Asset and liability management can be divided into broad sense and narrow sense. In a broad sense, asset-liability management refers to the allocation of funds by financial institutions according to certain strategies to achieve the goal combination of liquidity, safety and profitability. In a narrow sense, asset-liability management mainly refers to achieving the goal of financial institutions by strategically changing the allocation of interest-sensitive funds under the environment of interest rate fluctuation, or maintaining the positive net worth of financial institutions by adjusting the duration of overall assets and liabilities. The definition of ALM by Actuarial Association of North America is: ALM is an activity of managing enterprises, which is used to coordinate the decisions made by enterprises on assets and liabilities; It is a process of making, executing, supervising and revising the decisions related to the assets and liabilities of enterprises in order to achieve the financial objectives of enterprises under the given risk tolerance and constraints. Asset-liability management is an important and applicable financial management tool for any organization that uses investment to balance its liabilities. Asset-liability management originated in the United States in the 1960s, and was originally developed to deal with interest rate risks. Before the deregulation of interest rates in the United States, the market value of financial products or liabilities fluctuated little, but after the deregulation of interest rates in the United States, financial assets and liabilities fluctuated greatly, which led investment institutions to pay more attention to considering assets and liabilities at the same time in decision-making. Although ALM was originally produced to manage interest rate risk, with the development of ALM method, non-interest rate risks such as market risk are also included in ALM, making ALM one of the important tools for financial institutions to manage risks. At present, both investors and regulators have paid enough attention to the applicability of ALM method. Asset-liability management part Asset-liability management has several necessary parts: 1, specific evaluation objectives or financial objectives, such as maximizing statutory surplus, minimizing the risk of surplus, maximizing shareholder returns, etc. 2. Various constraints, such as the state in state simulation and the given distribution in random simulation. These conditions are expressed in various forms, such as time series model, stochastic difference equation and so on. 3. Solutions and calculation results. These methods include decisive analysis, stochastic programming and stochastic control. Asset-liability management principle Asset-liability management is based on the "symmetry principle" among the subjects in the balance sheet, which alleviates the contradiction between liquidity, profitability and safety and realizes the coordination and balance of the three. The so-called symmetry principle mainly means that the term and interest rate between assets and liabilities should be symmetrical, and the asset structure and liability structure should be constantly adjusted according to the requirements of term symmetry and interest rate symmetry, so as to minimize risks and maximize benefits in operation. Its basic principles are: 1 and the principle of scale symmetry. This means that the scale of assets and liabilities are symmetrical with each other, and the S-balance is unified. Symmetry here is not a simple equivalence, but a dynamic balance based on reasonable economic growth. 2. The principle of structural symmetry, also known as the principle of repayment period symmetry. The distribution of bank funds should be determined according to the circulation speed of capital sources, that is, the repayment period of bank assets and liabilities should maintain a certain symmetry, and its corresponding calculation method is the average liquidity method, that is, the average liquidity rate is obtained by comparing the average maturity date of assets and the average maturity date of liabilities. If the average turnover rate is greater than 1, it means that the assets are over-utilized; On the other hand, if the average turnover rate is less than 1, it means that the assets are underutilized. 3, the principle of complementary goals. This principle holds that the balance of the three natures is not absolute, but can complement each other. For example, under certain economic conditions and business environment, the decrease of liquidity and security can be compensated by the improvement of profitability. Therefore, in practical work, we can't stick to a certain goal and simply decide the asset allocation according to a certain goal. Instead, it is necessary to comprehensively consider safety, liquidity and profitability, fully ensure the realization of the bank's goals, and maximize the total utility. 4. The principle of asset diversification. The use of bank assets should be appropriately dispersed among two types and customers to avoid risks and reduce bad debt losses. Typical models of asset-liability management Most early asset-liability management models can only solve short-term problems or multi-stage problems that can be clearly expressed by formulas. However, with the actual needs, more and more people put forward the multi-stage model. Kusy and Ziemba put forward a multi-stage stochastic programming linear model for five-year planning. Their work shows that their model is better than the five-year decisive model. There are many successful multi-stage stochastic asset-liability management models. Among all ALM models mentioned in the literature, mathematical programming is the main method of most models. Brennan and others suggested that stochastic optimal control model should be used to replace the model based on mathematical programming in their articles. The traditional ALM model is criticized by Riskmetrics of JP Morgan because it uses book value instead of market value. In addition, JP Morgan suggested that VaR be an alternative to asset-liability management. However, on the one hand, the current ALM model can consider both book value and market value. On the other hand, generally speaking, VaR is only used for short-term (generally no more than 65,438+00 days) market risk management (in an article on annuity fund management, it is proposed to use VaR instead of ALM to manage two-year risk). Unlike VaR, ALM can manage liquidity risk and credit risk in addition to market risk. When managing the corresponding risks, ALM model will consider legal and policy restrictions. Another criticism of ALM is its reliability in long-term forecasting. However, the modern ALM model shows various possibilities in the future through scene setting or simulation, and the result can be the probability of various situations rather than a single prediction result. At present, there are many methods used in asset-liability management, among which the most commonly used methods are efficiency frontier simulation, duration matching (or immunization), cash flow matching and so on. The mathematical methods used mainly focus on optimization, stochastic control and so on. 1, efficiency frontier model Efficiency frontier was originally proposed by Kyle Weitz and developed as a method of portfolio selection. It uses expectation to represent income and the corresponding variance (or standard deviation) to represent the degree of risk, so it is also called expectation-variance model. The model produces a series of efficiency boundaries, rather than a single suggestion. These efficiency boundaries include only a small part of all possible asset portfolios. One of the most commonly used methods of asset-liability management is to find the efficiency frontier strategy based on expected variance through simulation. Assuming that there are two investment strategies, we can easily calculate their expected values and variances. If we randomly add paths and strategies, the upper bound of the expectation-variance scatter plot will reach the so-called efficiency frontier, which means that the optimal risk/return investment strategy is determined. 