(Here is a link to the original post)
I received this interesting problem from a friend today:
Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence team has identified the following investment opportunities (here Expected Return and Expected StdDev stand for Expected Monthly Return and Expected Standard Deviation of Monthly Return and Price = Price of each investment unit):
Hedge Fund 1: Expected Return = .0101, Expected StdDev = .0212, Price = $2 million
Hedge Fund 2: Expected Return = .0069, Expected StdDev = .0057, Price = $8 million
Hedge Fund 3: Expected Return = .0096, Expected StdDev = .0241, Price = $4 million
Hedge Fund 4: Expected Return = .0080, Expected StdDev = .0316, Price = $1 million
What is the optimal allocation to each hedge fund (use MATLAB)?
The responses to the original post were things I had considered, but the loss of correlation among assets still seems like a big issue. Under the assumption that the assets are independent, the covariance matrix is diagonal, and using the standard constrained portfolio allocation tools in MATLAB seem to fail. Should I be choosing a specific objective function like Mike Spivey suggested in the original post while assuming independence?