1
Test Bank FINC 351
Test Bank
FINC 351
Problems
Problems that appeared on a past exam are marked with [X]. Problems with no [X] are practice problems that
never appeared on an exam. Solutions begin on page 50.
Margin Purchases and Short Sales
1. Bowie sold short 500 shares of Superior Co stock at $42 per share. The initial margin requirement was
65% and the maintenance margin was 40%. Three weeks later, the stock price was P and Bowie had lost
10% (HPR = –10%).
A. Calculate the percentage change in the price of the stock.
B. What is the lowest stock price that will trigger a margin call?
2. [X] Shorty sold short 1 share of Berkshire Hathaway (BRK) at $90,000 per share. At the same time, Marge
bought 1 share of BRK on margin. The initial margin for both accounts was 70% and maintenance margin
for both was 40%. One week later, Marge’s actual margin was 75%. Calculate Shorty’s one-week holding
period return. For simplicity, ignore dividends, interest, and commissions.
3. [X] Sarge shorted 100 shares at $50. The initial margin requirement was 60% and the maintenance
margin was 30%. Rounded to the nearest penny, what is the lowest price that will cause Sarge to receive
a margin call?
4. [X] Marge bought 250 shares of stock on margin at $70 per share. When the price of the stock increased
by 25%, the equity in her account increased by 40% (that is, HPR = 40%).
A. The total dollar value of the shares in Marge’s account increased by $ .
B. The total dollar value of equity in Marge’s account increased by $ .
C. Let X represent the beginning dollar value of equity in Marge’s account (when stock price = $70). Using
your answer to part B, express the ending dollar value of equity in terms of X (after price increased by
25%).
D. Calculate Marge’s beginning debt and equity. What was the initial margin?
5. [X] Jeb sold short 500 shares at $38 and deposited $14,250 of his own funds to satisfy the initial margin
requirement. Calculate Jeb’s margin if stock price increases to $45.87. Round your answer to the nearest
100th of 1% (##.##%).
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Test Bank FINC 351
6. [X] Jack bought $100 worth of Stock X on margin. The value of the shares increased by 10% but Jack’s
holding period return was 25%. What was the initial margin in Jack’s account?
7. [X] Martin bought 150 shares of stock on margin at $34 per share. The initial margin was 75% and the
maintenance margin was 40%. One month later, the stock paid a dividend of $0.12 per share, the stock
price was 𝑃1, and Martin’s holding period return of was 20%. Calculate 𝑃1. For simplicity, ignore interest
and commissions.
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8. [X] Elmer sold short 100 shares of WabbitCo stock at $65 per share. At the same instant, Sam bought 100
shares of WabbitCo on margin. Elmer’s initial margin is 80% and his maintenance margin is 50%. Sam’s
initial margin is 60% and his maintenance margin is 45%. After three days, WabbitCo’s share price was
equal to the lowest possible price that would cause Elmer to receive a margin call (rounded to the nearest
penny). Calculate Sam’s holding period return over the three-day period. For simplicity, ignore
commissions, dividends, and interest.
9. [X] Mayfly sold short 200 shares at $30 each at 𝑡 = 0. The initial margin requirement was 80% and the
maintenance margin was 25%. Mayfly used as little of his own money as possible to establish the account.
At 𝑡 = 1, the margin in the account was 100%. Mayfly withdrew as much excess collateral as he could and
spent it on something nice.
At 𝑡 = 2, the margin was once again 100%. What was the price of the stock at 𝑡 = 2?
10. [X] Aurelio shorted 1,000 shares of XYZ stock at $26 per share, using as little of his own cash as possible.
The initial margin requirement was 75% and the maintenance margin was 30%. Assume interest,
dividends and commissions are all zero for this problem.
A. Use a T-account to summarize the status of Aurelio’s account immediately after shorting the stock.
B. Use a T-account to summarize the status of Aurelio’s account if the price of XYZ stock falls to $20. Assume
dividends, commissions, and interest are all zero. What is Aurelio’s percentage margin?
C. At a stock price of $20, is it possible for Aurelio to increase the size of his short position without using any
more of his own cash? If so, what is the largest possible number of shares he could add to his short
position? Assume any cash generated from shorting shares is left on deposit in his brokerage account.
11. [X] Bose bought 100 shares of XYZ stock on margin (initial margin = 60%, maintenance margin = 30%) and
Selena sold 200 shares of XYZ short (initial margin = 80%, maintenance margin = 35%). Both orders were
filled at exactly the same instant, both at $82 per share.
One month later, XYZ’s price was equal to the lowest price that would trigger a margin call for Selena.
Calculate Bose’s one-month holding period return. Assume interest, dividends, and commissions are all
zero.
12. [X] Sunil sold short 500 shares of XYZ stock at $18 per share, depositing as little of his own funds as
possible. The stock decreased in value by 30%, but Sunil’s holding period return was 50%. What was the
initial margin requirement for Sunil’s account?
