Security Analysis and Portfolio Management
Introduction
Agenda
• Syllabus
• What is finance? What are financial markets and financial
assets.
• Time Value of Money
– Calculating Present Values (Discounting)
– Calculating Future Values (Compounding)
• Statistics
– Mean, Expected Value
– Variance, Standard Deviation
– Sharpe Value
– Covariance, correlation
– Normal distribution
2
Logistics
• No cell phones or laptops.
• Only Scientific Calculator Allowed
People and Places
Instructor:
Abdullah Al Mahmud, Ph.D.
PhD (USA), MBA in Finance (USA), M.Sc. in Int. Econ & Fin. (USA)
Associate Professor
Office:
9001
shawonis@gmail.com, amahmu.bin@du.ac.bd
Course Enrollment Link: https://piazza.com/du.ac.bd/fall2019/b307
Class Hours:
Tuesday & Thursday 9:30am (Section A)
Class Room:
Tuesday & Thursday 11:00am (Section B)
7003
Readings
• Textbook: Bodie, Kane, and Marcus (BKM), Investments, 10th
Edition.
• Reilly and Brown, Investment Analysis and Portfolio Management, 10th
Edition
• Wall Street Journal, Financial Times, Economist
Learning Goals
• Understand the definition and properties of the main financial assets:
bonds, stocks and options.
• Understand how prices of each of these assets are determined. Be able to
correctly perform quantitative calculations for determining prices and
returns on these assets.
• Understand what determines the risk of different investment strategies
and learn methods for reducing investment risk.
• Obtain a basic working knowledge of Excel.
Coursework and Grading
Assessment criteria
Weight (%)
1st Mid term
15
2nd Mid term
15
Final Examination
60
Assignments, Report
and Presentation
Total
10
100
Course Outline
•
What is finance? Review of basic financial and mathematical concepts
•
Risk, return, risk aversion and capital allocation.
•
Portfolio selection
•
Capital Asset Pricing Model (CAPM)
•
Equity, e.g. stocks. Valuation.
•
Options, e.g. stock option.
•
Future, Swaps
What’s interesting about investments?
• Attributes
– Dividends, yields, returns, prices.
• What do we want to explain/predict?
– Prices, volatility, returns
• Risk
–
–
–
–
What does it mean?
What are the types of risk? Default, price
Is an insurance contract risky?
When is a mortgage risky?
Financial Markets
• Money Market Accounts
– Savings Accounts, CDs, Money Market accounts
– Liquid, Safe
• Capital Market
– Stocks, Bonds
– Less liquid, riskier
Money Market
• Instruments
– T-bill
– CD
– CP
• Who Invests
– Risk adverse
– Need money soon (e.g. tuition).
Capital Market
•
•
•
•
Bond market
Equity market
Stock market indexes
Derivatives
Bond Market
• Fixed income stream.
• Instruments (different issuers):
– Government: Federal, state, local
– Corporate bonds
– Securitized Debt: Mortgages, Loans
• Issues
– Default
– Inflation
Equity
•
•
•
•
Stock: ownership in part of a company
Characteristics:
– Exchange traded
– Dividends
– Voting rights
– Can be private.
Issues
Riskier cash flow
Speculation
Indexes
Dow, S&P, Wilshire, Nikkei, FTSE
Derivative
• Value derives from an asset.
• Examples
– Stock option
– Future
– Swap
– Credit Default Swap
Trading
• Exchanges
– NYSE, NASDAQ, AMEX
– Specialists
• Orders
– Market Order
– Limit Order, Stop loss
• Prices
– Ask price – buy at
– Bid price – sell at
• Costs
– Trading costs, broker fees
Leverage and Short Sales
• Buying on margin – leverage
– Borrow money to buy stock
– Riskier
$10 stock. Falls to $5. Lose 50% or 100%
– Housing
• Short sale
– Borrow stock
– Pay back stock in the future.
