# Math Help - Maximization problem

1. ## Maximization problem

Hi, I need urgent help on this assignment so thanks in advance.

I am supposed to choose a portfolio of 5 stocks, % daily gain in my portfolio is a. % daily gain in the S&P500 is b.

I need to maximize P where

P=E(d)-0.5Var(d)
and d=a-b

Can anybody try to solve the inequality for E(d)<0.5Var(d) in terms of a and b? Is it correct to approximate my summation of ai2 as an integral in this case? Cos my number of terms do not tend towards infinity but is fixed at 60 observations.

Thanks again.

2. Originally Posted by guangzhao
Hi, I need urgent help on this assignment so thanks in advance.

I am supposed to choose a portfolio of 5 stocks, % daily gain in my portfolio is a. % daily gain in the S&P500 is b.

I need to maximize P where

P=E(d)-0.5Var(d)
and d=a-b

Can anybody try to solve the inequality for E(d)<0.5Var(d) in terms of a and b? Is it correct to approximate my summation of ai2 as an integral in this case? Cos my number of terms do not tend towards infinity but is fixed at 60 observations.

Thanks again.
Off-hand I'd say that not much can be done without knowing anything about the distributions that a and b follow.

3. Yep, but since its stock price movement I'd assume it to be log normal right?

4. If anybody can help solving the inequality for

E(d)>Var(d)

in terms of just d and in a differentiable form it be much appreciated.

Thanks.