FIN 6160
Investment Theory
Lecture 3-4
How Securities are Traded
Primary Market: When firms need to raise capital they may
choose to sell or float securities. These new issues of stocks,
bonds, or other securities typically are marketed to the public by
investment bankers in what is called the primary market.
There are two types of primary market issues of common stock.
Initial Public Offerings or IPOs are stocks issued by a formerly
privately owned company that is going public by selling stock to
the public for the first time. Seasoned or Right equity offerings
are offered by companies that already have floated equity. For
example a sale of new shares of stock by Square Pharmaceuticals
would constitute a seasoned or right new issue.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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How Securities are Traded
In case of bonds we also distinguish between two types of primary
market issues, a public offering and a private placement.
A public offering of bond refers to an issue of bonds sold to the
general investing public that can then be traded on the secondary
market.
Private placement of bonds refers to an issue that usually is sold to
one or a few institutional investors and is generally held to maturity.
Secondary Market: Secondary market facilitate trading of existing
securities among investors.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Securities Firms: Securities firms may provide single or all of the following
variety of functions in financial markets:
Broker 2) Underwriter 3) Dealer
Broker: Brokers charge a fee for securities transactions between two parties
1)
Underwriter or investment banker: Some securities firms place newly issued
securities in the primary market for corporations and government agencies
When securities firms underwrite newly issued securities, they may sell the
securities at a guaranteed price or at the best price for a client.
Another investment banking activity offered by securities firms is advisory
services on mergers and other forms of corporate restructuring.
Securities firms may not only help a firm plan its restructuring but also execute
the change in the firm’s capital structure by placing the securities issued by the
firm.
Dealer: Securities firms often act as dealers, making a market in specific
securities by adjusting their inventory of securities. A dealer’ income is
influenced by the performance of the security portfolio maintained.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Buying on Margin: When purchasing securities, investors have easy access to
a source of debt financing called broker’s call loans. The act of taking advantage
of broker’s call loans is called buying on margin.
Purchasing stocks on margin means investors borrows part of the purchase
price of the stock from a broker. The margin in the account is the portion of the
purchase price contributed by the investor, the remainder is borrowed from the
broker. All securities purchased on margin must be maintained with the
brokerage firm as collateral for the loan.
Short Sales: Normally, an investor would first buy a stock and later sell it.
With a short sale, the order is reversed. A short sale allows investors to profit
from a decline in a security’s price. An investor borrows a share of stock from a
broker and sells it. Later the short seller must purchase a share of the same stock
to replace the share that was borrowed. This is called the covering the short
position.
The short seller anticipates the stock price will fall, so that the share can be
purchased later at a lower price than it initially sold for, and reap a profit out of
it.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
5
Regulation on Securities Markets
In general, securities markets are regulated to ensure that the participants are
treated fairly. Many regulations were enacted in response to fraudulent practices.
Since the use of incorrect information can result in poor investment decisions,
many regulations attempt to ensure that businesses disclose accurate information.
Securities Act was enacted to ensure complete disclosure of relevant financial
information on publicly offered securities traded in the primary market and
secondary market.
Securities and Exchange Commission (SEC) was established to oversee the
securities markets. A variety of deceptive practices was declared illegal, such as
misleading financial statements and trading strategies designed to manipulate the
market price, insider trading etc.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Regulation on Securities Markets
Insider Trading: Security market regulation also prohibit insider trading. It is
illegal for anyone to transact in securities to profit from inside information, that is,
private information held by officers, directors, or major stockholders that has not
yet been divulged to the public.
But the definition of insiders can be ambiguous. While it is obvious that the chief
financial officer of a firm is an insider, it is less clear whether the firms biggest
supplier can be considered an insider. Yet a supplier may deduce the firm’s near
term prospects from significant changes in orders. The distinction between legal
private information and illegal inside information can be fuzzy.
The SEC requires officers, directors, and major stockholders to report all
transactions in their firm’s stock.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Investment Companies
Investment companies are financial intermediaries that collect funds from
individual investors and invest those funds in a potentially wide range of securities
or other assets. Pooling of assets is the key idea behind investment companies.
Each investor has a claim to the portfolio established by the investment company
in proportion to the amount invested. These companies thus provide a mechanism
for small investors to team up to obtain the benefits of large scale investing.
Investment companies perform several important functions for their investors:
Record keeping and administration: Investment companies issue periodic
status reports, keeping track of capital gains distribution, dividends,
investments, redemptions, and they may reinvest dividend and interest income
for shareholders.
Diversification and divisibility: By pooling their money, investment
companies enable investors to hold shares of many different securities. They
can also act as large investor.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Investment Companies
Professional management: Many investment companies have full time staff
of security analysts and portfolio managers who attempt to achieve superior
investment results for their investors.
Lower transaction costs: Because they trade large blocks of securities,
investment companies can achieve substantial savings on brokerage fees and
commissions.
Mutual Funds: Mutual funds sell shares to surplus units and use the funds
received to purchase a portfolio of securities. Some mutual funds concentrate their
investment on capital market securities like stocks and bonds while others, known
as money market mutual funds, concentrate on money market securities.
By purchasing shares of mutual funds, small savers are able to invest in a
diversified portfolio of securities with a relatively small amount of funds.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Investment Companies
Hedge Funds: Like mutual funds, hedge funds allow private investors to pool
assets to be invested by a fund manager. Unlike mutual funds, however, hedge
funds are commonly structured as private partnerships and thus subject to only
minimal SEC regulation. They typically are open only to wealthy or institutional
investors. Many hedge funds require investors to agree for lock ups that periods as
long as several years in which investment can not be withdrawn.
Lock ups allow hedge funds to invest in illiquid assets without worrying about
meeting demands for redemption of funds. Because hedge funds are only lightly
regulated, managers can pursue risky investment strategies like heavy use of
derivatives, short sales, etc.
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
10
Determinants of Interest Rates
Interest rate movements have a direct influence on the market values of debt
securities, such as money market securities, bonds, mortgages and have an indirect
influence on equity security values.
Following factors have direct or indirect impact on interest rate movement in the
economy:
Demand & Supply of loanable funds
Economic growth
Inflationary expectation
Money supply
Budget deficit
Foreign flow of funds
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Returns and Risk
Holding Period Return: Rt 
Including dividend:
Pt  Pt 1
P
 t 1
Pt 1
Pt 1
Pt  Pt 1  Dt Pt  Dt
Rt 

