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Unformatted text preview: FIN 397.1: SPRING 2007 Exam # 1: Basic Concepts
February 6, 2007 (SOLUTIONS) NAME:
Time allowed: 1 hour, 15 minutes.
Mamlmum possible score: 100. NOTE: 0 If I cannot understand your calculations, I will not be able to give you full credit even
if your ﬁnal answer is correct. You cannot say “these calculations are obvious.” o If a problem is missing some key information that you think is necessary to solve
the problem, please ask me to clarify the question or state your confusions clearly.
Alternatively, please make appropriate assumptions, state them clearly and proceed.
No credit will be awarded if you fail to state your confusions or assumptions explicitly
even if the question is wrong. 0 Partial credits may be awarded if you show your calculations or provide arguments
to support your answers. I Multiple Choice Questions (24 points, 15 minutes) 1. (2 points) The owner of a put option has to  a speciﬁc stock, on or
before a speciﬁc date, at a speciﬁc price. (a) an obligation, sell
(b) an obligation, buy @a right, sell ((31) a right, buy 2. (2 points) An Initial Public Offering (IPO) in which the underwriter purchases the
shares from the issuing ﬁrm and takes the risk of selling the shares to the public is
referred to as: A ﬁrm commitment underwriting (b) A competitive bid underwriting
(c) A best efforts underwriting (d) A negotiated bid underwriting 3. ( 5 points) Suppose that you believe the past performance of a mutual fund is indicative
of the mutual fund’s future performance and you believe the returns of a mutual fund
reﬂect the manager’s skill. You are an individual making a single investment decision
and you plan to invest your money in the riskfree asset and in one of these threeFour
actively managed mutual funds. Given the data provided below, which fund will you
invest in? Assume that the riskfree rate is 6% per year. @Mutual Fund A: Average Annual Return = 12.0%, Standard Deviation = 15%.
 Mutual Fund B: Average Annual Return = 13.1%, Standard Deviation = 25%. (c) Mutual Fund C: Average Annual Return = 12.4%, Standard Deviation = 30%.
((1) Mutual Fund D: Average Annual Return = 13.6%, Standard Deviation = 40%. Remand Pet and Of Ta‘sk [‘5 highest
WWW :. 12 6
IS 4. ( 5 points) You purchased 200 shares of AAA common stock on margin for $40 per
share. The initial margin is 60% and the stock pays no dividend. Your rate of return would be if you sell the stock at $35 per share.
(a) 21% Tow cost : 200x40 :: $8000. (b) 13% Year inin capH3 : aeoxgooe : $4300
(Cl13% Loss clue +0 Price decline. :: 200 (40'35) :. $l°°°‘
~21? a
0 $ Ratlg 9.1: return 2 —looo moo .2 ~21/. 4800 5. ( 5 points) You purchased 400 shares of XYZ common stock on margin at $20 per share.
Assume the initial margin is 60% and the maintenance margin is 30%. You would get a margin call if the stock price is below . Assume the stock pays no dividend and ignore interest on margin. Tel4.! cost : $8000. Inib‘aﬂ eunlj : $4900. (a) $15.71 .$11_43 I‘F "H‘\e Ph‘tc fans +9 P (5‘3): (c) $1357 Margin = W .—. 0.50
(d) $10.14 ”00? =7 P 2 {HI#3. 6. ( 5 points) You are considering an investment in a mutual fund with an annual expense
ratio of 0.5% and 12b—1 fees of 0.75% per year. The front—end load is 1.50%. You can
invest instead in a bank CD paying 6% interest. If you plan to invest for three year,
What is the minimum annual rate of return must the mutual fund earn for you to be
better off in the fund than in the CD? (Assume annual compounding of returns.) (a) 6.40%
(b) 7.25% '
@7.75% Annual cost :3 05 + 0'75 + 1'29. 3,) [.75 /. 3
(d) 9.31% .
# Must“ Earth at least (31" L75 3775 A +0 be hell?" “ff II Option Payoff Diagrams (12 points, 10 minutes) You purchase an European call option on stock XYZ with a strike price of $60 and a put
option on the same stock with a strike price of $30. You pay $3 for the call option and $2
for the put option. Draw a graph indicating your net proﬁt from this investment at the
expiration date for stock prices in the range of $0 to $90. Please label the axes clearly. OP’n‘on .
