Ordered mean difference model (OMD model) OMD model was put forward by Roger. J. bowden in 2000. This model can be used to evaluate fund performance, arbitrage strategy, immunization strategy and portfolio enhancement strategy. For your convenience, let's take a look! Let's share with you the application of OMD model in fund performance. Welcome to read!

Overview of OMD mode

The OMD model was put forward by Roger. J. bowden in 2000. This model can be used to evaluate fund performance, arbitrage strategy, immunization strategy and portfolio enhancement strategy. This paper introduces its research in fund performance evaluation. When evaluating fund performance, the advantage of OMD model is that it does not need strict assumptions of CAPM model, and because of the nonparametric estimation characteristics of this model, it does not require the probability distribution of fund and market return to be normal distribution or symmetrical distribution.

Ordered average model is introduced to evaluate fund performance, which solves the limitations of traditional fund performance evaluation indicators and can meet the individual investment needs of investors. This paper analyzes the market performance of three funds with different investment styles of the same fund management enterprise through empirical analysis, and compares and analyzes the superiority of this index compared with the traditional index in evaluation.

Application of OMD model in fund performance evaluation

1, equivalent deposit

Construct a portfolio, and the investment ratios of the fund to be evaluated (return is γ) and the market benchmark portfolio (return is R) are X and (1-x) respectively. If the investor has the von Neumann-Morgenstein utility function u (), then the optimal combination should satisfy.

maxEr，R[U(xr+( 1_x)R)]( 1)

When evaluating the fund performance with equivalent marginal indicators, we use (r-t) instead of R to represent the fund's rate of return, where T can be regarded as the commission extracted from the excess profits obtained by the fund manager's market timing ability. If you buy a fund, the actual rate of return of the fund will be reduced because of the existence of T, and with the increase of T, investors will reduce their holdings of the fund and eventually reduce their holdings to zero. From another perspective, the higher the T that investors can accept, the better the performance of the fund. In other words, the higher the T, the higher the evaluation of fund managers' unique market timing ability. This is the equivalent boundary. It is worth noting that this evaluation reflects the personalized aspect of equivalent margin, which can be the subjective evaluation of any investor.

Equivalent allowance is defined as:

If investors are crisis-averse, that is, the utility function is concave, then the optimal investment portfolio should meet the first-order condition of the above formula:

e(R _ R _ t)U '[x(R _ t)+( 1 _ x)R])= 0

Let x=0, and the equivalent marginal index can be obtained.

(2)

and

2. Practical generators

The biggest difficulty in calculating the equivalent margin lies in the determination of the utility function of input. Therefore, we construct a special form of utility function-utility generator. This function has a special form, as shown in figure 1. The utility generator consists of two linear parts, and the node is the rate of return P. We can regard P as the "target rate of return", that is, investors are more concerned about whether the rate of return can reach this value, rather than the situation after the rate of return exceeds this value. Therefore, point P reflects the degree of crisis aversion of different investors: with the right shift of point P, the degree of crisis aversion of investors is lower. Usually, P>0.

For a fixed value p, the utility generator function is: it can be proved that the utility function of investors with arbitrary crisis characteristics can be decomposed into a set of weighted utility generators to distinguish P points, that is, the degree of crisis aversion. For example, in the utility function of investors who avoid crisis, the utility generator with lower P value has higher weight in the utility function of investors.

3.OMD sample function

Since any utility function can be decomposed into a set of weighted utility generating functions Up(R), if the equivalent margin of the utility generating function at Point P can be calculated (denoted as t p or t(P)), the equivalent margin tU of any utility function can be obtained in the same way. We call t(P) the OMD sample function, which is defined as follows:

,

Where n(P)={#Ri≤P}(2)

According to the market benchmark rate of return and t(P), the OMD curve of the fund can be drawn. If the OMD curve of the fund to be evaluated is always at the top, then for any investor with crisis characteristics, it can be said that the fund is superior to the market benchmark portfolio, or that the fund manager has better market timing and stock selection ability.

Because OMD function has nonparametric characteristics, it doesn't need to make any assumptions about the distribution of income and evaluate the value of securities, and it also avoids the effectiveness of CAPM model, so it is better than the traditional fund performance evaluation index to some extent.

Empirical research and analysis

1, research object and data processing

Since September, 20001year, the first open-end fund, Huaan Innovation Fund, was issued in China's securities market. By the end of August, 2004, the fund scale had reached 100. In order to facilitate comparison, three funds of the same fund enterprise are selected for analysis, namely China Merchants Antai Stock Securities Investment Fund, Balanced Securities Investment Fund and Bond Securities Investment Fund. The data is ***300 days from June 2, 2003 to August 30, 2004. For daily data, the calculation formula of the fund's net asset value is as follows:

Among them: RPt is the yield of T-day fund; NAVt is the net asset value of the fund on T day; Dt is the cash dividend of the fund on t day.

According to China's "Interim Measures for the Management of Securities Investment Funds", the investment of funds in the stock market shall not be higher than 80% of the total investment, and the investment in bonds and cash holdings shall not be lower than 20%. We choose SSE 180 index as the comprehensive index of the stock market and SSE government bond index as the comprehensive index of the national debt market. The weighted average values of the two indexes are 0.8 and 0.2 respectively, and the market benchmark rate of return is calculated, that is, the market benchmark rate of return =80%×

2. Empirical analysis of three securities investment funds.

(1)OMD curve and its analysis

From Figure 2 to Figure 4, it can be seen that the OMD curves of balanced and bond funds are all above the horizontal axis in the sample interval, indicating that these two funds are superior to the market benchmark portfolio, or their fund managers have better market timing and stock selection capabilities. It is worth noting that when the market benchmark rate of return R is negative, the equivalent marginal tU has a higher positive value, while in areas with higher market rate of return, the equivalent marginal tU drops "rapidly", especially in bond funds. It shows that the balanced and bond funds, which aim at pursuing stable income and avoiding the crisis of market price fluctuation, still maintain good market performance in the case of market downturn, but the performance of these two funds is not as good as that of stock funds pursuing higher income.

(2) Comparative analysis of equivalent marginal index of 2)OMD model and traditional evaluation index.

Among the three traditional evaluation indexes, we choose Zhan Sen α index to compare with the equivalent deposit, and the calculation results are shown in Table 1.

It can be seen that when the equivalent marginal index is used to evaluate the performance of the fund, the Zhan Sen α index can not evaluate the performance of the fund well, especially for bond funds.