Guidance of Portfolio Rebalancing (MANG 2004)
1个步骤投资组合再平衡

•确定最佳权重。 （许多方法可以做到这一点，其中之一是通过MV优化和

•确定每个组成资产的当前头寸。
•相应地调整投资组合。

2问题设置

Pt,1 Pt,2 Pt,3 Wt,1 Wt,2 Wt,3 Vt
Pt+1,1 Pt+1,2 Pt+1,3 Wt+1,1 Wt+1,2 Wt+1,3 Vt+1
Pt,1, Pt,2, and Pt,3 are the prices for Asset 1, 2, and 3 at time t; Pt+1,1, Pt+1,2, and Pt+1,3 are the prices
for Assets 1, 2, and 3 at time t + 1; Wt,1, Wt,2, and Wt,3 are the weights we assigned to the assets at time
t (optimal/target weights); Wt+1,1, Wt+1,2, and Wt+1,3 are the weights associated with the assets at time
t + 1. These weights at t + 1 are different from those at t due to the price variation of the assets. Finally,
Vt and Vt+1 denote the value of our portfolio at times t and t + 1.
So the problem now is to solve the values for Wt+1,1, Wt+1,2, Wt+1,3, and Vt+1 given other entries of the
table.
3解决方案

Q1 =
Wt,1Vt
Pt,1
where Wt,1Vt is the amount of money we invested in Asset 1 at time t. If we divide it by the share price, we
have the number of shares.
Therefore, Asset 1 we hold in our portfolio is worth Pt+1,1Q1 = Pt+1,1
Wt,1Vt
Pt,1
at time t + 1. This is true
for all the assets in our portfolio. So the whole portfolio at t + 1 is worth:
Vt+1 = Pt+1,1
Wt,1Vt
Pt,1
+ Pt+1,2
Wt,2Vt
Pt,2
+ Pt+1,3
Wt,3Vt
Pt,3
Then we can easily solve the values for Wt+1,1, Wt+1,2, and Wt+1,3:
Wt+1,1 =
Q1Pt+1,1
Vt+1
=
Wt,1Vt
Pt,1
Pt+1,1
Pt+1,1
Wt,1Vt
Pt,1
+ Pt+1,2
Wt,2Vt
Pt,2
+ Pt+1,3
Wt,3Vt
Pt,3
Wt+1,2 =
Q2Pt+1,2
Vt+1
=
Wt,2Vt
Pt,2
Pt+1,2
Pt+1,1
Wt,1Vt
Pt,1
+ Pt+1,1
Wt,2Vt
Pt,2
+ Pt+1,2
Wt,3Vt
Pt,3
Wt+1,3 =
Q3Pt+1,3
Vt+1
=
Wt,3Vt
Pt,3
Pt+1,3
Pt+1,1
Wt,1Vt
Pt,1
+ Pt+1,2
Wt,2Vt
Pt,2
+ Pt+1,3
Wt,3Vt
Pt,3
Now we have got values for all entries in the table. To rebalance the portfolio we just need to sell the
overweighted and buy the underweighted by the difference between current position and optimal position.
4 Transaction costs
Another issue you may want to consider is the transaction costs incurred during the rebalancing. Since the
transaction costs are paid regardless of trading direction, we just need to compute the turnover in absolute
term and multiply that with overall value of our portfolio and the transaction cost ratio. That is:
T C = (|Wt,1 − Wt+1,1| + |Wt,2 − Wt+1,2| + |Wt,3 − Wt+1,3|) × Vt+1 × 0.5%
2

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