– Price speculation
Mutual Funds
• Own shares in the fund
• Managers pool money and invest in lots of options
• Examples: American, Fidelity, Vanguard
• Loads
• Fees
Time Value of Money
19
Time Value of Money
• Incremental cash flows in earlier years are more
valuable than incremental cash flows in later
years.
– Why?
– Exactly how much?
20
Present Value / Future Value
• Cash flows across time cannot be added up. They have
to be brought back to the same point in time before we
aggregate them.
• The process of moving cash flows in time is:
– Discounting, if future cash flows are brought to the present
• Present Value of Cash Flows
– Compounding, if present cash flows are taken to the future
• Future Value of Cash Flows
21
Time Line
$100
0
$100
$100
$100
2
3
4
1
10%
10%
10%
10%
• This time line represents a cash flow stream of $100 at
the end of each of the next 4 periods.
• The period discount rate is 10% for each period.
22
Discount Rate
• Why to discount the future cash flows?
– Individuals prefer present consumption to future
consumption,
– Monetary inflation,
– Uncertainty about future cash flows.
23
Types of Cash Flows
➢Simple cash flows
➢Annuities
➢Growing annuities
➢Perpetuities
➢Growing perpetuities
➢Note: Any other type of cash flow can be represented by
a combination of the above…
24
Notation
Notation
PV
FV
CFt
A
r
g
n
Stands for:
Present Value
Future Value
Cash flow at the end of period t
Annuity
Discount Rate
Expected Growth Rate
Number of years
25
Compounding a Simple Cash Flow
• A simple cash flow is a single cash flow at a
specified time.
CF0
FVt
0
t
26
Discounting a Simple Cash Flow
• A simple cash flow is a single cash flow at a
specified time.
PV
CFt
0
t
27
Example
• Assume that you own Infosoft, a small software firm. You
are currently leasing your office space, and expect to make a
lump sum payment to the owner of the real estate of
$500,000 ten years from now. Assume that an appropriate
discount rate for this cash flow is 10%. The present value of
this cash flow can then be estimated as:
28
Discount Rates and Present Values –
Negative Relationship
29
Present Value of Annuities
• An annuity is a constant cash flow that occurs
at regular intervals for a fixed period of time.
$100
0
1
$100
$100
$100
2
3
4
30
Example: Budget decision
• Assume that you are the owner of Infosoft, and that you
have the following two alternative:
– Buying a copier for $10,000 cash down or
– Paying $ 3,000 a year for 5 years for the same copier.
• If the opportunity cost is 12%, which would you rather do?
31
3,000 3,000 3,000 3,000 3,000 5 3,000
+
+
+
+
=
1.12 1.122 1.123 1.124 1.125 i =1 1.12i
where the general formula is :
n
PV = 
i =1
CF
i = 1,2,..., n
(1 + r ) i
Or use the annuity formula…
32
32
Future Value of Annuities
FV=?
$100
0
1
$100
$100
2
$100
3
4
33
Example
• An individual sets aside $2,000 at the end of every
year for three years.
• She expects to make 8% a year on her investments.
The expected value of the account on the end of
the 3 years:
2,000 + 2,000 *1.08 + 2,000 *1.082
where the general formula is :
n
FV =  CF (1 + r )i i = 1,2,..., n
i =1
34
Example
• An individual sets aside $2,000 at the end of every
year, starting when she is 25 years old, for an
expected retirement at the age of 65.
• She expects to make 8% a year on her investments.
The expected value of the account on her
retirement date would be:
35
Present Value of Growing Annuities
• A growing annuity is a cash flow that grows at a
constant rate for a specified period of time.
A(1+g)
0
1
A(1+g)2
A(1+g)3
2
3
A(1+g)n
……….
n
36
Example
• Suppose you have the rights to a gold mine for the next 20 years,
over which period you plan to extract 5,000 ounces of gold
every year.
• The current price per ounce is $300, but it is expected to
increase 3% a year.
• The appropriate discount rate is 10%.
• The present value of the gold that will be extracted from this
mine would be:
37
Present Value of a Perpetuity
• A perpetuity is a constant cash flow at regular
intervals forever.
