I. Definition and measurement of risk
When an investor makes an investment decision, the possible income (R) of the decision-maker (X) depends not only on the action (A) he chooses, but also on other conditions or actions (B) taken by others. Let the action set that decision-maker X may choose be A: {A 1, A2, ... A n}, while the possible state of economy and society (y) or actions that others may take are B: {B 1, B2 ... bi, ... B n}. The decision-maker's payment function is expressed as: R=f(a, b), a∈A, b ∈ B This function indicates that the decision-maker X's action on A is related to his choice, as well as to the economic and social situation (or the actions taken by others). The interest of action B taken by Y relative to X can be "neutral" (it is not intended to make X's situation better or worse); If the interests of X and Y conflict, Y may be inclined to take action to reduce the interests of X; If the interests of X and Y are the same, Y may take actions decided by Y. But generally speaking, for X, Y's actions are uncertain, so X makes decisions under uncertain conditions.
When there is uncertainty, the decision of decision makers is risky. Risk is an act that does not increase X's return. From the perspective of decision theory, what X does and what X makes depends on certainty, which comes from incomplete information or asymmetric information. The necessary condition of risk is that decision-making faces uncertain conditions. When a decision-maker executes under uncertain conditions, the meaning of risk is: from a pre-agreed point of view, determine the possibility and scope of the expected return change of the purchased assets; Post-employment perspective refers to the decision-making loss or relative loss caused by uncertain factors. In econometrics, risk is usually measured by statistical standard deviation.
Second, the securities investment risk and its classification
The main purpose of investors (including institutional investors and individual investors) to invest in securities is to obtain high returns, but the returns of securities investment (especially stock trading) are affected by many uncertain factors, and the stability of returns is obviously not as good as that of bank deposits, which leads to the risks of securities investment. This kind of risk is accompanied by income, high income and high risk, low income and low risk. Therefore, we can also regard securities income as a kind of compensation for investors to take risks. Specifically, the risk of securities investment refers to the possibility that securities investors can't get the expected returns and suffer losses. Investors hope to get expected returns when investing in securities, but what they really get is actual returns, which may be lower than expected returns. At this time, risks occur and investors suffer losses.
Different investment choices will bring different investment risks, and the causes and degrees of risks are also different. Generally speaking, according to the causes of risks, they can be divided into the following categories:
(1) Market risk. This is the most common and common risk in financial investment. Whether investing in securities or other physical projects, almost all investors have to bear this risk. This kind of risk comes from the price fluctuation caused by the imbalance between supply and demand of buyers and sellers in the market, which brings losses to investors.
(2) Interest rate risk. Interest rate risk is the possibility that the change of market interest rate affects the price of securities market, thus bringing losses to investors.
(3) the risk of accidents. This sudden risk is what most investors must bear, and its severity and timeliness vary from thing to thing. Such as natural disasters, the danger of war, the government's monetary policy, exchange rate changes, patent applications and other emergencies are unpredictable when investors invest.
(4) depreciation risk. Also known as inflation risk or purchasing power risk. The consumer price index is usually used to measure the inflation rate.
(5) operational risks. Enterprise management risk refers to the change of profitability due to the good or bad operation, which leads to the loss of investors' income or principal.
(6) Enterprise financial risk. Enterprise financial risk refers to the risk brought by different financing methods.
In addition to the above risks, there are other risks in securities, such as moral risk, legal risk, political risk and so on.
Three, the analysis of the measurement method of securities investment risk
In order to compare the risks in securities investment, we divide the risks into two categories, namely total risk and market risk. Total risk is the sum of system risk and non-system risk; Market risk is to study the correlation between return on assets and return on portfolio. For single securities, the total risk is mainly considered, while for portfolio securities, the market risk is mainly considered.
1. Measurement of total risk
(1) Since the rate of return is the result of investment, the risk analysis also focuses on this random variable. The variance of return is often used to measure risk.
