2. Course description
Number of hours: 45 (3 credits)
Level: Undergraduate
Aims:
Provide students with a fundamental and advanced knowledge
of investment theory
To guide students in the practical application of investment
analysis
To demonstrate to students the techniques of financial
valuation
2
3. Course outline
• Chapter 1: Introduction to Investment
• Chapter 2: Portfolio theory
• Chapter 3: Asset pricing models
• Chapter 4: Stock analysis and valuation
• Chapter 5: Bond analysis and valuation
3
4. Grading
Class Preparation/Participation: 20%
Regular attendance 5%
Participation in class 5%
Two short tests 10%
Test 1: Chapters 1-2
Test 2: Chapters 3-5
Assignment and presentation in class 20%
Final exam 60%
4
5. 5
Materials and manuals
Manuals:
Bodie, Z., Kane, A., Marcus, A. J., Essentials of Investments, Fifth
Edition
Reilly, F. K., Brown, K. C., Investment Analysis and Portfolio
Management, 7th Edition, Thomson - South Western, 2003.
Chapter 1 – 2, 6 – 16, 19
7. Chapter 1:
Intro to Investment
1. Investment definition
2. Financial assets vs Real assets
3. Major classes of financial assets
4. Investment process
5. Measuring the return and risk of an investment
6. Utility, Risk Aversion and Portfolio selection
7
8. 1. Investment Definition
An investment is the commitment of current resources in
the expectation of deriving greater resources in the future.
Investment example:
Buying a stock/bond
Putting money in a bank account
Study for a college degree
8
9. 1. Investment Definition
The nature of financial investment:
Reduced current consumption
Planned later consumption
An investment will compensate the investor for:
The time the funds are committed
The risk of the investment
Inflation
9
10. 2. Real Assets versus Financial Assets
Real Assets
Assets used to produce goods and services: Buildings, land,
equipment, knowledge…
Real assets generate net income to the economy
Financial Assets
Claims to the income generated by real assets: stocks, bonds…
Define the allocation of income or wealth among investors
10
11. Debt securities: Money market instruments, Bonds
Equity security: common stock, preferred stock
Derivatives: Options, Futures, Forward, Warrants.
Alternative investments: Real estate, artwork, hedge funds,
venture capital, crypto currencies, etc.
3. Major Classes of Financial Assets
11
12. 4. Investment Process
Portfolio: an investor’s collection of investment assets.
Two types of decisions in constructing the portfolio:
Asset allocation: Allocation of an investment portfolio across
broad asset classes
Security selection: Choice of specific securities within each asset
class
Security analysis: Analysis of the value of securities
12
13. 5. Measuring Return and Risk
5.1. Measuring return
Holding-period Return (HPR)
Arithmetic Mean (AM) vs. Geometric Mean (GM)
Risk and Expected return
5.2. Measuring risk
Measuring risk using variance and standard deviation.
5.3. Measuring risk and return of a portfolio
The return of a portfolio
Correlation and portfolio risk.
13
14. 5.1. Measuring Return
Return:
Profit/loss on an investment.
Can be expressed in $$$ or in percentage (%).
Rate of return = return expressed in %.
From now on, “rate of return” will be simply called “return”
(Unless specified otherwise).
14
16. 5.1. Measuring Return
Example 5.1
You bought a share of Vingroup for VND 50,000 on 01/09/2017. And
then you sold it for VND 75,000 after 1 year. What is the HPR on
your investment?
𝐻𝑃𝑅 =
75,000
50,000
− 1 = 0.5 = 50%
16
17. 5.1. Measuring Return
Example 5.2
You bought a share of Hoa Phat for VND 40,000 on 01/09/2017 and
sold it 1.25 year (15 months) later for VND 75,000. What is the HPR
on your investment?
𝐻𝑃𝑅 =
75,000
40,000
− 1 = 0.875 𝑜𝑟 87.5%
Which investment performed better?
17
18. 5.1. Measuring Return
Holding period: day, week, month, year, etc.
How to compare HPRs with different holding periods?
How to measure the average return over multiple periods?
