Question

Steve bought ABC stocks on margin, while Larry shorted it. Suppose the share price of ABC at the time of their trading was $100. Initial margin was 50% for margin trading and short selling. One year later, ABC’s per-share price had risen to $115 and they both closed their positions. ABC issued $2-per-share dividends during the year. Interests on margin loans were negligible. Answer the following questions. 1. What was Steve’s rate of return on his investment? (Note: these questions do not require knowledge of their initial investment. You can use one share as the basis of your calculation.) 2. What was Larry’s rate of return on his investment? 3. Suppose right after the margin trade (no dividends announced or paid), there was a big stock price movement and Steve got a margin call. If the maintenance margin was 30%, ABC’s shares must have dropped below price P per share. Find P

Answer 1

Margin amount required by both Steve and Larry for one share =  50% of $100 = $50

1. Steve received $2 as dividend as well as $115 after one year and returned the $50 borrowed to purchase the share on margin. So, in the end , Steve received $115+$2 - $50 (along with negligible interest)  = $67 on his investment of $50

Steve's rate of return = 67/50-1 = 34%

2. Larry invested $50 as margin along with $100 received as short sale proceeds in the margin and had to pay $2 as dividend (to the share lender) and purchase the share at the end for $115.

So, in the end , Larry got =$50+$100 - $115- $2 =$33 on his investment of $50

So,  Larry's rate of return = 33/50-1 = -34%

4. Steve would get a margin call only when the stock price goes down

At price P , Value of equity = 50+P-100 = P-50

So, (P-50)/P <30% to receive a margin call

P-50 < 0.3P

P<50/0.7

or P < 71.43

So, Steve will get a margin call when price falls below $71.43 . So, P = $71.43