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EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022
EF3320 Security Analysis and Portfolio Management – Problem Set 1
This problem set is to be turned in by Friday, 28 January 11:00 pm. Please present your work using MS
Word or PDF and submit online on Canvas. You may use Excel for calculation but the final solution should
be presented in MS Word or PDF.
1. Price-Weighted Index
Consider a price-weighted index of the following three stocks:
Stock
Price per share on day 0
Shares outstanding (millions)
A
80
40
B
120
10
C
200
2
a) Suppose that we construct the price-weighted index on day 0. What is the current index level?
Solution: At the beginning, the index level is the simple average of prices:
80 + 120 + 200
= 133.333
3
b) On day 0, stock B splits three for one so that its share price becomes $40 and the number of shares
outstanding becomes 30 millions. What should be the new divisor for the index?
Solution: The divisor d satisfies the following equation:
133.333 =
80 + 40 + 200
.
d
Solving for the unknown, we find d = 2.4.
c) Following are stock prices on day 1.
1
Instructor: Yongjin Kim
EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022
Stock
Price per share on day 1
Shares outstanding (millions)
A
88
40
B
36
30
C
190
2
What is the index level on day 1? What is the return on the stock index from day 0 to 1?
X
88+36+190
88+36+290
X
X
Using the divisor that was updated on day 0, the index on day 1 is =
X
2.4 X
2.4
130.833. The rate of return on the index from day 0 to 1 is
Solution:
130.833 − 133.333
= −1.88%.
133.333
2. Limit and Market Orders
Suppose that the current limit order book of Tencent shares are as follows:
Bid/Ask
Price
Size
Ask
456.00
200
Ask
455.90
700
Ask
455.80
400
Bid
454.20
300
Bid
454.10
100
Bid
454.00
100
a) A new market order arrives to buy 500 shares of Tencent. What will be the average price that this market
order is executed? How will the limit order book change?
Solution: The new market orders will be matched to multiple existing orders – order to sell 400 shares
at $455.80 and order to sell 100 shares at $455.90. The average price of the market order is
400
100
(455.80) +
(455.90) = $455.82.
500
500
2
Instructor: Yongjin Kim
EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022
After this market order, the limit order book will change to
Bid/Ask
Price
Size
Ask
456.00
200
Ask
455.90
600
Bid
454.20
300
Bid
454.10
100
Bid
454.00
100
b) Afterwards, a new limit order arrives to buy 300 shares at $454.30. Will this order be executed immediately? How will the limit order book change?
Solution:
The new limit order cannot be executed immediately, as there are no existing orders to sell
at a price of $454.30 or lower. Then, the new limit order is added, so the limit order book will change to
Bid/Ask
Price
Size
Ask
456.00
200
Ask
455.90
600
Bid
454.30
300
Bid
454.20
300
Bid
454.10
100
Bid
454.00
100
c) Finally, a new limit order arrives to sell 200 shares at $454.25. Will this order be executed immediately?
Solution:
The new limit order is executed immediately as it is matched to the existing orders to buy
at $454.30.
3
Instructor: Yongjin Kim
EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022
3. Buying on Margins
A trader purchases 300 shares of stock at $40 per share. She borrows $4,000 from her broker to help pay for
the purchase. The maintenance margin requirement is 30%.
a) If the share price next day falls to $30, will she receive a margin call?
Solution: With the new share price, the percentage margin is
300 × 30 − 4000
= 55.56%.
300 × 30
As the percentage margin is still higher than the maintenance margin, there will be no margin call.
b) In what range of stock price of S will she receive a margin call?
Solution: The margin call takes place when
300 × S − 4000
< 0.3.
300 × S
Thus, when S < $19.048, the investor receives a margin call.
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Instructor: Yongjin Kim