Question

You opened a brokerage account a year ago. At that time, you bought $10,000 worth of shares of XYZ stock on margin - you used $5,000 of your own cash and borrowed $5,000 from the brokerage Örm.

1. (a) Right now, XYZ stock is up 6% from a year ago and you decide to get out of your XYZ holdings. Assume the brokerage Örm charges 4% interest on its margin loans, Compute your investmentís holding period return.

2. (b) Would you have had a higher holding period return if you had only borrowed $2,000 and used $8,000 of your own money in this investment? Explain.

3. (c) If the brokerage Örm charges a higher interest rate on its margin loans, would you reverse your answer to (b)? If no, how high does the interest rate need to be for you to reverse your answer to (b)? Explain.

Answer 1

a) Given investment amount = 10000

Own cash = 5000

Margin loan =5000

Given interest rate = 4% on margin loan

Hence interest = 4% of 5000= 200

Given return on stock = 6%

Hence return on stock = 6% of 10000= 600

Hence Net return = Return on stock - interets expense = 600-200=400

Holding period return = Net retun/ Own Cash*100

=400/5000*100= 8%

B) Given Own cash = 8000

Margin loan = 2000

Hence interest on margin loan = 4% of 2000= 80

Return on stcok = 6% of 10000 =600

Net return = 600-80- 520

Holding period return = 520/8000*100

=6.5%

Hence the Holding period return of 6.5% will be lower at own cash investment of 8000 as compared to answer a.

The reason for decrease is increase in the value of own capital . Even though interest cost has decreased by 80, due to increase in the own cash the denominatior has increase substantially whereby reducing the holding period return on investment

c) Let the interest rate charged by Brokerage firm be x%

For part a)

interest on brokerage in case a= x% of 5000

Hence net return =600-x% of 5000

Holding period return =(600-x% of 5000)/5000

For part b)

interest on brokerage in case a= x% of 2000

Hence net return =600-x% of 2000

Holding period return =(600-x% of 2000)/8000

To compute the indifferent point

Holding period return of part a=  Holding period return of part b

or (600-x% of 5000)/5000= (600-x% of 2000)/8000

or 600*8000- x% of 5000*8000= 600*5000-x% of 2000*5000

or 4800000-x% of 40000000= 3000000- x% of 10000000

or 4800000-3000000= x% of 40000000- x% of 10000000

or 1800000= x% of 30000000

or x%= 1800000/30000000

=X% = 0.06

i.e 6%

The answer would not reverse at any interest rate below 6%.At 6% Both the holding period return will be equal and any interest rate higher than 6% answer in part b will be higher than asnwer in part a.

the calculation is shown below

		4%	4%	6%	6%	8%	8%
		Loan amount = 5000	Loan amount = 2000	Loan amount = 5000	Loan amount = 2000	Loan amount = 5000	Loan amount = 2000
A	Investment income	600	600	600	600	600	600
B	Interest (Loan amount * Interest rate)	200	80	300	120	400	160
C	Return(A-B)	400	520	300	480	200	440
D	Own cash	5,000	8,000	5,000	8,000	5,000	8,000
E	Holding period return ( C/D)	8%	7%	6%	6%	4%	6%