Pauoﬁ ' III Security Pricing (12 points, 10 minutes) Which security should seH at a greater price? 1. (4 points) (a) A threemonth maturity call option with an exercise price of $40 or
@a three month maturity call option on the same stock with an exercise price of $35. 2. (4 p0ints}.A three—month maturity put option with an exercise price of $40 or
(b) a three month maturity put option on the some stock with an exercise price of $35. 3. (4 points) (a) A three—month maturity call option with an exercise price of $999 or
’a three month maturity put option on the same stock with an exercise price of
‘999. Assume that the current stock price is $50. Please explain brieﬂy (2—3 lines). In all 3 insi’anceS, 41M pwobabfiii'j a; ﬂe‘iﬁuj a Posih‘v: Paflc'H: is Maker.
r? EXPccieoi —leure Fade—PF is higher. =37 CUXTva'i: Fm'cc is kl‘jhcr. IV Mutual Fund Performance (12 points, 10 minutes) Suppose you observe the investment performance of 256 mutual fund managers for an ex—
tended period of time. At the end of each year, you divide the managers into 2 broad
categories, good and bad, depending upon their performance relative to the market return. 1. ( 6 points) After 8 annual observations, how many managers are expected to fall in the
“good” category in each and every year during the 8—year sample period even if they
did not have any skill? 2. (6 points) After 10 annual observations, two managers were classiﬁed into the “good”
category in each and every year during the 10year sample period. Are these two
managers skilled? Please explain brieﬂy (45 lines). ® Expected. :11: 2F managers in the good ca’reaopa_ .. l _L ,...x_‘_) x256 = 1
“(1"1" 2. W
9 ‘HMeS  in +ke goose «+2307: 3F managerS ® ExEcdecl 3H: —.
— (.311)le 256 = 0‘25' “n colMil #I: Q? mama as in 44m $0050 Cali9307:! .. .
6 ﬂ _ 2
W AclMﬂ 7 Expected ? “:3 are likclj +0 be skilled. V Limit and Market Orders (16 points, 10 minutes) You start investing with an equity of $10,000 in your brokerage account. The stock of
Shamrock Corporation is selling at $28 a share. You place a market order to buy 100 shares
of Shamrock. Immediately after your market order is executed, you place a stop loss limit
order for 100 shares at $24 and a stop buy limit order for 100 shares at $32. During the next
three months, the stock price slowly rises to $36 and then gradually declines to $20. What is
your rate of return on this investment? Ignore transaction costs and brokerage commissions. But} [00 shares. $14 Seu 100 shares. VI Margin Trading and Short Selling (24 points, 20 minutes) Dee Trader opens a brokerage account, and purchases 500 shares of Internet Dreams at $40
per share. She borrows $15,000 from her broker to help pay for the purchase. The interest
rate on the loan is 5%. 1. (5 points) What is the margin (in percent) in Dee’s account when she ﬁrst purchases
the stock? 2. ( 6 points) Using her long position in Internet Dreams as collateral, Dee would like to
short sell Krispy Kreme Doughnuts which is currently trading at $80 per share. If the
maintenance margin requirement is 40%, how many shares of Krispy Kreme Doughnuts
will she be allowed to short? 3. { 8 points) Assume that Dee short sells the maximum number of shares allowed by her
broker. If the share price of Internet Dreams falls to $30 per share and the share price
of Krispy Kreme Doughnuts falls to $60 per share by the end of the year, what is the
remaining margin in her account? Will she get a margin call if the maintenance margin
requirement is 40%? 4. ( 5 points) What is the one year holding period return on her investment? ® Teld Cost as: +ke Fortﬁsh‘s) _: 500x 49.1.0 : $20,000
AMOun‘l‘ looTroLuecl : $5,000 (SEW“Q. 203,000153,000 :. $5.000. =‘?Dec's own ecluiijjmarain : 7d MQTaln : 5000 x00 :. 2.5 7.
20.000 ~ ~ ‘ mu
(9 mil not be allowed. +19 hold +hc amt Possum because no Nafain \‘5 below +he malnlevance maxam, " 5000
@ LOSS clue +0 Puke decline. : 500 (flu—950) .. $ ‘ "' DO :2 0.
g Remaining maraln 5000 ‘50 $3 a. maral‘n 54H  $750 in in'l'errS‘l? P“d"“""+5 0&1 Course, sine will Tecewe 5k: wandd also owe 15.000xi 3 E , \ 1,, account
. 1 wer MC 0“" +akc m
@ Rate 9; Taiwan = "400/" (or, ignm‘lzwst 03M“) ...
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