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Sample Midterm Answer Key
Econ 133, UCSC
Part I: Multiple Choice
Please circle your answers!
1. You sold short 100 shares of common stock at $30 per share. The initial margin is 60%.
Your initial investment was __________.
A) $1,200
B) $1,500
C) $1,800
D) $3,000
2. A __________ gives its holder the right to buy an asset for a specified exercise price on or
before a specified expiration date.
A) call option
B) futures contract
C) put option
D) none of the above
3. If you purchase a stock for $50, receive dividends of $2, and sell the stock at the end of the
year for $55, what is your holding period return?
A) 5%
B) 10%
C) 14%
D) 18%
4. You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is
your maximum possible gain ignoring transactions cost?
A) $50
B) $150
C) $10,000
D) unlimited
5. The bid-ask spread exists because of
A) market inefficiencies
B) poor communication
C) the need for dealers to cover expenses and make a modest profit
D) none of the above
6. Assume that you have recently purchased 100 shares in an investment company. Upon
examining the balance sheet, you note the firm is reporting $225 million in assets, $30
million in liabilities, and 10 million shares outstanding. What is the Net Asset Value (NAV)
of these shares?
A) $25.50
B) $22.50
C) $19.50
D) $1.95
Part II: Longer Answers
1. (26 points) On January 1, you sold short one round lot (i.e. 100 shares) of Zenith stock at $40
per share. The initial margin requirement was 50% and the maintenance margin is 30%. The
margin account pays no interest. On March 1, Zenith paid a dividend of $2 per share. On
April 1, the share price rises suddenly to $45 at the opening of trading.
a) (5 points) List all assets and liabilities. What is the remaining margin (equity) in the
account on April 1 (in dollars)?
EquityJanuary = Initial %margin x sale proceeds = 50% x $4,000 = $2,000 = Initial margin
Assets
Sale proceeds
Initial margin
4,000
2,000
Total assets
6,000
Liabilities and Equity
4,500 Value of shares owed
200 Dividends owed
1,300 Equity
6,000 Total liabilities and equity
EquityApril = 4,000 + 2,000– 4,500 – 200 = 1,300
b) (6 points) What is the percentage margin? Do you receive a margin call?
Percentage margin = Equity/Value of shares owed = 1,300/4,500 = 28.9%
Yes, I receive a margin call from the broker.
c) (5 points) What is the minimum price for the broker to issue a margin call?
Equity
6000 − 100P − 200
=
Value of shares owed
100P
P = 44.62
30% =
If the price rises to $44.62 or more, the broker issues a margin call.
d) (5 points) If you cover the short sale on April 1 after the price increase, what is your rate
of return (HPR)?
HPR = (EquityApril-EquityJanuary)/EquityJanuary = (1,300 – 2,000)/2000= -35%
e) (5 points) What is your EAR?
EAR = (1-35%)4-1 = -82%
2. (10 points) You have just purchased a corporate bond that has a coupon rate of 10% and a
maturity of 4 years. The yield to maturity on the bond is 8%.
a) (2 points) What is the current price of the bond?
P0 =
50 ⎡
1 ⎤ 1000
= $1,067.33
1−
+
⎢
0.04 ⎣ (1.04)8 ⎥⎦ (1.04)8
b) (3 points) If interest rates increase from 8% to 8.2% one year from now and coupons are
not reinvested, what would be the 1-year holding period rate of return on the bond?
P1 =
50 ⎡
1 ⎤
1000
= $1,047.03
1−
+
6 ⎥
⎢
0.041 ⎣ (1.041) ⎦ (1.041) 6
HPR = Coupon Payment + Capital Gains = 100 + (1,047.03 – 1,067.33) = 7.47%
Initial Bond Price
1,067.33
c) (3 points) If yields stay at 8.2% for the remaining 3 years and coupons are reinvested,
what is the effective annual return on this bond over the 4-year period?
Period
CF
YTM
FV
0
-1,067.33
1
50
66.18
2
50
4%
63.63
3
50
4.10%
61.13
4
50
4.10%
58.72
5
50
4.10%
56.41
6
50
4.10%
54.18
7
50
4.10%
52.05
8
1,050
4.10%
1,050.00
Sum
1,462.29
HPR = 1,462.29/1067.33 -1 = 37.01%
EAR = 1.37011/4-1 = 8.19%
d) (2 points) A different bond has a coupon rate of 7%, one year to maturity, and its price is
quoted as 100.19. What is its yield to maturity?
We need to find the period rate r that solves 1,001.90 = 35/1+r + 1035/(1+r)2
We can use trial and error, or use the quadratic formula for x2 + ax + b =0
Let x = (1+r) óx2 - 35/1,001.9 x- 1035/1,001.9=0
x=-a/2 ±(a2/4 -b)0.5 = 1.747% ± 1.01653 = 1.03400 = 1+r
r=3.4% => YTM = 6.8%
3. (15 points) Assume that the S&P 500 tracks only the following 3 stocks. Stock B just had an
SEO.
Price, Feb. 8
Shares, Feb. 8
Price, Feb. 9
Shares, Feb. 9
Stock A
60
10 million
52
10 million
Stock B
80
20 million
70
30 million
Stock C
30
50 million
31
50 million
a) (5 points) What is the index return from Feb. 8 to Feb. 9?
Index level on Feb. 8 = (60 * 10 + 80 * 20 + 30 * 50)/(10+20+50) = 46.25
Index level on Feb. 9 = (52 * 10 + 70 * 30 + 31 * 50)/(10+30+50) = 46.33
HPR = 46.33/46.25 -1 = 0.173%
b) (5 points) What's the EAR?
EAR = (1+0.173%)365-1 = 87.91%
c) (5 points) If inflation were 1% per month, what would be the real annualized return?
EAR = 1.0112-1 = 12.68%
Fisher equation: real rate = 1.8791/1.1268 -1 = 66.7%
4. (15 points) The table below shows the S&P 500 for the last 5 years.
Adj
Date
Close
HPR
Deviation
Squared
1/3/2011 1271.87 18.44%
15.12% 0.022867
1/4/2010 1073.87 30.03%
26.71%
0.07135
1/2/2009 825.88 40.09%
-43.41% 0.188414
1/2/2008 1378.55 -4.15%
-7.47% 0.005574
1/3/2007 1438.24 12.36%
9.04% 0.008171
1/3/2006 1280.08
-Sum
0.296377
a. (5 points) Calculate the HPRs
HPR = Closet/Closet-1 -1 (see table)
b. (5 points) What are the arithmetic average and geometric average rates of return?
ra = 3.32%
1280.08 (1+rg)5= 1271.87
rg=(1271.87/1280.08)1/5-1 = -0.13%
rg is also called the CAGR (Compound Annual Growth Rate) in this context
c. (5 points) What is the standard deviation of returns?
SD = (sum of squared deviation / n-1)1/2 = (0.296377 / 4)0.5 = 27.22%
d. (5 points) If the past is a good guide to the future, what level do you expect the index
to reach on 1/3/2012 and on 1/3/2021?
E(Index)1/3/2012= 1271.87 * (1+ra) = 1,314
E(Index)1/3/2021= 1271.87 * (1+rg)10 = 1,256