Problem #1: Seven months ago, Ms. Investor purchased 400 shares of stock on marg

Question

Problem #1: Seven months ago, Ms. Investor purchased 400 shares of stock on margin at a price per share of $36. The initial margin requirement on her account is 70 percent and the maintenance margin is 40 percent. The annualized call money rate is 3.50% per annum, and based on her credit risk, she pays 150 basis points of spread. Today, she sold these shares for $37.50 each. What is her annualized holding period rate of return? Assume that the stock paid a dividend of $0.25 a share one day before Ms. Investor sold the shares. Also, assume that Ms. Investor never received a margin call in these seven months.

Explanation / Answer

Shares purchased from own funds (initial Margin) =400*36 *70%= $10080

Shares purchased from borrowed funds = 400*36*30%= $4320

Call money rate = 3.5%+1.5% = 5%

Dividend = 0.25*400 = $100

Interest on initial margin = 5% * 4320 * 7/12 = $126

Proceeds from sale of equity = 400*37.50 = $15000

Holding period return in simple form is calculated as below:

(15000+100-4320-126-10080) / 10080 = 5.69%

Now we have to convert the above yield into an annualized return

(1 + 0.0569)12/7 -1 = 1.09951- 1 = 9.95%

Hence the annualized HPR is 9.95%

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