Homework #1

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Loyola University Chicago *

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335

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Finance

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Jan 9, 2024

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FINC 335 Homework #1 1. T-bill, APR = 4.92%, maturity = 30 days. a. FV = $100 0.0492 = 365/30 x r r = 0.0492/(365/30) = 0.004044 0.004044 = (100 – P)/P 0.004044P = 100-P 0.004044P + P = 100 1.004044P = 100 P = 100/1.004044 P = 99.597 The ask price is $99.60. b. Invest in par value of $75,000 75,000/100 = 750 750 x 99.597 = 74,697.75 You would have to pay $74,697.75 2. (1) 3-month T-bill for $9,901, (2) 6-month T-bill for $9,804 a. FV = $10,000 HPR = (10,000-9,901)/9,901 = 0.00999 APR = 365/90 x 0.00999 = 0.040515 APR for T-bill (1) is 4.052% HPR = (10,000-9,804)/9,804 = 0.01999 APR = 365/180 x 0.01999 = 0.040535 APR for T-bill (2) is 4.054% b. EAR = (1 + 0.00999) ^365/90 – 1 1.04114 – 1 = 0.04114 EAR for T-bill (1) is 4.114% EAR = (1 + 0.01999) ^365/180 – 1 1.04095 – 1 = 0.04095
EAR for T-bill (2) is 4.095% EAR of T-bill (1) is higher because EAR will always be higher, or equal, than APR since it calculates the compounding effect of the return. 3. $20,000 for a CD. Bank A 3-month CD, 5% APR Bank B 3-month CD, 5% EAR 0.05 = 365/90 x r 0.05/(365/90) = r r = 0.01233 EAR = (1 + 0.01233) ^365/90 – 1 EAR = 0.0509 5.09% I would choose to buy the CD from Bank A because it has a higher EAR than the CD offered by Bank B. 20,000 (1 + 0.01233) = 20,246.60 Once the CD matures, you will get back $20,246.60. 4. 4 years ago, $50,000 in stock ABC. a. r(G) = [(1 + 0.2) (1 + -0.5)(1 + -0.2)(1 + 0.1)]^1/4 – 1 r(G) = [0.528] ^1/4 – 1 = 0.85243 – 1 = -0.14757 The geometric average annual return is -14.76% r(A) = (0.2 + -0.5 + -0.2 + 0.1)/4 r(A) = -0.4/4 = -0.1 The arithmetic average annual return is -10% b. 50,000 (1.2) (0.5)(0.8)(1.1) = 26,400 My ABC stock holding at the end of 2022 is worth $26,400. c. The geometric average annual return reflects my actual performance over the past 4 years because each year the actual annual return has dropped way more over the years than 10%, which is what the arithmetic average annual return states.
d. 2019 2020 2021 2022 0.00 10,000.00 20,000.00 30,000.00 40,000.00 50,000.00 60,000.00 70,000.00 ABC Stock Portfolio Geometric Return Actual Return Year Actual Return Geometric Return 2019 $60,000 $42,621.50 2020 $30,000 $36,331.85 2021 $24,000 $30,970.36 2022 $26,400 $26,400.06 5. Intel stock is listed on NASDAQ and its listing symbol is INTC. Closing price on 09/07 for INTC is $38.18. a. Market buy order: 38.18 + 0.02 = 38.20 My order is likely executed at $38.20. b. Market sell order: 38.18 – 0.02 = 38.16 My order is likely executed at $38.16. c. Limit sell $38.19 The limit order to sell will most likely not be executed because the ask price is above the $38.16 ask price mark. d. Limit buy $38.21 The limit order to buy will most likely be executed because the stipulated price is above the bid price.
