Question

You want to short sell 100 shares of PQR using a 60% margin. The maintenance margin is 30%. The current price of PQR is $40. How much money did you have to invest today? What price will trigger a margin call? What is the overall rate of return on your investment if the stock is selling at a price of $48 in 1 year? What is the overall rate of return on your investment if the stock is selling at a price of $34 in 1 year?

) You want to buy 100 shares of MNO using a 60% margin. The maintenance margin is 30%. The current price of MNO is $70. How much money did you have to invest today and how much money did you borrow? What price will trigger a margin call? What is the overall rate of return on your investment if you sell the stock 6 months later at a price of $77? What is the overall rate of return on your investment if you sell the stock 6 months later at a price of $65.   (assume the margin loan (call rate) rate is 8% per year).

Answer 1

Current Stock Price = $ 40 and Number of Shares bought = 100, Total Value of Shares Shorted = 40 x 100 = $ 4000

Required Initial Margin = 60 %

Therefore, Margin Posted = 0.6 x 4000 = $ 2400

A maintenance margin of 30% implies that at any point of time the margin account's equity contribution of $ 2400 should be ATLEAST equal to 30% of the total account value.If the price moves beyond(above) this limiting condition margin call will be trigerred

Let the price at which margin call will be trigerred be $ K

Therefore, Account Value at This Price = 2400 + 100K

Limiting Case for Margin Call: 30 % of (2400 + 100K) > = 2400

0.3 x 2400 + 0.3 x 100K >= 2400

30K >= 2400 - 720 = 1680

K >= 1680/30 = $ 56

At a price above $ 56 margin call will be trigerred.

If Price is $ 48 after a year, Payoff from Short Account = (40-48) x 100 = - $ 800

Initial Investment = $ 2400

Therefore, Total Return = -800 / 2400 = - 0.3333 or -33.33 %

If Price is $34 after a year, Payoff from Short Account = (40-34) x 100 = $ 600

Initial Investment = $ 2400

Total Return = (600/2400) x 100 = 25 %

NOTE: Please raise a separate query for solution to the second unrelated question as one query is restricted to the solution of only complete question (with a maximum of four sub-parts)