Statistics
13. [X] Over the past three years, the realized returns for Stock X have been –6%, 0%, and 15%. Calculate the
variance of returns for Stock X.
14. [X] Calculate the variance of the following asset.
State p(s) r(s)
1 0.2 –8%
2 0.3 0%
3 0.4 8%
4 0.1 24%
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15. [X] Calculate 𝜌𝐴,𝐵, given 𝜎2 = 244 and 𝜎2 = 91.
𝐴 𝐵
𝒔 𝒑(𝒔) 𝒓𝑨(𝒔) 𝒓𝑩(𝒔) 𝒓𝑨(𝒔) − 𝑬(𝒓𝑨) 𝒓𝑩(𝒔) − 𝑬(𝒓𝑩)
Bad 0.2 –15 15 –26 1
OK 0.3 5 0 –6 –14
Good 0.5 25 22 14 8
16. [X] The following table reports annual returns for the S&P 500 and Apple for the five-year period ending
June 1, 2011. Calculate the correlation of returns between the S&P 500 and Apple over this period.
S&P 500 Apple
𝒕 𝒓𝒕 𝒓𝒕 − 𝒓̅ (𝒓𝒕 − 𝒓̅)𝟐 𝒓𝒕 𝒓𝒕 − 𝒓̅ (𝒓𝒕 − 𝒓̅)𝟐
2007 0.18 0.15 0.0225 1.13 0.632 0.399424
2008 –0.15 –0.18 0.0324 0.37 –0.128 0.016384
2009 –0.28 –0.31 0.0961 –0.15 –0.648 0.419904
2010 0.12 0.09 0.0081 0.77 0.272 0.073984
2011 0.28 0.25 0.0625 0.37 –0.128 0.016384
Average 0.03 0.498
Variance 0.0554 0.231520
17. [X] Shane just sold short 600 shares of SuperCo stock at $100 per share. The probability distribution of
prices for SuperCo over Shane’s holding period is given below. The initial margin requirement is 80% and
the maintenance margin is 30%. Ignore all interest, dividends and commissions when performing your
calculations.
𝒔 𝒑(𝒔) Price(𝒔)
1 0.3 $120
2 0.5 $112
3 0.2 $60
A. Calculate Shane’s expected holding period return.
B. Calculate the standard deviation of Shane’s holding period return.
C. Calculate the standard deviation of SuperCo’s return (without a short sale or margin purchase).
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Test Bank FINC 351
Test Bank
FINC 351
Problems
Problems that appeared on a past exam are marked with [X]. Problems with no [X] are practice problems that
never appeared on an exam. Solutions begin on page 50.
Margin Purchases and Short Sales
1. Bowie sold short 500 shares of Superior Co stock at $42 per share. The initial margin requirement was
65% and the maintenance margin was 40%. Three weeks later, the stock price was P and Bowie had lost
10% (HPR = –10%).
A. Calculate the percentage change in the price of the stock.
B. What is the lowest stock price that will trigger a margin call?
2. [X] Shorty sold short 1 share of Berkshire Hathaway (BRK) at $90,000 per share. At the same time, Marge
bought 1 share of BRK on margin. The initial margin for both accounts was 70% and maintenance margin
for both was 40%. One week later, Marge’s actual margin was 75%. Calculate Shorty’s one-week holding
period return. For simplicity, ignore dividends, interest, and commissions.
3. [X] Sarge shorted 100 shares at $50. The initial margin requirement was 60% and the maintenance
margin was 30%. Rounded to the nearest penny, what is the lowest price that will cause Sarge to receive
a margin call?
4. [X] Marge bought 250 shares of stock on margin at $70 per share. When the price of the stock increased
by 25%, the equity in her account increased by 40% (that is, HPR = 40%).
A. The total dollar value of the shares in Marge’s account increased by $ .
B. The total dollar value of equity in Marge’s account increased by $ .
C. Let X represent the beginning dollar value of equity in Marge’s account (when stock price = $70). Using
your answer to part B, express the ending dollar value of equity in terms of X (after price increased by
25%).
D. Calculate Marge’s beginning debt and equity. What was the initial margin?
5. [X] Jeb sold short 500 shares at $38 and deposited $14,250 of his own funds to satisfy the initial margin
requirement. Calculate Jeb’s margin if stock price increases to $45.87. Round your answer to the nearest
100th of 1% (##.##%).
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Test Bank FINC 351
6. [X] Jack bought $100 worth of Stock X on margin. The value of the shares increased by 10% but Jack’s
holding period return was 25%. What was the initial margin in Jack’s account?
7. [X] Martin bought 150 shares of stock on margin at $34 per share. The initial margin was 75% and the
maintenance margin was 40%. One month later, the stock paid a dividend of $0.12 per share, the stock
price was 𝑃1, and Martin’s holding period return of was 20%. Calculate 𝑃1. For simplicity, ignore interest
and commissions.
