Portfolio optimization with factor tilting while constraining volatility
Posted: June 13th, 2017, 3:32 am
Hi, what optimizer I can use (preferably in R) to solve the following portfolio optimization problem:
min(fTx)
st:
1. -a <= SUM x(i) <= b
2. -c <= x(i) <= d
3. e <= SUM |x(i)| <= f
4. SQRT (xT COV x) <= g
a,b,c,d,e,f,g - positive. f is a vector. x - weights. COV var-covar matrix estimated from historical data. The problem without constrain 4 can be solved with linear solver ( with some tricks for condition 3). Condition 4 makes constrain non-linear, but quadratic. Any suggestion would be helpful. Thanks.
min(fTx)
st:
1. -a <= SUM x(i) <= b
2. -c <= x(i) <= d
3. e <= SUM |x(i)| <= f
4. SQRT (xT COV x) <= g
a,b,c,d,e,f,g - positive. f is a vector. x - weights. COV var-covar matrix estimated from historical data. The problem without constrain 4 can be solved with linear solver ( with some tricks for condition 3). Condition 4 makes constrain non-linear, but quadratic. Any suggestion would be helpful. Thanks.