple form of CAPM needs to be revised. The equilibrium risk premium of risky assets comes from many risks, which are not only sensitive to the market portfolio yield, but also sensitive to systemic risks such as changes in interest rates, expected returns on assets and changes in consumer prices.
Question 3: Using CAPM model, assuming that the risk-free discount rate is 10%, the expected return of market portfolio is 20%, and β=0.7, what is the recovery rate of an investment requirement? (such as question 1)
Solution: The required investment recovery rate =10%+0.7 * (20%-10%) =17%.
Question 4: What is CAPM model? When and how was this model established?
(1) What is CAPM model?
The basic idea of capital asset pricing model is to know the market reward of people taking risks when they reach equilibrium. Its purpose is to help investors determine the price of capital assets, that is, the linear relationship between the required rate of return of securities and the market risk (systemic risk) of securities in market equilibrium.
(2) When was this model established?
The capital asset pricing model was developed in the early 1960s. William sharpe won the 1990 Nobel Prize in Economics for his CAPM paper published in 1964. John Lint and Jane Mohsin also launched CAPM at almost the same time.
(3) How is this model established?
CAPM is based on Markowitz model, and the assumptions of Markowitz model are naturally included:
1. Investors want more wealth, the better. Utility is a function of wealth, and wealth is a function of return on investment, so utility can be considered as a function of return.
2. Investors can know in advance that the probability distribution of return on investment is normal.
3. Investment risk is identified by the variance or standard deviation of investment return.
4. The main factors affecting investment decision are expected rate of return and risk.
5. Investors abide by the law of superiority, that is, under the same risk level, choose securities with higher yield; In the case of the same rate of return, choose securities with lower risk.
Additional assumptions of CAPM:
6. You can borrow or lend money at the risk-free discount rate R without restriction. ..
7. All investors have the same view on the probability distribution of securities returns, so the market has only one efficiency boundary.
8. All investors have the same investment term, and there is only one term.
9. All securities investments can be subdivided infinitely, and any portfolio can contain non-integer shares.
10. There is no tax burden and transaction cost for buying and selling securities.
1 1. All investors can get enough market information free of charge in time.
12, no inflation, the discount rate remains unchanged.
13, investors have the same expectation, that is, they have the same expectation for the expected rate of return, standard deviation and covariance between securities.
The above assumptions show that: first, investors are rational, diversify their investments in strict accordance with the rules of Markowitz model, and will choose a portfolio from somewhere in the efficient boundary; Second, the capital market is a completely effective market, and there is no friction that hinders investment.