Question

Richard was a computer engineer working for a payroll outsourcing company. His professional knowledge led him to believe that a small-cap firm specializing in developing new AI technology for warehousing had great potential. Richard withdrew all his savings of $38,000 and opened a margin account with a local brokerage company. The initial and maintenance margin requirements for that account were 50% and 30% respectively, and the call-money interest rate for the margin loan was 9%. Richard decided to maximize his purchase of the small firm’s stocks, which was trading around $7 per share: he entered a GTC limit order to buy 11,000 shares at $6.90 per share. A few days later, his limit-buy order was executed; Richard then immediately entered a GTC limit-sell order to sell all the shares at $7.95 and expected to earn 30% return on investment. During the following 8 months, the stock’s prices gradually dropped to $5.10. The company was scheduled to make its quarterly earnings announcement and Richard nervously waited for the results. Unfortunately, the earnings announcement, which was made after the market closed, was a bad one; the next morning, the stock had a huge gapping-down open price of $3.95. A few minutes after the market opened, Richard received a margin call from the brokerage firm. He did not have extra money to meet the call; thus, the brokerage firm made a forced-sale of a sufficient number of shares in order to remove the margin call. The selling price for the forced-sale was $3.89 per share. Later that day, the stock’s price rebounded a little to close at $4.08. Richard’s ex-fiancée Sally had also followed the stock closely. She had had a big fight with Richard three weeks earlier and decided to breakup with him. The fight was about their planned wedding needing to be postponed indefinitely due to Richard’s savings being tied up in stock. Sally told Richard that he should have applied the stop-loss and gotten out of that stock long time ago. After the break-up, Sally also opened a margin account with all her savings of $9,000. She was waiting for the right time to sell-short the stock with the intention to prove Richard wrong. On the day Richard got the margin call, Sally was influenced by the company’s bad earning news and decided to sell short 4,500 shares at a limit price of $4 per share. Her short-sale limit order was executed about 30 minutes before the market closed on that day. In the following three months, the stock price fluctuated in a relatively wide range between $4.06 and $4.63. It was time for another quarterly earnings announcement. This time it was a very good news: 30% above the average of lower earnings estimates adjusted by the financial analysts since the last earnings season. Since the company had been plowing back all its earnings for growth, its stocks had never paid cash dividends in the past and would not pay the dividends in the near future. The stock responded to the good earnings news and jumped to $4.96 at the open the next day, then fluctuated between $4.70 and $5.46 over the next two months Afterward, the stock prices started to move up. Seven months later, the stock’s price reached a new high of $8.00. Around that time, Richard’s limit-sell price of $7.95 was reached and all his shares were sold at that price. As for Sally’s short position, she had covered all 4,500 short shares long ago when she received a margin call. Answer the following questions. 1. What was Richard’s %margin when the stock’s price went down to $3.95 due to the bad earnings news and triggered the margin call? 2. To meet the margin call, how many shares were sold by the brokerage company at $3.89 per share? 3. Richard finally was able to sell all the remaining shares at his target selling price of $7.95 per share. What was his 20-month holding-period rate of return (HPR)? Convert this HPR to the effective annual rate of return (EAR). 4. At what stock price did Sally receive a margin call? 5. If Sally covered all the short shares at the margin call price, what would be her holding-period rate of return (HPR)?

Answer 1

Ans.1:

Purchase price = 11,000 x 6.9 = $ 75,900

Initial margin requirement = $75,900 x 50% = $37,950

Maintenance margin = $75,000 x 30% = $22,770

Amount lost = (6.9 - 3.95) x 11,000 = $2.95 = $32,450

Balance in initial margin account = $37,950 - $32,450 = $5,500 (the call is triggered as the amount left is below the Maintenance margin amount)

Variation margin required = $32,450

%Margin = $32,450/$37950 = 0.85507246 ~ 85.51%

Ans.2:

Number of shares to be sold = $32,450/$3.89 = 8,341.90231 ~ 8,342

Ans. 3:

Number of shares left = 11,000-8,342 = 2,658

Sell price = 7.95 x 2,658 = $21,131.1

Interest to be paid = 37,950 x 0.09 x (20/12 months) = $5692.5

Profit = 21,131.1 - $5,692.5 = $15,438.6

HPR = $15,438.6/$37,950 = 0.40681423 ~ 40.68%

EAR = (1 + 0.4068)^12/20 - 1= 0.2273 ~ 22.73%

Ans.4:

Sally’s sell price = 4,500 x 4 = $18,000

Initial margin requirement = $18,000 x 50% = $9,000

Maintenance margin = $75,000 x 30% = $5,400

Sally will loose start to loose money from the margin account when the stock price start to rise above $4

Amount of loss for Margin call = $9,000 - $ 5,400 = $3,600

Loss per share = $3,600/4500 = $0.8

Price for trigger of the call = $4 + $0.8 = $4.8