# Leverage Ratio and Return

A trader pays \$100 per share to buy 500 shares of a non-dividend-paying firm. The purchase is done on margin, and the leverage ratio at purchase is 3.0X. Three months later, the trader sells the shares for \$90 per share. Ignoring transaction costs and interest paid on the margin loan, the trader’s 3-month return was closest to:

A)

–10%.

B)

–40%.

C)

–30%.

I went through the process of D/E of 3X means 3/4 is debt and 1/4 is equity so your margin (your money) is 25%. Using this method I got a loss of 40% after calculating the decrease in price and the repayment of the borrower money (75% * \$37,500). However this is the explanation provided:

With a leverage ratio of 3 and a 10% decrease in share value, the investor’s return is 3 × –10% = –30%.

Can someone explain the logic behind this?

Thanks.

Leverage is Assets/Equity, not Debt/Equity.

I’m still getting -40% loss. 3x assets/equity means 1/4 is equity what is owned by you, right? So out of the \$50,000 initial value you own \$12,500 and borrower \$37,500. Once the shares drop to \$90 each the value becomes \$45,000. Once you pay back the loan of \$37,500 you are left with (\$45,000 - \$37,500) = \$7,500. (ending-beginning)/beginning. = (\$7,500 - \$12,500)/\$12,500 = -40%. What am I missing?

If I used 75% is what you own I get a loss of -13.33% using the steps above.

No, leverage ratio of 3x means your total purchasing power is 3x your own equity. So that means 1/3 is your own and 2/3 is borrowed.

Because you took a position that is 3x your equity, you would incur. 3x the loss.

That makes sense! Can you explain why 1/3 is what you own and not 1/4? I think I’m getting confused with D/E ratio:

3x. D/E means 1/4 is what you own.

3x Leverage means 1/3 and not 1/4?

No.

Try some numbers.