(2) Generally speaking, the standard deviation can only measure the risk degree of each item when the expected return is not much different and the standard deviation is not big. If the expected return of each project is highly correlated, the difference coefficient should be used to evaluate the risk of each project. The difference coefficient is actually the risk borne by the expected income of the unit.
(3) If the risk is regarded as the possible fluctuation of the stock price, then the price difference is a good indicator to measure the stock risk.
Spread rate =2 (highest price-lowest price)/(highest price+lowest price)
The greater the spread, the greater the risk. It should be pointed out that in order to overcome the influence of short-term factors, the average spread over a period of time should be investigated to understand the overall situation.
(4) It is also a method to measure the risk of securities investment based on the rate of return. The income from securities investment can be regarded as risk-free income and risk compensation income. The higher the yield of a security, the greater the risk compensation income and the higher the risk degree. The specific method is to compare many securities that are the same in many aspects but differ significantly in only one aspect, so as to measure the risk level of a certain securities.
(5) Here is another measurement method-risk compensation method. Assume that there are only two possible values for the random variable R as the investment return, namely, R 1 and R2, and the probability distributions of its values are P 1 and P2= 1-P 1, and the expected return of securities is:
ER=P 1R 1+P2R2
Its expected utility is:
EU(R)= p 1 * U(R 1)+( 1-p 1)* U(R2)
2. Returns and risks of portfolio assets
The combination of various securities as investment objects is called portfolio assets. Markowitz's portfolio theory solves the risk measurement problem of portfolio assets. In short, Markowitz's theory shows that under certain conditions, investors' portfolio selection can be simplified as a trade-off between two factors, namely, the expected return of the portfolio and its variance.
If all the securities that may be selected in the market constitute a portfolio asset weighted according to its market proportion, it is called market portfolio assets. When investors only hold market portfolio composed of risky assets, the relationship between the return rate of each security and the market portfolio return rate is that the part of the return rate of each security that has nothing to do with market portfolio will disappear completely because of holding market portfolio, that is, the risk of each security is determined according to the covariance with market portfolio. It reflects the relationship between the return of a single security and the return of market portfolio as a whole, and β I describes the sensitivity of a single security to the change of market portfolio's return. System risk is called β I securities i. Because β m = 1, the system risk of securities can be divided into two categories. For β >; 1 The risk of securities is greater than the average system risk; On the contrary, the risk is less than the average system risk. So β can measure the relative risk of securities.
3. Three equivalent definitions of incremental risk
In order to compare the risks of two kinds of securities or investments, the following three equivalent definitions of incremental risk are given:
Definition 1 There are two investments W 1 and W2 with the same expected value, if
E{U(W 1)}≥E{U(W2)}
If each concave function holds, then the risk that W 1 is less than W2 is said.
Definition 2 If W 1 and W2 are two investments and there is a random variable ξ, so that W2= W 1+ξ, ξ is noise and E{ξ| W 1}=0, then the risk of W1is less than.
Definition 3 Let the distribution functions f and g of W 1 and W2 be limited in the interval [a, b], and
T(Y)=∫ay[G(x)-F(x)]d x
If T(y)≥0 and T(b)=0, the risk of W 1 is less than W2.
The definition of incremental risk is very useful for studying the essence of optimal investment.
4. A new risk measurement method
Let the securities yield be r, and its expected yield be μ, R=μ +ξ.
Where e {ξ} = 0 and μ = e {r}. Define random variables,
ξ+= ξ (when ξ≥0), ξ+=0 (when ξ < 0);
ξ-=0 (when ξ≥0), ξ-= ξ (when ξ < 0).
-E{ξ-} is the risk measure of securities, which is called average loss.
For two securities R 1, R2 should have corresponding.
R 1= E{ R 1}+ξ 1
R2= E{ R2}+ξ2
if-E {ξ 1-} & gt； -E{ξ2-}, then we say that the risk of securities 1 is greater than that of securities 2.
Investing in securities is to properly manage our property, and minimizing the risk of securities investment is a problem that every investor must consider! For reference only. . .