18
19. 5.1. Arithmetic Mean vs. Geometric Mean
Arithmetic Mean:
AM =
HPRi
n
n
i=1
Geometric Mean
GM = 1 + HPRi
n
i=1
1
n
− 1
19
20. 5.1. Arithmetic Mean vs. Geometric Mean
Example 5.3: Mutual fund DUE has the following returns in the last 4
years as follow: 35%, -25%, 20%, -10%.
What is the mutual fund’s AM?
𝐴𝑀 =
35% − 25% + 20% − 10%
4
= 5%
What is the mutual fund’s GM?
𝐺𝑀 = 1 + 0.35 1 − 0.25 1 + 0.2 1 − 0.1
1
4 − 1
𝐺𝑀 = 2.26%
20
21. 5.1. Arithmetic Mean vs. Geometric Mean
If an investor invests in the DUE fund, what return should
he expect to earn next year?
Which number is better at representing the actual
return/performance of the DUE fund for the last 4 years?
Arithmetic Mean or Geometric Mean?
21
22. 5.1. Arithmetic vs Geometric Mean
Example 5.4
AM = [1+(–0.50)] /2 = 0.5/2 = 0.25 = 25%
GM = (2 × 0.5)1/2
– 1 = (= (1)1/2
– 1 = 1 – 1 = 0%
22
23. 5.1. Expected return and Risk
Example 5.5
Risk is uncertainty regarding the outcome of an investment
W = 100
W1 = 150 Profit = 50
W2 = 80 Profit = -20
1-p = .4
23
24. Risky Investment with three possible returns
5.1. Expected return and Risk
24
25. The return that investment is expected to earn on average.
𝐸 𝑅𝐴 = [𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦
𝑛
𝑖=1
𝑜𝑓 𝑅𝑒𝑡𝑢𝑟𝑛 × 𝑃𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑅𝑒𝑡𝑢𝑟𝑛]
𝐸 𝑅𝐴 = 𝑝𝑖𝑅𝑖
𝑛
𝑖=1
𝑤ℎ𝑒𝑟𝑒 𝑝𝑖 is the probability of scenario i,
𝑅𝑖 is the return of investment A in scenario i.
5.1. Expected Return
25
26. Probability
Pi
Recession 0.15 -15%
Normal 0.60 5%
Boom 0.15 10%
Strong Boom 0.10 20%
Expected
Return
4.25%
Scenario Return
5.1. Expected Return
Example 5.6: Calculate the expected return of stock ABC
given the following data
26
28. Measuring the risk of an individual investment
Var RA = σA
2
= pi Ri − E RA
2
n
i=1
𝑝𝑖: The probability of scenario i.
𝑅𝑖: The return of investment A in scenario i.
𝐸(𝑅𝐴): The expected return of investment A.
5.2. Risk
28
29. Standard deviation
𝜎𝐴 = 𝑉𝑎𝑟(𝑅𝐴) = pi Ri − E RA
2
n
i=1
Standard deviation is the square root of the variance
Measure the volatility of an investment.
The higher the 𝜎, the riskier (more volatile) the investment.
Risk-free asset (F): 𝜎𝐹= 0
5.2. Risk
29
30. Possible Rate Expected
of Return (Ri) Return E(Ri)
-15% 0.15 4.3% -0.19 0.0371 0.005558
5% 0.60 4.3% 0.01 0.0001 0.000034
10% 0.15 4.3% 0.06 0.0033 0.000496
20% 0.10 4.3% 0.16 0.0248 0.002481
Variance 0.008569
Pi Ri - E(Ri) [Ri - E(Ri)]
2
[Ri - E(Ri)]
2
Pi
5.2. Risk
Example 5.6: 𝜎 = 0.008569 = 9.26%
30
31. 31
Using historical rate of return
Calculate return and risk over time:
𝐸 𝑅𝐴 =
1
𝑛
𝑅𝑖
𝑛
𝑖=1 ,
𝜎𝐴 =
1
𝑛−1
𝑅𝑖 − 𝐸 𝑅𝐴
2
𝑛
𝑖=1 ,
where n is the number of observations,
𝑅𝑖 is return during the period i.
