The requirement of constructing interest rate risk elimination method is to make the duration of investment bond portfolio equal to your investment period. Performance: duration of assets = duration of liabilities; At the same time: present value of assets ≧ present value of liabilities.

What is the concept of asset-weighted duration? !

Every asset has a term (such as bank loans, bonds held, etc.). ). If you hold multiple assets at the same time, you need to calculate the duration of the asset portfolio. Weighted duration of assets is a method to calculate the duration of asset portfolio, that is, the market price of assets is taken as the weighted average to get the duration of asset portfolio.

How long is the term of the bond?

The so-called duration is used to measure how long bondholders have to wait on average before receiving cash payment. Zero coupon bond with a maturity of n years has a duration of n years, while coupon bonds with a maturity of n years have a duration of less than n years.

In bond investment, duration is used to measure the interest rate risk of bonds or bond portfolios. Generally speaking, the duration is inversely proportional to the yield to maturity of bonds, and directly proportional to the remaining life of bonds and coupon rate. For ordinary interest-bearing bonds, if the coupon rate of the bond is equal to its current rate of return, the duration of the bond is equal to its remaining life. When the bond is a discounted bond without coupon rate, the remaining life of the bond is its duration. The longer the duration of bonds, the greater the impact of interest rate changes on bond prices, so the greater the risk. Interest rate cuts, long-term bonds rose sharply; When raising interest rates, bonds with long maturities also fell sharply. Therefore, investors can choose short-term bonds when they expect to raise interest rates in the future. In bond analysis, duration has surpassed the concept of time, and investors use it more to measure the sensitivity of bond price changes to interest rate changes. After some modifications, it can accurately quantify the impact of interest rate changes on bond prices. The longer the correction lasts, the more sensitive the change of bond price yield, the greater the decline of bond price caused by the increase of yield, and the greater the increase of bond price caused by the decrease of yield.

What is the term of the debt?

Debt duration should be an insurance term, which refers to the matching of assets and liabilities of insurance companies.

For example, the policy sold can be regarded as the liability of the insurance company because it is to be repaid in the end, so the repayment period of the policy is the liability period of the insurance company.

High scores are rewarded. Who can explain to me why? Duration gap = weighted average asset duration-(total liabilities/total assets) * weighted average debt duration

Duration gap

Banks can use duration gap to measure the interest rate risk of their assets and liabilities. Duration gap is the product of the difference between the weighted average duration of assets and the weighted average duration of liabilities and the asset-liability ratio, namely:

Duration gap = weighted average asset duration-(total liabilities/total assets) × weighted average debt duration

When the duration gap is positive, the weighted average duration of assets is greater than the product of the weighted average duration of liabilities and the asset-liability ratio. When the duration gap is negative, the market interest rate rises and the bank's net worth increases; When the market interest rate falls, the bank's net worth will decrease. When the gap is zero, the market value of the bank's net worth is not affected by interest rate risk.

In short, the greater the absolute value of the duration gap, the more sensitive the bank is to the change of interest rate, and the greater the bank's interest rate risk exposure, so the higher the interest rate risk that the bank ultimately faces.

What is duration matching?

Given a set of cash flows, the duration of securities 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.

Examples of Duration Matching Models

There are many kinds of immune models, and the most common one is to take the return of portfolio as the objective function. We take one of the models as an example, which is expressed by the following mathematical formula:

Model: goal:

Restrictions:

These include:

U = {1, 2, 3, …I} is a complete set;

T = {1, 2,3, ... tmax} is a discontinuous time point set;

Xi: securities holdings I;

Ri: cash flow income;

Pi: the present value of security I;

Ki: safety period i.

It can be seen from the assumptions of the model that the duration matching model is suitable for asset-liability management with fixed income. Even so, it is doubtful whether long-term matching assets and liabilities can be truly immune. If the price is regarded as a function of the necessary rate of return, the duration and convexity depend directly on its first derivative and second derivative respectively. People have done a lot of research, trying to determine whether the dynamic asset portfolio that rebalances the asset portfolio to achieve the specified duration can be effectively immunized. A research report using stochastic process seems to confirm that immunization can effectively avoid risks, but it also points out that such a satisfactory result is based on a common assumption that the market is efficient and the description of the interest rate change process is correct. For other cases that violate this common assumption, the report concludes that it may not be spared. It can be seen that the success of immune strategy obtained by random simulation or "lattice construction" method is not robust to the whole process of real asset-liability management, or its practical use is doubtful. The success of this method may only show that it is beneficial to do some theoretical research with complex mathematical simulation technology, which can explore any complex random structure.

The meaning of bond maturity is the response of the price change rate of assets to the change of interest rate. What is the interest rate?

You are a little confused conceptually. The interest rate refers to the bond yield to maturity (the bond yield to maturity is used to calculate the term of the bond). When bonds are issued, generally only the coupon rate and issue price of bonds are determined. Generally speaking, the coupon rate of bonds is fixed (except for floating interest rate bills), the future cash flow of bonds is certain, and it is true that there is no default. However, due to these deterministic factors, the market will change with the passage of time. On the whole, the fluctuation of market interest rate (there is a positive correlation between market interest rate and bond yield to maturity, and sometimes the relationship between market interest rate and bond yield to maturity is equivalent, which may not be true. Only when the bond risk is equal to the market risk) will it be reflected in the negative correlation between bond market price and interest rate, that is, yield to maturity will rise, bond price will fall and yield to maturity will rise. In many cases, investment bonds will not be held until maturity, so we need to pay attention to the rate of return during the holding period. The sensitivity of duration will affect the rate of return during the holding period, which is called riding coefficient in the field of bond investment.

What's the difference between duration and duration?

Duration is generally different from Macaulay duration and modified duration, in which modified duration measures the percentage of bond price relative to interest rate change, that is, interest rate change 1%, and Macaulay duration is the ratio of cash flow to bond present value in each bond term multiplied by the time when cash flow occurs, that is, the weighted average of terms.