Suggested_Solution_to_EQ_chap_12_13

# Suggested_Solution_to_EQ_chap_12_13 - Chapter 12 EQ # 1:...

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1/5 Chapter 12 EQ # 1: Returns to an investment You purchased 333 shares of Outel stock at a price of \$30.00 per share. One year later, the shares are selling for \$33.33 per share. In addition, a dividend of \$3.00 per share is paid at the end of the year. Calculate: Income = dividend * # of shares = \$3x333= \$999 Capital gain = [(\$33.33 – \$30.00)/ \$30.00] * 333 = \$1108.89 The total dollar return = \$999 + \$1108.89 = \$2107.89 Dividend yield = dividend/original price = 3/30=10% Capital gain yield = (\$33.33 - \$30)/\$30 =11.1% Total percentage return = dividend yield + capital gain yield = 10% + 11.1% = 21.1% EQ # 2: Variance and standard deviation of Returns Given the following historical annual returns: R1 in Year 1 = 5%; R2 = -15%; R3 = 8%; R4=3%; R5= - 6%. What are the average return, variance, and standard deviation? *Average Return = [(.05) + (-.15) + (.08) + (.03) + (-.06)]/5 = -.05 / 5 = - 0.01 *Deviation form the Mean = Actual Return – Average Return Year Actual Return Average Return Deviation from the Mean Squared Deviation 1 0.05 -0.01 .06 36 (%) 2 2 - 0.15 -0.01 .14 196(%) 2 3 0.08 -0.01 .09 81(%) 2 4 0.03 -0.01 .04 16(%) 2 5 - 0.06 -0.01 -.05 25(%) 2 Total 354(%) 2 Variance =354 x (%) 2 / (5 – 1) =88.5 (%) 2 , standard deviation = 2 (%) 5 . 88 = 9.41% EQ # 3: Historical Returns Given the following historical data over the 1926 – 2000 period, Asset Average Return Standard Deviation Large-cap stocks 13.0% 20.2% Small-cap stocks 17.3% 33.4% Long-term gov. bonds 5.7% 9.4% T-bills 3.9% 3.2% The historical risk premium on large-cap stocks = 13 – 3.9 = 9.1% The historical risk premium of large stocks over LT gov. bonds = 13 – 5.7 = 7.3% The reward for bearing the risk of owning small rather than large stocks = 17.3 – 13 = 4.3% EQ # 4: Return Distribution Using the data in EQ # 3, assume the return on each asset is normally distributed. 1. With 68% confidence, what is the highest return you would expect to earn on T-bills? 2. With 68% confidence, what is the lowest return you would expect to earn on small stock? 3. With 99% confidence, what is the highest return you would expect to earn on T-bills? 4. With 95% confidence, what is the lowest return you would expect to earn on large stock? Using the normal distribution table (page A-10 of the textbook), 5. What is the probability of earning at most 4.5% on T-bills? 6. What is the probability of earning at least 20% on small stocks? Solution: 1. 68% confidence is within 1 standard deviation Æ 3.9% +/– 3.2% Î the range is (0.7%, 7.1%), thus the highest is 7.1%; 2. 17.3% +/– 33.4%; the lowest return on small stock is –16.1%; 3. 3.9% +/– (3.2% x 2.58); the highest is 3.9%+3.2 x 2.58 = 12.156%; 4. 13.0% - 2 x 20.2% = -27.4%; or 13.0% - 1.96 x 20.2% = -26.59% 5. d=(4.5 – 3.9)/3.2 = .1875; N(d) = .575. 6.

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## This homework help was uploaded on 02/19/2008 for the course H ADM 221 taught by Professor Gpotter during the Spring '05 term at Cornell.

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Suggested_Solution_to_EQ_chap_12_13 - Chapter 12 EQ # 1:...

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