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8. [X] Elmer sold short 100 shares of WabbitCo stock at $65 per share. At the same instant, Sam bought 100
shares of WabbitCo on margin. Elmer’s initial margin is 80% and his maintenance margin is 50%. Sam’s
initial margin is 60% and his maintenance margin is 45%. After three days, WabbitCo’s share price was
equal to the lowest possible price that would cause Elmer to receive a margin call (rounded to the nearest
penny). Calculate Sam’s holding period return over the three-day period. For simplicity, ignore
commissions, dividends, and interest.
9. [X] Mayfly sold short 200 shares at $30 each at 𝑡 = 0. The initial margin requirement was 80% and the
maintenance margin was 25%. Mayfly used as little of his own money as possible to establish the account.
At 𝑡 = 1, the margin in the account was 100%. Mayfly withdrew as much excess collateral as he could and
spent it on something nice.
At 𝑡 = 2, the margin was once again 100%. What was the price of the stock at 𝑡 = 2?
10. [X] Aurelio shorted 1,000 shares of XYZ stock at $26 per share, using as little of his own cash as possible.
The initial margin requirement was 75% and the maintenance margin was 30%. Assume interest,
dividends and commissions are all zero for this problem.
A. Use a T-account to summarize the status of Aurelio’s account immediately after shorting the stock.
B. Use a T-account to summarize the status of Aurelio’s account if the price of XYZ stock falls to $20. Assume
dividends, commissions, and interest are all zero. What is Aurelio’s percentage margin?
C. At a stock price of $20, is it possible for Aurelio to increase the size of his short position without using any
more of his own cash? If so, what is the largest possible number of shares he could add to his short
position? Assume any cash generated from shorting shares is left on deposit in his brokerage account.
11. [X] Bose bought 100 shares of XYZ stock on margin (initial margin = 60%, maintenance margin = 30%) and
Selena sold 200 shares of XYZ short (initial margin = 80%, maintenance margin = 35%). Both orders were
filled at exactly the same instant, both at $82 per share.
One month later, XYZ’s price was equal to the lowest price that would trigger a margin call for Selena.
Calculate Bose’s one-month holding period return. Assume interest, dividends, and commissions are all
zero.
12. [X] Sunil sold short 500 shares of XYZ stock at $18 per share, depositing as little of his own funds as
possible. The stock decreased in value by 30%, but Sunil’s holding period return was 50%. What was the
initial margin requirement for Sunil’s account?
Statistics
13. [X] Over the past three years, the realized returns for Stock X have been –6%, 0%, and 15%. Calculate the
variance of returns for Stock X.
14. [X] Calculate the variance of the following asset.
State p(s) r(s)
1 0.2 –8%
2 0.3 0%
3 0.4 8%
4 0.1 24%
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15. [X] Calculate 𝜌𝐴,𝐵, given 𝜎2 = 244 and 𝜎2 = 91.
𝐴 𝐵
𝒔 𝒑(𝒔) 𝒓𝑨(𝒔) 𝒓𝑩(𝒔) 𝒓𝑨(𝒔) − 𝑬(𝒓𝑨) 𝒓𝑩(𝒔) − 𝑬(𝒓𝑩)
Bad 0.2 –15 15 –26 1
OK 0.3 5 0 –6 –14
Good 0.5 25 22 14 8
16. [X] The following table reports annual returns for the S&P 500 and Apple for the five-year period ending
June 1, 2011. Calculate the correlation of returns between the S&P 500 and Apple over this period.
S&P 500 Apple
𝒕 𝒓𝒕 𝒓𝒕 − 𝒓̅ (𝒓𝒕 − 𝒓̅)𝟐 𝒓𝒕 𝒓𝒕 − 𝒓̅ (𝒓𝒕 − 𝒓̅)𝟐
2007 0.18 0.15 0.0225 1.13 0.632 0.399424
2008 –0.15 –0.18 0.0324 0.37 –0.128 0.016384
2009 –0.28 –0.31 0.0961 –0.15 –0.648 0.419904
2010 0.12 0.09 0.0081 0.77 0.272 0.073984
2011 0.28 0.25 0.0625 0.37 –0.128 0.016384
Average 0.03 0.498
Variance 0.0554 0.231520
17. [X] Shane just sold short 600 shares of SuperCo stock at $100 per share. The probability distribution of
prices for SuperCo over Shane’s holding period is given below. The initial margin requirement is 80% and
the maintenance margin is 30%. Ignore all interest, dividends and commissions when performing your
calculations.
𝒔 𝒑(𝒔) Price(𝒔)
1 0.3 $120
2 0.5 $112
3 0.2 $60
A. Calculate Shane’s expected holding period return.
B. Calculate the standard deviation of Shane’s holding period return.
C. Calculate the standard deviation of SuperCo’s return (without a short sale or margin purchase).
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