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%.

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.