32. 5.3. Return and Risk of a Portfolio
Example 5.7: Portfolio P is made up of 3 securities (A, B, and C)
with the following weights. Calculate the return on P when the
economy is booming?
A 0.50 11.50%
B 0.20 5.00%
C 0.30 24.00%
P 1.00 13.95%
Return when
Boom
Security Weight
32
33. Return on a portfolio:
RP = wiRi
n
i=1
where wi is the weight of the asset i in the portfolio,
Ri is the return on asset i.
The expected return on a portfolio: E RP = wiE Ri
n
i=1
5.3.1. Return on a Portfolio
33
34. 5.3.1. Return of a Portfolio
Example 5.8: Calculate the expected return of Portfolio P using
the following data
Security Weight Boom Normal Recession E(R)
0.3 0.5 0.2
A 0.50 11.5% 5.0% -4.0% 5.2%
B 0.20 5.0% 15.0% 18.0% 12.6%
C 0.30 24.0% 13.0% -5.0% 12.7%
P 14.0% 9.4% 0.1% 8.9%
34
35. 5.3.1. Return of a Portfolio
Example 5.9: Calculate the expected return, the variance and
standard deviation of portfolio P using the following data.
0.5 0.2 0.3
Scenario Probability A B C P
Boom 0.3 11.5% 5.0% 24.0% 14.0%
Normal 0.5 5.0% 15.0% 13.0% 9.4%
Recession 0.2 -4.0% 18.0% -5.0% 0.1%
Expected
Return
5.2% 12.6% 12.7% 8.9%
Portfolio Weight
35
36. 5.3.2. Risk of a Portfolio
The variance and standard deviation of portfolio P
Scenario Probability Return R - E(R) [R - E(R)]^2
Boom 0.30 14.0% 5.1% 0.002550
Normal 0.50 9.4% 0.5% 0.000025
Recession 0.20 0.1% -8.8% 0.007744
8.9% Variance 0.002326
Stdev 4.82%
Expected Return
36
37. 5.3.2. Risk of a Portfolio
Is the risk of a portfolio the average/the sum of the risk of
individual assets in the portfolio?
We’ll need to know the covariance/correlation between
assets’ returns in the portfolio to calculate the portfolio
variance and standard deviation.
cov RA, RB = σA,B = pi R𝐴,i − E RA [RB,i−E RB ]
n
i=1
A measure of the degree to which two variables “move
together” relative to their individual mean values over time
37
39. Security Weight Boom Normal Recession E(R) σ
0.3 0.5 0.2
A 0.50 11.5% 5.0% -4.0% 5.2% 5.37%
B 0.20 5.0% 15.0% 18.0% 12.6% 5.10%
C 0.30 24.0% 13.0% -5.0% 12.7% 10.05%
P 14.0% 9.4% 0.1% 8.9% 4.82%
5.3.2. Risk of a Portfolio
Example 5.9: The standard deviation of the portfolio is smaller
than each asset’s standard deviation in this case. Why?
39
40. The negative covariance between B and A, C helps lower
the volatility of the portfolio
CovAB = − 0.002454
CovBC = − 0.004452
CovAC = 0.005389
5.3.2. Risk of a Portfolio
40
41. Coefficient of Correlation:
The correlation coefficient is obtained by standardizing
(dividing) the covariance by the product of the individual
standard deviations
𝜌𝑖𝑗 =
𝐶𝑜𝑣𝑖𝑗
𝜎𝑖𝜎𝑗
𝜌𝑖𝑗 measures how strong the returns of i and j move
together or in opposite direction.
5.3.2. Risk of a Portfolio
41
42. Covij tells us whether the returns of asset i and j tend to
move in the same direction or in opposite direction
But Covij doesn’t tell whether they move together strongly
or not.
𝝆𝒊𝒋 measures the strength of the co-movements of the
returns of i and j.
