Allocation according to percentages.

Question

How to allocate assets when Drawdowns vary and want to limit total drawdown to 15%

E.G. Five assets: A B C D E

Drawdowns: 34.3% 22.0% 22.0% 19.7% 13.2%


If investment capital $5000, how much to allocate to each? What is the math formula? Total drawdown should be $750.

 

Answer 1

A+B+C+D+E = 5000

 

343A + 220B + 220C + 197D + 132E = 750000 <--- clears the decimal by multiplying everything by 1000

 

There are 5 unknowns with only 2 equations.

Hence, there are 3 free variables (3 degrees of freedom)

with which the solutions are derived numerically.

I'll choose C,D,E to be the free variables.

 

The first equation becomes A+B = k where k = 5000-c -d -e

The second equation becomes 343A + 220B = 750000 - 132e - 197d - 220c

 

Let t = 750000 - 132e - 197d - 220c

Solving the first equation for A, it is A = k - B

The second equation is  343(k-B) + 220B = t

 

                                   343k - 343B + 220b = t

                                   343k - 123b = t

 

                                   343k - t = 123b

 

                                    b = (343k - t)/123

 

 

So once C, D, E are selected, K and t can be calculated

Once k and t are calculated, b can be calculated.

Once b is calculated, then A can be calculated using the equation above in 

bold that reads A = k - B

 

 

For example:

  For C=250, D=500, E = 4000 The results are

   B = 140.24 and A = 109.76

 

 

I have uploaded the spreadsheet FUNDS ALLOCATION

which allows you to specify values for C,D, and E and

will calculate A and B so that these conditions are met.

The filename is FUNDS ALLOCATION.xls