38
Example
• A console bond is a bond that has no maturity and pays
a fixed coupon. Assume that you have a $60 coupon
console bond. The value of this bond, if the interest
rate is 9%, would be:
39
Present Value of a Growing Perpetuity
• A growing perpetuity is a cash flow that is
expected to grow at a constant rate forever.
40
Example
• Valuing a Stock with Stable Growth in Dividends
– In 1992, Southwestern Bell paid dividends per share of
$2.73. Its earnings and dividends had grown at 6% a year
between 1988 and 1992 and were expected to grow at the
same rate in the long term. The rate of return required by
investors on stocks of equivalent risk was 12.23%. What
is the value of this stock?
41
Statistics
42
Return, Risk, Co-movement
• When investing in financial assets, we care about performance of
the assets, the riskiness of the assets and the co-movement of
the prices of different assets.
– Measure performance by “expected returns”.
– Measure risk by the “variance of the expected returns”.
– Measure co-movement by the covariance (or correlation)
of the expected returns.
43
Rates of Return for Stocks:
Single Period
P
1 − P 0 + D1
HPR =
P0
HPR = r = Holding period return
P0 = Beginning price
P1 = Ending price
D1 = Dividend during period one
44
Rates of Return:
Single Period Example
Ending Price =
Beginning Price =
Dividend =
48
40
2
HPR = (48 - 40 + 2 )/ (40) = 25%
Problem: When we invest in a stock, we do not know the
ending price.
One Solution: Assign probabilities to the expected ending
prices, and calculate the expected returns.
45
Expected Returns
(Mean Returns)
ps= probability of a state
rs = return if a state occurs
N = Number of probable states
The expected return (the mean return) is a measure of
performance.
46
Scenario Returns: Example
State
1
2
3
4
5
Prob. of State
.1
.2
.4
.2
.1
r in State
-.05
.05
.15
.25
.35
E(r) = (.1)(-.05) + (.2)(.05)… + (.1)(.35)
E(r) = .15
47
Characteristics of Probability
Distributions
1) Mean: most likely value
2) Variance or standard deviation
3) Skewness
• If a distribution is approximately normal, the
distribution is described by characteristics 1
and 2.
48
Variance
• Measure how spread out variable is:
N
var[ r ] = E[( r − E[r ]) ] =  pi (ri − E[r ]) 2
2
i =1
• Why subtract mean [E(r)]? Why squared?
• Standard deviation
 = sd[r ] = var[ r ]
• Example
Var(r)=.25*(-23 – 6.5)2+.25*(0-6.5)2
+.25*(15-6.5)2 +.25*(35-6.5)2=449.25
Sd(r) = 21.2%
•
What’s point of sd?
Properties
•
Multiplying by a constant changes variance by the square of the constant.
• But
var[ aX ] = a 2 var[ X ]
sd[aX ] = a * sd[ X ]
• Not true: Var(X+Y) = Var(X) + Var(Y)
Calculating EV and Variance
•
•
•
Using data on stock returns {r(1), r(2),…,r(N)}
Calculate the mean and standard deviation:
Compute the sample average and the sample variance:
1
X=
N
N
X
i =1
i
N
1
S2 =
( X i − X )2

N − 1 i =1
•
Standard deviation
sd = S 2
Using our example…
Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2…+ .1(.35-.15)2]
Var= .01199
S.D.= [ .01199] 1/2 = .1095
52
Measuring Co-movement:
Covariance and Correlation
• Imagine you are holding IBM and Google stocks
in your portfolio.
• The risk of your portfolio return will depend on
whether or not the prices of IBM and Google
move together.
– If the returns move together, your risk is higher.
53
Covariance
•
•
To what extent do variables move together?