2. Duration matching model If a set of cash flows is given, the duration of a security can be calculated. Conceptually, duration can be regarded as the time-weighted present value of cash flow. Duration matching (or immunization) method is to match the interest rate risk of assets and liabilities in the portfolio. The traditional model of this method assumes that the term structure of interest rate is flat and changes in parallel. Of course, many models have been expanded to manage the risk of cash flow fluctuation, liquidity risk and credit risk caused by the shape change of interest rate term structure curve. Because the duration changes with the fluctuation of interest rate, even if the duration of assets and liabilities is matched at first, their duration may no longer match the change of interest rate, so a concept of "effective duration" is put forward. Effective duration depends on the rate of change of asset price relative to interest rate, and is measured by its convexity. In other words, in order to ensure the matching of assets and liabilities, financial institutions not only require the matching of the duration of assets and liabilities, but also require to avoid risks more accurately by controlling the convexity of assets and liabilities. 3. Cash flow matching model In their article "The Optimal Investment Strategy of Investor Debt", Elton and Gruber re-examined the portfolio management of different indebted companies. They found that managers of companies with different liabilities generally divide their assets into several parts, one is the daily operating account, the other is the immunization account, and the other is the cash flow matching account. After re-examining CAPM's expectation-variance method, they think, "It is important to note that different investors may face different efficiency frontiers, not only because they have different ideas, but also because they have different liabilities." "When assets are priced in a balanced way, the specific efficiency frontier of accurate asset-liability matching of enterprises will degenerate into a point." Elton and gruber concluded, "If all assets are priced in a balanced way, no investor is willing to adopt the immunization (that is, duration matching) strategy unless it is a portfolio with cash flow matching. On the other hand, if some assets are not priced in a balanced way, it is always beneficial to match some assets and liabilities with cash flow matching method, and at the same time invest in some asset portfolios that are immune but have mismatched cash flows. " Based on this, Elton and Gruber proposed that the optimal ALM strategy should be the optimization under the constraint of cash flow matching. They said, "since cash flow matching is the only way to avoid the residual risk of debt, of course we should do so." The best solution is to accurately match the cash flow of all meaningful asset/liability paths. Note that cash flow matching is a sufficient condition for duration matching, and the portfolio with cash flow matching must be duration matching, but the cash flow of the portfolio with long-term matching does not match. 4. Multi-criteria decision-making model The above models are all single-objective models, but some conflicting objectives may need to be considered in actual management. For example, the bank's goal may consider expected return, risk, liquidity, capital adequacy ratio, growth, market share and so on. If we consider these goals one by one and seek the final solution, the model will be extremely complicated, and there may be many solutions, which will make it very troublesome for decision makers to make effective analysis, so we have developed a multi-constraint decision-making model. Take the goal programming model as an example. This model is one of the most commonly used multi-constraint decision-making models, and its main advantage lies in its flexibility, allowing decision makers to consider multiple constraints and objectives at the same time. 5. Stochastic programming or stochastic control ALM model At present, ALM model is more and more used in stochastic programming or stochastic control methods. The stochastic programming ALM model is actually a model, which provides a method to simulate general objectives. These objectives can include transaction costs, taxes, legal and policy restrictions and other requirements. Due to many factors considered, there are more and more variables in the model, which leads to a large number of optimization problems, and its calculation cost is quite high, and its practicability is in doubt. Let's take the "opportunity constraint model" as an example. The opportunity limitation model was first proposed by Charnes and Kirby. In their paper, the future deposit and loan expenditure is regarded as a random variable with joint distribution, and the capital adequacy ratio formula is used as the opportunity limit. The disadvantage of this model is that violations of constraints will not be punished according to their number. Charnes and others applied this method to balance sheet management, and two other articles used this model to analyze the asset portfolio of insurance companies. Dert developed this model into a multi-stage opportunity-constrained ALM model that specifies the beneficiary annuity field. Unlike Charnes and Kirby, the author uses scenarios to simulate uncertainty, rather than making distribution assumptions. Taking this model as an example, the objective function of this model is to achieve the minimum financing cost under the constraint that the solvency risk level is acceptable and the ability to pay the specified income in time is stable. Among them, the solvency requirement is the product of the fund's remaining liabilities and the corresponding solvency ratio, and the asset value level below the requirement is simulated through scenario setting. 6. Dynamic financial analysis model As a method of asset-liability management, dynamic financial analysis has only recently developed. It may not be reasonable to classify it as one class, because it can use many methods such as stochastic programming and stochastic control. But his mind changed. The above methods all adopt various methods, and use discrete state assumptions (deterministic assumptions or random generation) to express future uncertainty. Dynamic financial analysis hopes to describe future uncertainty in a continuous state.