From Brad Delong, economics professor at UC Berkeley:
His framework is similar to mine. Let’s say you decided you only want 2X leverage. So whenever your portfolio rises beyond 2X you buy more to take on more debt, and when it falls you sell to lessen the debt. At all times you try to maintain a constant leverage ratio. Then the question arises: what is the optimal leverage ratio?
Answer: 2.42.
Being all in bonds at β = 0 turns $1 of real value into $35 over the past century and a half. Moving from bonds to stocks—from β = 0 to β = 1—multiplies your portfolio value today by an additional 450-fold. Borrowing your wealth and adding leverage—β = 2—gets you from $16,000 to $380,000: an additional nearly 25-fold wealth amplification. And then going from β = 2 to β = 2.42 gets you an additional 40% to $528,000.