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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.

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Leverage is Assets/Equity, not Debt/Equity.

Simplify the complicated side; don't complify the simplicated side.

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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:
I’m still getting -40% loss. 3x assets/equity means 1/4 is equity what is owned by you, right?

No.

Try some numbers.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

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?

I already explained it.

Leverage means A/E, not D/E.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

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) … .

Not in this context it isn’t.

It’s A/E.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

True. Question gives asset value,  so going by multiplier would be wise.