Portfolio
– 100% in AOL to 50% in Apple and 50% in AOL
– Is this riskier? Less risky
– Depend on how these two assets move together
cov( x, y ) =  xy = E[( x − E[ x])( y − E[ y ])]
N
cov(x, y ) =  pi (xi − E[ x])( yi − E[ y ])
i =1
• Note can be positive or negative
Correlation
•
Correlation
cov( x, y )
corr ( x, y ) =  xy =
sd ( x) sd ( y )
Measuring Comovement:
Correlation
•
•
The correlation between two variables is:
– Positive when they move together
– Negative when they move in the opposite directions.
The correlation ranges from –1 to 1.
•
By combining securities whose returns are not perfectly positively correlated
with each other in a portfolio, the portfolio standard deviation
characteristically falls.
•
The lower the correlation coefficient between investments, the greater the
benefit of diversification.
56
Calculating Portfolio Risk and Return
Two-asset model
• The expected return is calculated as:
E(rP ) = w1E(r1 ) + w 2 E(r2 )
Where: E(r1)
= Expected return on the first asset
E(r2)
= Expected return on the second asset
w
= weights
Calculating Portfolio Risk and Return
• The risk of a portfolio with two assets is
calculated as
 P = w  + w  + 2w1w1COV (r1, r 2)
2
1
2
1
2
2
2
2
 P = w12 12 + w 22 22 + 2w1w 2 1 2 12
Where: σ = standard deviation of assets
 = correlation coefficient of the two assets
Example
You are thinking about investing your money in the stock market. You have the following two
stocks in mind: stock A and stock B. You know that the economy can either go in recession or it
will boom. Being an optimistic investor, you believe the likelihood of observing an economic boom
is two times as high as observing an economic depression. You also know the following about your
two stocks:
State of the Economy
Boom
Recession
Probability
RA
10%
6%
RB
–2%
40%
a)
b)
c)
d)
Calculate the expected return for stock A and stock B
Calculate the total risk (variance and standard deviation) for stock A and for stock B
Calculate the expected return on a portfolio consisting of equal proportions in both stocks.
Calculate the expected return on a portfolio consisting of 10% invested in stock A and the
remainder in stock B.
e) Calculate the covariance between stock A and stock B.
f) Calculate the correlation coefficient between stock A and stock B.
g) Calculate the variance of the portfolio with equal proportions in both stocks using the
covariance from answer e.)
59
Multiple Asset Model
• Portfolio Return:
N
E(rP ) =  w i E(ri )
i =1
• Portfolio Risk:
N
N -1 N
 P =  w  +   w i w j i j  ij
i =1
2
i
2
j
i =1 j=i +1
Example:
Three-Security Portfolio
rp = W1r1 + W2r2 + W3r3
2p = W1212 + W2212 + W3232
+ 2W1W2 Cov(r1r2)
+ 2W1W3 Cov(r1r3)
+ 2W2W3 Cov(r2r3)
Systematic and Unsystematic Risk
VARIANCE
Total Risk
=
Diversifiable Risk
(unsystematic)
+
Market Risk
(systematic)
Portfolio of
U.S. stocks
Total
risk
1
Systematic
risk
10
20
30
40
50
Number of stocks in portfolio
By diversifying the portfolio, the variance of the portfolio’s return relative to the variance of the market’s return (beta) is
reduced to the level of systematic risk -- the risk of the market itself.
Excess Returns
• The reward for investing in a stock is the return in excess of the
risk-free rate
• Risk-free rate
– Depositing the money to a savings account,
– Buying government bonds.
• The difference between the return on a risky investment and
risk-free investment is called the “risk premium,” or “excess
return.”
63
How do We Compare Different
Investments?
➢Remember: We care for both return and risk.
➢Sharpe Ratio
– The ratio of the expected excess returns to the
standard deviation of excess returns.
➢An investment with a higher Sharpe Ratio is a
better investment…
– Why?
64
Sharpe Ratio
• The Sharpe Ratio is:
E[ Ri ] − rf
Excess Return
=
Standard deviation of excess return
i
65
Risk of a Portfolio
➢The variance of a portfolio depends on the
variances of the individual stocks and the
covariance (correlation) between the individual
stocks
66