1
Pt 1
Pt 1
 Pt 

P
 t 1 
Continuously compounded return : Rt  ln 
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
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Returns and Risk
Expected Return: This is the return that an investor expects a security to earn
over the next period. Off course this is only an expectation, the actual return may
be either higher or lower. An investor’s expectation may simply be the average
return per period a security has earned over the past.
r

Without probability: E (r )  r 
n
With probability: E (r )  r   rp
Here, r  return and p  probability of corresponding return
Risk: The uncertainty about the future return from an investment is called the risk
or volatility and can be measured using variance or standard deviation of the
return.
2
2
(ri  r )
( ri )
1
2
Variance,  

[ ri 
]
n 1
n 1
n
 2  (r  r ) 2 p   r 2 p  [ E (r )]2
2
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
13
Returns and Risk
Security
A
B
C
D
Rate of
return
Prob
Rate
of
return
Prob
Rate of Prob
return
Rate of Prob.
return
6%
1
5%
1
-10%
¼
-20%
¼
0
¼
10
½
20
½
40
¼
Expected return:
Security A: 6%
Security B: 5%
Security C: -(0.25x10%)+(0.25x0)+(0.5x20%) =7.5%
Security D: -(0.25x20%)+(0.5x10%)+(0.25x40%) =10%
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
14
Returns and Risk
Purchase price=$100
State of the
Year-end
Cash
Prob
Holding Period Return (HPR)
Economy
price Dividends
Boom
Normal
0.3
0.5
129.5
110.0
4.5
4.0
(129.5+4.5-100)/100=0.34
(110+4-100)/100=0.14
Recession
0.2
80.5
3.5
(80.5+3.5-100)/100=-0.16
Expected Return = (0.34x0.3)+(0.14x0.5)+(-0.16x0.2) =0.14
Variance, 2   r 2 p  [ E (r )]2
 [(0.342 x0.3)  (0.142 x0.5)  ( 0.162 x0.2)]  0.14 2  0.03
Standard Deviation,    2  0.03  0.1732
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
15
Returns and Risk
Portfolio Expected Return: When we invest on more than one asset, the
portfolio expected return is the weighted average of the expected returns of all
asset held in your portfolio.
If wi are weights, i.e. the investment proportions.
And E(Ri) expected return on individual asset, we have: E ( R p ) 
n
 w E(R )
i 1
i
i
Calculate the expected return on a portfolio that has one third of your wealth
invested in GM and two thirds in BP;
Year
Probab.
GM
BP
Portfolio
2
¼
0.10
0.15
0.1333
¼
-0.05
0.10
0.05
¼
0.08
0
0.0267
¼
0.15
-0.01
0.0433
0.07
0.06
0.0633
Expected Rate of return
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
16
Returns and Risk
Covariance and Correlations: Returns on individual securities are related to one
another. Covariance is a statistic measuring the inter-relationship between two
securities. Alternatively, this relationship can be restated in terms of the correlation
between the two securities.
A sample covariance is
n
Cov( x, y )   xy 
 ( x  x)( y  y)
i 1
i
i
n 1

1
 x y ]
[ xy 
n 1
n
( xi )( yi )
 xy
n
Correlation Coefficient ( x, y )  rxy 

x y
( xi ) 2
( yi ) 2
2
2
{ xi 
}{ yi 
}
n
n
 xi yi 
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
17
Returns and Risk
State of the
Economy
Rate of Return from
Security A
Rate of Return from
Security B
Boom
Normal
Recession
Depression
-20%
10%
30%
50%
5%
20%
-12%
9%
x y 1
1
0.7 x0.22

Covariance,  xy 
[ xy 
]  [ 0.019 
]
n 1
n
3
4
 0.0065
 A  0.2586;  B  0.115;
Correlation Coefficient ( x, y )  rxy 
 xy
x y

0.0065
 0.2185
0.2586 x0.115
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
18
Returns and Risk
Variance of a portfolio: The formula for the variance of a portfolio composed of
two securities A and B is:
2p  wA2  2A  wB2  2B  2wA wB  AB
Here, 2p  Portfolio Variance;  2A  Variance of Security A
2B  Variance of Security B; wA  Proportion of investment on A
wB  Proportion of investment on B;  AB  Covariance between A &B
Out of $100, if an investor invests $60 in Security A and remaining $40 in
security B, then the variance of the portfolio,
2p  wA2  2A  wB2  2B  2wA wB  AB
 0.62 x0.25862  0.42 x0.1152  2 x0.6 x0.4 x(0.0065)  0.023
Standard Deviation of the portfolio,  p   2p  0.023  0.1518
Mohammad Kamrul Arefin, MSc. in Quantitative Finance, University of Glasgow
19