We will encounter such a problem in our life: there are two funds: Fund A and Fund B.. Generally speaking, funds with high expected returns will have greater risks. Described in mathematical language: the higher the fund's income, the greater the variance. That is, if there is:

generally speaking, there is.

Otherwise, the fund's income is large and the risk is small. Everyone went to buy a fund, so the fund went bankrupt, didn't it?

As the saying goes, don't put your eggs in one basket. The same is true for the allocation of assets, so when I have a sum of money, I use it to invest in two funds. It can be achieved better than betting on a fund.

this article takes the portfolio of the two simplest funds as an example to talk about the scientific basis of the "egg theory".

Let's consider the following question first: What are the expected returns and variances of the asset portfolios of Fund A and Fund B?

at this time, I guess some students will say: the expectation of combination must be between A and B, and the variance of combination must be between them. In fact, this statement is not correct, because in real life, AB funds often have a certain correlation, which may make the variance of the portfolio laugh more than both. A look at the following cases will prove this fact.

mathematical basis

here is a column about the calculation of portfolio expectation and variance: we assume that the weight of fund A is and the weight of fund B is . So the expected return of the portfolio is: the variance of the portfolio is: of course, we can also bring in some numerical values here to verify that the variance of the portfolio calculated as above may be more ridiculous than the variance of the portfolio of the two funds. Interested students can verify it by themselves, or they can be reflected intuitively through the following examples.

let's give an example for simulation first.

now assume that the expected return of fund a is 2% and the standard deviation is 3%, and the expected return of fund b is 12% and the standard deviation is 15%. And the correlation coefficient between them is .1. Now it is required to make the variance-expected return curve of the two fund portfolios. The steps are as follows:

We use the first column to represent the weight of Fund A, enter ,.1 and drop it down, and it will be completed automatically according to geometric progression.

the weight of fund b is equal to 1 minus the operation of fund a. Enter "= 1-A2" in B2 and then drop it down to complete it.

standard deviation is obtained after rooting:

With the standard deviation as the abscissa and the expected return as the ordinate, the drawing is as follows:

The above figure shows the return-standard deviation curve of the portfolio. As can be seen from the figure, there is a

combination mode with less risk than AB. Among them, we call this point with the smallest variance the smallest square difference. As you can see, in the least square difference. The expected return is larger than that of asset B, but the variance is smaller. This is the benefit of "don't put your eggs in one basket": spreading risks.