Question

At the beginning of the year Donald opens a margin account and purchases 500 shares of FIN Corp at $40. Donald borrows $5000 from his broker at an annual interest rate of 10% to fund the purchase.
a) What is the initial margin?
b) What would be the margin if the price of FIN Corp fell to $30 at the end of the year?
c) What is the annual return that Donald would make from his investment if the price of FIN Corp fell to $30 at the end of the year?
d) What is the annual return that Donald would make from his investment if the price of FIN Corp rose to $50 at the end of the year?
e) Discuss the implications of margin trading for the risk of Donald’s portfolio.
f) What is the stock price of FIN Corp that would lead to Donald receiving a margin call? Assume that the price decline happens immediately. A margin of 30% will lead to a margin call.

Answer 1

a]	Initial margin = 500*40-5000 =	$        15,000
b]	Balance in margin on fall in price = 15000-500*(40-30) =	$        10,000
c]	Interest on the margin account at the year end = 5000*10% =	$              500
	Balance in the margin account = 10000-500 =	$          9,500
	Annual return = 9500/15000-1 =	-36.67%
d]	Balance in margin on rise in price = 15000+500*(50-40) =	$        20,000
	Interest on the margin account at the year end = 5000*10% =	$              500
	Balance in the margin account = 20000-500 =	$        19,500
	Annual return = 19500/15000-1 =	30.00%
e]	Margin trading gives financial leverage to the investment. Higher
	the leverage, higher the risk. As can be seen a $10 decrease in
	price yields a greater loss % than a $10 increase in price.
f]	The equality would be:
	15000-(40-p1)*500 = 500*p1*0.3, where p1 = the max price at which margin call would not be received.
	Solving for p1
	15000+500*p1-20000 = 150*p1
	5000 = 350*p1
	p1 = 5000/350 = $14.29
	CHECK:
	Balance in margin acccount when price falls to 14.29 = 15000-500*(40-14.29) =	$          2,145
	Maintenance margin required = 500*14.29*30% =	$          2,144