Tony purchased 100 shares of T-Rex stock for $43 a share. On the same day, Sam also purchased 100 shares of T-Rex stock for $43 a share. Tony paid cash for his purchase while Sam used margin. The initial margin requirement on this stock is 60% while the maintenance margin is 40%. Both Tony and Sam sold their shares after eight months at a price of $40 a share. The stock pays no dividends. Tony had a holding period percentage return of ________% as compared to Sam's ________% return. Ignore margin interest and trading costs.

Question

Quizplus · Accepted Answer

First, let's calculate the initial margin that Sam had to pay: 
Initial Margin = 60% of (100 shares × $43/share) = $2,580

Therefore, Sam borrowed the remaining amount from the broker: 
Loan = Total Value of Shares - Initial Margin = ($4,300 - $2,580) = $1,720

Now, let's calculate the maintenance margin: 
Maintenance Margin = 40% of (100 shares × $43/share) = $1,720

Since Sam's loan was equal to the initial margin, he had no equity in the account. Thus, as soon as the stock price fell below the initial margin, he would receive a margin call.

Let's calculate the price at which Sam would receive a margin call: 
Margin Call Price = (Loan + Initial Margin) / 100 shares = ($2,580 + $1,720) / 100 shares = $44

Since the stock price did fall below the margin call price of $44, Sam would have to sell his shares to meet the margin call.

Now, let's calculate the total amount that Tony paid for his shares: 
Tony's Total Cost = 100 shares × $43/share = $4,300

Now, let's calculate the total amount that Sam paid for his shares: 
Sam's Total Cost = Initial Margin + Loan = $2,580 + $1,720 = $4,300

After eight months, both Tony and Sam sold their shares for $40/share.

Let's calculate Tony's total proceeds from the sale: 
Tony's Total Proceeds = 100 shares × $40/share = $4,000

Tony's Holding Period Return = (Total Proceeds - Total Cost) / Total Cost = ($4,000 - $4,300) / $4,300 = -0.0698 or -6.98%

Let's calculate Sam's total proceeds from the sale: 
Sam's Total Proceeds = 100 shares × $40/share = $4,000

Sam would have received a margin call when the stock price fell to $44, which means he would have sold his shares at that price.

Let's calculate Sam's gain/loss from the sale: 
Sam's Gain/Loss = Total Proceeds - Total Cost - Interest Paid - Margin Call (if any)

Interest Paid = Loan × Interest Rate × Time = $1,720 × (10% / 12 months) × (8/12) = $114.67

Since the stock price fell below the margin call price, Sam had to sell his shares as soon as the price fell to $44. Therefore, he sold his shares at a loss.

Margin Call = Initial Margin - Maintenance Margin = $2,580 - $1,720 = $860 (This is the amount that Sam lost due to the margin call)

Sam's Gain/Loss = $4,000 - $4,300 - $114.67 - $860 = -$1,274.67

Sam's Holding Period Return = Gain/Loss / Total Cost = -$1,274.67 / $4,300 = -0.2965 or -29.65%

Therefore, Tony had a holding period percentage return of -6.98% as compared to Sam's -29.65% return. The answer is D.

Tony Purchased 100 Shares of T-Rex Stock for $43 a Share