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6. 100 shares of MSFT stock Invest: $18,000 Interest rate: 6% Selling at: $329.91/ share Borrowed: 100(329.91) – 18,000 = $14,991 a. Price increased 15% 329.91 x 0.15 = 49.4865 + 329.91 = $379.3965 Assets Liab + equity 100 shares of MSFT = $37,939.65 $14,991 (liab, borrowed) $22,948.65 (residual equity) Invested: $18,000 End up with: $37,939.65 - $14,991 (1 + 0.06) = 22,049.19 HPR = (22,049.19 – 18,000)/ 18,000 = 0.2249 22.5% If the price of the MSFT stock increased by 15% over the next year, the holding period return would be 22.5% b. Price increased 2% 329.91 (1 + 0.02) = $336.5082 Assets Liab + equity 100 shares of MSFT = $33,650.82 $14,991 (liab, borrowed) $18,659.82 (residual equity) Invested: 18,000 End up with: 33,650.82 – 14,991 (1 + 0.06) = 17,760.36 HPR = (17,760.36 – 18,000) / 18,000 = -0.0133 If the price of the MSFT stock increased by 2% over the next year, the holding period return would be -1.33% c. Maintenance margin requirement: 35% Assets Liab + equity 100 p $14,991 (liab, borrowed) 100p – 18000 (equity) Margin = (100p –14,991)/ 100p = 35% 0.35 x 100p = 100p – 14991
35p = 100p – 14991 -65p = -14991 P = 230.63 The market price of MSFT stock can fall as far as $230.63 before I get a margin call. d. 100 shares of MSFT stock Invested: $22,000 Interest: 6% Selling at: $329.91/ share Borrowed: 329.91(100) – 22,000 = $10,991 If price increased 15% New price: $379.3965 Assets Liab + equity 100 shares of MSFT stock = $37,939.65 $10,991 (liab, borrowed) $26,948.65 (residual equity) Invested: $22,000 End up with: 37,939.65 – 10,991 (1 + 0.06) = 26,289.19 HPR = (26,289.19 – 22,000)/ 22,000 = 0.19496 19.496% If the price of the MSFT stock increased by 15% over the next year, the holding period return would be 19.50% If price increased 2% New price: $336.5082 Assets Liab + equity 100 shares of MSFT stock = $33,650.82 $10,991 (liab, borrowed) $22,659.82 (residual equity) Invested: $22,000 End up with: 33,650.82 – 10,991 (1 + 0.06) = 22,000.36 HPR = (22,000.36 – 22,000)/ 22,000 = 0.00001636 0% If the price of the MSFT stock increased by 2% over the next year, the holding period return would be 0% Maintenance margin requirement: 35%
Assets Liab + equity 100p $10,991 100p – 10,991 Margin = (100p – 10,991)/ 100p = 0.35 35p = 100p – 10,991 -65p = -10,991 P = $169.09 The market price of MSFT stock can fall as far as $169.09 before my friend gets a margin call. e. If the price of MSFT stock had increased by 15%, my holding period return would have been 3% higher than my friend’s, since I invested less money on the stock and therefore, I grew my investment more than my friend. The same goes if the price of MSFT stock had increased by 2%, only my friend would have no debt because they only lost their original investment, but I also lost part of my loan. For the margin call, my friend has the opportunity for the margin price to be lower because they have a smaller loan than I do. 7. Price/ share = $251.49 a. Margin = equity/ stock value = x/ (200 x 251.49) = x/50,298 = 0.5 x = 25,149 If the initial margin requirement is 50%, you must put $25,149 into your brokerage account. b. Maintenance margin req: 30% Equity/ value of shares owed = [(50,298 + 25,149) – 200p]/ 200p = 0.3 75,447 – 200p/ 200p = 0.3 75,447 – 200p = 60p 75,447 = 260p P = 290.18 TSLA stock price can rise as high as $290.18 before a margin call. c. Price = $170/ share Assets Liab + equity Own cash = $25,149 200 shares = $34,000 Proceeds = $34,000 $25,149 (equity) HPR = [(251.49 – 170) x 200]/ 25,149 = 0.6481
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Your holding period return if the price is $170/ share is 64.81%.