From Kaplan:
" using leverage to increase the portfolio’s return over a long time horizon is unlikely to increase its compounded return. Leverage increases volatility, which reduces the expected compounded or geometric return in a multiperiod setting."
Is there any proof of this or reasoning for this? Particularly for leverage and a long-term horizon, the logic of higher risk and higher return breaks down? Is it because leverage is deemed diversifiable risk over the long run?
I don’t about academic proof but I tried to run a simulation.
With low volatility and series of positve of returns leverage is ok.
But with high volaitility the possibility of big negative year, especially near the start, means it can take a long time for returns to turn back to favouring leverage.
I aslo excluded the need to re-margin if losses got too big as I realised I would have to move from Excel to pythin and I it would take too long relative to my interest
In extreme think a stock market crash could make you bust with no possibility to recouping loss.
The idea behind the statement is that while leverage may boost returns in the short term, it also heightens volatility, increasing the likelihood of larger losses during market downturns. Over a long time horizon, this volatility becomes more significant, making it less probable for leveraged portfolios to outperform unleveraged ones. Leverage introduces additional risk that may not necessarily be rewarded over time, as the potential for higher returns is counterbalanced by the increased risk of significant drawdowns. Therefore, the trade-off between risk and return becomes less favorable when employing leverage for extended periods.
The theory is not the hard part.
Is there mathematical proof?