# How to calculate leverage ratio while buying stocks?

I was recently studying 2008 research study by Yale researchers Ian Ayres and Barry J. Nalebuff in which they tell to use 2 to 1 leverage ratio while buying stocks in your young age and gradually lower the leverage ratio in retirement stages in order to maximize the returns? So I wonder how is this leverage ratio calculated? Lets say I keep 10,000 dollars as collateral in my brokerage account and ask for rest 10,000 dollars from the broker itself and invest entire 20,000 dollars in stocks. Is my leverage ratio 1:1 in this case? And how does this leverage help to reduce risk instead of increasing it ? Please help.

• Leverage increases the possible returns, while significantly increasing risk. It does not reduce risk. Young people often have a higher tolerance for risk, and have more years in their life to make up for poor returns, so increasing average returns for a young person might be a benefit even with the risk. However I think a blanket recommendation for investing with debt is not great, you really need to be careful you don't get in over your head. Jul 7, 2022 at 12:37

The leverage ratio is just the total amount invested divided by the invested amount that is not borrowed. So if you invest $10,000 of your money, borrow$10,000 and invest it, your leverage ratio is $20,000/$10,000 = 200%. The amount you keep in collateral is not considered.
But leverage is pointless if you keep collateral in the amount that's borrowed. If you instead just invested all of your $20,000, you'd get the exact same returns as if you invested$10,000, borrowed $10,000, and kept$10,000 as collateral.
It does not. Leverage multiplies risk as well as return. If you invest $100 and borrow$200 for a leverage ratio of 300/100=300%, and the value of the investment drops 33%, you now have an investment worth $200 and owe$200, so you technically are bankrupt. This is why levered account require some amount of collateral. A 3X ETF could also in theory be wiped out if the market moves more than 33% - since the only funds the ETF has left would be borrowed. In reality there may be ways to survive but it would be a massive climb back to solvency.