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01-22-2017 11:02 PM

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?

Accepted Solutions

Solution

01-26-2017
01:57 AM

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Posted in reply to Amalik

01-25-2017 09:41 PM

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;
```

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Posted in reply to Amalik

01-24-2017 05:40 PM

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

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Posted in reply to RobPratt

01-25-2017 07:22 AM

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

Solution

01-26-2017
01:57 AM

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Posted in reply to Amalik

01-25-2017 09:41 PM

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;
```

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Posted in reply to Amalik

01-26-2017 01:56 AM

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