Leverage Ratio and Return

A

archived_user

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
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.
 
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?
 
wichertj wrote: 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?
Click to expand...
I already explained it.
Leverage means A/E, not D/E.
 
Leverage is either D/E or asset/equity (out of 3 parts, 1 part is equity) ….. If ya take latter, answer would be C.Otherwise, it is -40%.
 
Kireeti wrote: Leverage is either D/E or asset/equity (out of 3 parts, 1 part is equity) … .
Click to expand...
Not in this context it isn’t.
It’s A/E.
 
True. Question gives asset value, so going by multiplier would be wise.
 
You must log in or register to reply here.
Back
Top