So investors holding period return isHPR 35250 37500 2500 37500 067 iii If year

So investors holding period return ishpr 35250 37500

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So investor’s holding period return is HPR = ($35,250 - 37,500 + 2,500) / $37,500 = 0.67% (iii) If year-end ex-dividend price of stock goes down by 10%, the total value of stock is $75 × (1 - 10%) × 1000 = $67,500 The liability is $39,750. Therefore, the equity in account is $67,500 - $39,750 = $27,750. So investor’s holding period return is HPR = ($27,750 - 37,500 + 2,500) / $37,500 = -19.33% Method 2: (portfolio approach) Because there is no margin call concern. Given initial balance sheet is: Assets Liabilities and Owner’s Equity Value of stock $75,000 Loan from broker $37,500 Equity $37,500 The weight on the Facebook (FB) stock: 𝜔 ? = $75000 $37500 = 2 , while the weight on the margin loan 𝜔 ? = −$37500 $37500 = −1 . Because there is no margin call happening during the whole year, investor s overall portfolio (this margin position) has returns expressed as follows: ? 𝑝 = 𝜔 ? × ? 𝐹? + 𝜔 ? × ? ?𝑎?𝑔𝑖? 𝑖??𝑒?𝑒?? Where, ? 𝐹? is the 1year holding-period return of facebook and ? ?𝑎?𝑔𝑖? 𝑖??𝑒?𝑒?? is the interest rate required by the broker.
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i) ? 𝐹? = 10% + $2.5 $75 × 100% ≈ 13.333% , ? ?𝑎?𝑔𝑖? 𝑖??𝑒?𝑒?? = 6% ? 𝑝 = 2 × 13.333% − 6% ≈ 20.67% ii) ? 𝐹? = $75−$75+$2.5 $75 × 100% ≈ 3.333% , ? ?𝑎?𝑔𝑖? 𝑖??𝑒?𝑒?? = 6% . ? 𝑝 = 2 × 3.333% − 6% = 0.67% iii) ? 𝐹? = −10% + $2.5 $75 × 100% ≈ −6.667% , ? ?𝑎?𝑔𝑖? 𝑖??𝑒?𝑒?? = 6% ? 𝑝 = 2 × (−6.667%) − 6% ≈ −19.33% (c) Assume that the stock price is P when investor receives a margin call. Then the total value of stock is 1000P. The liability is still $39,750. So the equity in account is 1000P 39,750. The percentage margin is 25% when investor receives a margin call, that is, 25% = (1000P 39,750) / 1000P => P = $53 .
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Q9. You are bearish on Facebook stock, and want to sell short 1000 shares at current price. The initial margin is 50%. This time, you don t need to pay interest rate on the shares borrowed. (a) Assume that you earn no interest on the funds in your margin account. Facebook currently does not pay dividend . Assume that you don’t get any margin call during 2016. What will be your holding period return in 2016 if the stock price of Facebook (i) goes up by 10% (ii) is still $75 (iii) goes down by 10% during the next year? (b) How high can stock price rise before you get a margin call, if the maintenance margin is 25%? Short sales case: The initial sale proceeds from short selling 1000 shares of Facebook is $75 × 1000 = $75,000. Since the broker has a 50% initial margin requirement on short sales, investor must have other cash or securities in his/her account worth $75,000 × Initial Margin = $75,000 × 50% = $37,500 The initial balance sheet looks like this: Assets Liabilities and Owner’s Equity Sale proceeds $75,000 Short position in Facebook stock (1,000 shares owed) $75,000 Cash/security in account $37,500 Equity $37,500 (a) Method 1: (i) If stock price goes up by 10%, investor pays $75 × (1 + 10%) × 1000 = $82,500 to buy back 1,000 shares and replace them to the broker. Then the equity in account is changed to $75,000 + 37,500 82,500 = $30,000. Investor’s holding p eriod return is HPR = ($30,000 - 37,500) / $37,500 = -20% (ii) If stock price does not change, investor pays $75,000 to buy back 1,000 shares and replace them to the broker. Then the equity in account is still $37,500. Investor’s holding period return is HPR = 0%. (iii) If stock price goes down by 10%, investor pays $75 × (1 - 10%) × 1000 = $67,500
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to buy back 1,000 shares and replace them to the broker. Then the equity in account is changed to $75,000 + 37,500 67,500 = $45,000.
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