Calculating Margin Return

CFA Level I
#1
  1. Hi all, I have a questino with this problem… I don’t understand why it’s not 200% return. Thanks.
  2. A trader has purchased 200 shares of a non-dividend-paying firm on margin at a price of $50 per share. The leverage ratio is 2.5. Six months later, the trader sells these shares at $60 per share. Ignoring the interest paid on the borrowed amount and the transaction costs, what was the return to the trader during the six-month period?
  3. 20 percent.
  4. 33.33 percent.
  5. 50 percent.
#2

What’s your initial investment?

What’s your profit?

The return is profit / investment.

#3

initiail investment is $20, profit is $40. That’s why I thought it’s supposed to be 200%.

#4

Profit is $10, not $40.

#5

But initial investment was only $20, and they sold it for $60, why is profit $60-$50? How come the extra $30 due to leverage is not considered?

Thanks.

#6

You have to pay back your loan of $30 dollars before you earn any profit

#7

Purchase Your equity (20) + Your loan (30) = total (50)

At Sale: Original equity (20) + Your loan (30) + Gain (10) = total (60)

Pay back your loan: Total (60) - loan (30) = 30 = Original equity (20) + gain (10)

#8

I kinda figured that the people who lent you the $30 would want it back.

Call me crazy.

#9
#10
#11

this makes sense, however when I did the problem I calculated orignial use of debt to be 71.5% of the investment from the given 2.5 levergae ratio. looks like your solution and the correct answer involves a 60% orignial investment with debt.

How did you get 60%?

I got 71.4% by doing this… leverage ratio = debt/equity = 2.1/1… debt/ debt+equity = 2.5/ 3.5 =71.4%

#12

Leverage ratio is not D/E it is D+E/E . You get this quickly by 1/LR --> 1/2.5 --> .4.

Verify that with your original trade: Equity 20, Total position: 50 50/20 = 2.5

#13

Thanks! making a flash card for that …right now…