Finance mainly studies people’s optimal allocation of financial assets in an uncertain environment. The time value of assets, asset pricing theory (resource allocation system) and risk management theory are the core contents of modern financial economics. The core issue in the resource allocation system is the price of assets, and the biggest characteristic of financial assets is the uncertainty of the results. Therefore, the pricing of financial assets is one of the most important issues in financial theory.
At present, the pricing of financial assets mainly includes the pricing of single products represented by stocks, bonds, options, etc., as well as the asset portfolio pricing theory, arbitrage theory and multi-factor theory that use risk and return as the research basis. Different pricing theories and methods are constantly revised and improved with the development of time and the advancement of statistical methods and computer technology, making them gradually closer to realistic requirements.
Financial asset pricing is the core of contemporary financial theory. The time value of funds and the quantification of risk are the basis of financial asset pricing. The price of financial assets is determined by the time value of funds and risk.
(1) Cash flow discount method
The time value of funds means that funds will depreciate over time. Current funds are more valuable than future funds, or in other words Higher purchasing power. Therefore, it is difficult to compare the value of cash flows at different points in time. To discount future cash flows, the key is to determine the discount rate. The discount rate is not chosen arbitrarily. It should be the opportunity cost of using funds determined by the market, that is, the rate of return that can be obtained by using the same funds for the best of all other uses except the purpose under consideration. Opportunity cost is the rate of return of financial assets reflected by the market, and the rate of return (capital cost) of the asset must correspond to the risk level of the asset. Generally speaking, higher risk assets generally correspond to higher returns. In financial practice, the discount rate is often expressed as a risk-free interest rate plus a risk compensation rate. The risk-free interest rate refers to the rate of return that can be obtained on monetary funds without taking any risks, commonly represented by the short-term interest rate of treasury bills; the risk compensation rate depends on the size of the financial asset risk. The greater the risk, the higher the risk compensation rate required, so discounting The determination of the rate requires solving two problems, the risk-free rate and the risk compensation rate.
Theoretically, different discount rates are used for discounting in different periods, because the opportunity cost of capital will change with changes in market conditions in different periods. That is to say, the rate of return of the same asset is different for different investment periods. The study of this issue is the term structure of interest rates. Interest rates are one of the most important price variables in the financial market. It directly determines the price of related financial products. pricing and management of interest rate risk. The term structure of interest rates refers to the relationship between the yield to maturity and the maturity period of securities of different maturities. It is very important for the management of interest rate risk and the pricing of financial assets.
(2) Portfolio Theory (MPT)
Modern portfolio theory (Modern portfolio theory) proposed by Harry Markowit (1952) is the basis of modern finance. beginning. Under the basic assumptions: (1) all investors are risk averse, (2) all investors are in the same single investment period, (3) investors choose investment groups based on the mean and variance of returns, investment Portfolio theory believes that the investor's utility is a function of the expected return and standard deviation of the investment portfolio, which maximizes the expected return at a given level of risk or minimizes the risk at a given level of expected return. Rational investors maximize expected utility by choosing an efficient investment portfolio. This selection process is achieved with the help of solving a two-objective quadratic programming model. The essence of the model is to minimize the risk of the investment portfolio at a given expected rate of return, and to specify the types and weights of various risky assets in the portfolio at this rate of return. The solution is to obtain the standard deviation-expected return graph, which is a hyperbola convex to the left, in which the upper half of the hyperbola is the efficient portfolio frontier. Investors choose investment portfolios based on their risk-return preferences on the efficient portfolio frontier, and the result must be the tangent point between the investor's utility function and the efficient portfolio frontier. By increasing the types of assets in the portfolio, non-systematic risks can be reduced, but systematic risks cannot be eliminated. Only risks recognized by the market (systemic risks) can receive risk compensation.
(3) Capital Asset Pricing Theory (CAPM)
William F. Sharpe (1964) and Prof. John K. Lintner (1965) ) proposed the famous Capital Asset Pricing Model (CAMP) based on the Markowitz mean-variance portfolio investment model theory. Based on the assumptions (1) (2) (3), assuming (4) all investors have the same understanding of all statistical characteristics (mean, covariance) of the same security, (5) the market is complete, That is, there are no taxes, transaction fees, etc., (6) there are risk-free securities available for investment, and investors can borrow or short-sell a security without restriction at a risk-free interest rate. CAPM further discusses the pricing problem of individual I-risk assets in the market on the basis of portfolio theory, and derives the Security Market Line (SML).
(4) Arbitrage Pricing Theory (APT)
In response to some problems in the application of CAPM, such as strong assumptions and difficulty in calculating market risk, Stephen Ross proposed it in 1976 Arbitrage Pricing Theory. Similar to the capital asset pricing model, APT is also an equilibrium model that determines asset prices. It believes that the return rate of risky assets is not only affected by market risks, but also affected by many other factors (macroeconomic factors, certain indexes). Arbitrage is buying or selling an asset to take advantage of the price difference to make a risk-free profit. It is generally believed that there are no arbitrage opportunities in relatively mature markets, thus reaching an arbitrage-free equilibrium.
APT assumes: The market is perfectly competitive and there is no friction; the random rate of return of each asset is dominated by the same several factors.
1. Single-factor APT model: It is assumed that the return rate of an asset is determined by a certain factor (not necessarily the market combination of risky assets) and is a linear function of this factor. The factors here can be various macro factors. It can also be some index
2. Multi-factor APT model: When multiple macroeconomic factors affect the expected return of a risky asset at the same time, the expected return of the asset can be expressed as multiple Factors can be added with linear functions.
(5) Option Pricing Theory
In 1973, Fischer Black and Myron Schole conducted research on option pricing. , put forward seven important assumptions: (1) The stock price obeys a stochastic process with a constant expected rate of return and a constant rate of change; (2) Investors can short-sell derivative securities and use the proceeds from short-selling: (3) The market is frictionless, That is, there are no taxes and transaction costs; (4) All securities are highly divisible; options are European options, and there is no payment of cash dividends during the option validity period: (5) There are no risk-free arbitrage opportunities in the market; (6) The market provides investors with continuous trading opportunities; (7) The risk-free interest rate is constant and equal for all maturities. On this basis, the Black-Scholes model for European option pricing was established. Robert Merton (1973) established another very similar model. Option pricing formulas for underlying assets such as assets that pay dividends, futures, and foreign exchange can be given.