proc optmodel to minimize varience

[Amalik]

Hi,

I want to minimise the following function;

Varience (e) = Varience (R) - Varience (w1r1+w2r2+w3r3+w4r4)

However, I am not quite sure that how to state its objective function using the SAS coding, can someone help me out in that?

[RobPratt]

I'd like to help, but I need more detail.  Which are decision variables, and which are data?

[Amalik]

Hi Rob,

I am actually conducting style analysis of AMP fund on 4 benchmark returns,

I actually want to minimise the variance of the tracking error and find the weights that minimise the following function,

min VAR(R.f - SUM[w_i * R.s_i]) = min VAR(F - w*S)
  s.t. SUM(w_i) = 1; w_i > 0

where:
R.f   Fund returns
R.s   Style returns
w_i   Style weights

 For my case it becomes, 

min Var(AMP_AIT) –  Var (w1*US_Small_Val + w2*US_Small_Gr + w3*US_Large_Gr + w4*_US_Large_Val)

subject to the constraints where sum Wi = 1 and Wi >= 0

How to use the proc optmodel in this regard will be greatly helpful for me. I have also attaced my dataset for your reference.

Thanks

[RobPratt · Accepted solution]

I think the following does what you want, first calling PROC CORR to compute the covariance from the historical data and then calling PROC OPTMODEL to formulate and solve the optimization problem:

proc corr data=styledata(drop=date)
   out=corrout(where=(_type_ ne 'CORR')) cov noprint;
run;

data stats(drop=_name_);
   set corrout;
   if _type_ = 'COV' then delete;
run;
proc transpose data=stats out=stats;
   id _type_;
run;

proc optmodel;
   /* declare parameters and read data */
   set <str> ASSETS;
   str target = 'AMP';
   set BENCH = ASSETS diff {target};
   num cov {ASSETS, ASSETS};
   read data stats into ASSETS=[_name_];
   read data corrout(where=(_type_='COV')) into [_name_]
      {i in ASSETS} <cov[_name_,i]=col(i)>;

   /* declare optimization model */
   var W {BENCH} >= 0 <= 1;
   /* Var(X - Y) = Var(X) + Var(Y) - 2 Cov(X,Y) */
   min Variance = 
      sum {i in BENCH, j in BENCH} cov[i,j] * W[i] * W[j]
    + cov[target,target] 
    - 2 * sum {i in BENCH} cov[i,target] * W[i];
   con InvestAll:
      sum {i in BENCH} W[i] = 1;

   /* call solver and print optimal solution */
   solve;
   print W;
quit;

[Amalik]

I just can't thank you enough Rob, the coding worked. I am really grateful to you for this.