−𝟏 ≤ 𝝆𝒊𝒋 ≤ 𝟏
5.3.2. Risk of a Portfolio
42
43. 𝜌𝑖𝑗 = 1: perfect positive correlation. This means that
returns for the two assets move together in a completely
linear manner
𝜌𝑖𝑗 = −1 : perfect negative correlation. This means that the
returns for two assets have the same percentage
movement, but in opposite directions
𝜌𝑖𝑗 = 0: the movements of the rates of return of the two
assets are not correlated
5.3.2. Risk of a Portfolio
43
44. Standard deviation of a portfolio
σP = wi
2
σi
2
+ wiwjCovij
n
j=1
n
i=1
n
i=1
For a portfolio with 2 assets A and B:
𝜎𝑃 = 𝑤𝐴
2
𝜎𝐴
2
+ 𝑤𝐵
2
𝜎𝐵
2
+ 2𝑤𝐴𝑤𝐵𝐶𝑜𝑣𝐴𝐵
5.3.2. Risk of a Portfolio
44
45. Standard deviation of a portfolio
σP = wi
2
σi
2
+ wiwj𝜎𝑖𝜎𝑗𝜌ij
n
j=1
n
i=1
n
i=1
For a portfolio with 2 assets A and B:
𝜎𝑃 = 𝑤𝐴
2
𝜎𝐴
2
+ 𝑤𝐵
2
𝜎𝐵
2
+ 2𝑤𝐴𝑤𝐵𝜎𝐴𝜎𝐵𝜌𝐴𝐵
5.3.2. Risk of a Portfolio
45
46. Example 5.11
Calculate the expected return on the portfolio (P).
Calculate the SD of the portfolio (P) if the correlation
between the two assets is: +1, 0.5, 0, -0.5, -1.
5.3.2. Risk of a Portfolio
46
49. 5.3.2. Risk of a Portfolio
Negative correlation reduces portfolio risk
Combining two assets with -1.0 correlation reduces the
portfolio standard deviation to zero only when individual
standard deviations are equal
49
50. 5. Return and Risk: Further questions
Where does risk come from?
What is risk premium?
The relationship between risk and return?
What type of risk should investors be compensated?
50
51. 6. Utility, Risk aversion, and Portfolio selection
Utility function: Measures the satisfaction that we can derive
from the investment outcomes (wealth).
Assume that each investor can assign a Utility value to each
of the portfolio he/she can choose.
Higher utility portfolio is better.
Given an investor’s preferences (tastes), the best portfolio
is the portfolio that gives the highest utility he can choose
from.
51
52. 6. Utility, Risk aversion, and Portfolio selection
Investors’ preferences:
Like Expected Return
Risk Averse = Dislike Risk
Investor’s utility function:
Increasing in Expected Return
Decreasing in Risk
Risk is measured by standard deviation or variance.
52
53. 6. Utility, Risk aversion, and Portfolio selection
Investor’s Utility function:
U = E RP − 0.005AσP
2
𝐸(𝑅𝑃): Expected return of portfolio P.
𝜎𝑃: standard deviation of portfolio P.
A: The degree of risk aversion of the investor. Therefore, different
investors have different A, or different levels of risk aversion.
Higher A means the investor is more risk-averse (dislike
risk more strongly).
53
55. 6. Utility, Risk aversion, and Portfolio selection
Dominance Principle:
Given a level of expected return:
Investors prefer portfolios with Lower Risk (lower standard
deviation).
Give a level of standard deviation:
Investors prefer portfolios with Higher Expected Return.
Each portfolio is dominated by all the portfolios lies in the
“Northwest” of itself.
55
56. 6. Utility, Risk aversion, and Portfolio selection
2 dominates 1; has a higher return
2 dominates 3; has a lower risk
4 dominates 3; has a higher return
All Red portfolios dominates 3.
1
2 3
4
𝑬 𝑹𝑷
𝝈𝑷
56
57. 57
Utility and Indifference Curves
Represent an investor’s willingness to trade-off return and
risk.
Example
Exp Ret St Deviation A U=E ( r ) - .005As2
10 20.0 4 2
15 25.5 4 2
20 30.0 4 2
25 33.9 4 2
58. Indifference curve:
The set of all portfolios that have the same level of utility.
6. Utility, Risk aversion, and Portfolio selection
E(R)
σ
Increasing Utility
F
A
B
C
D
E
A and B has the same utility.
C and D has the same utility.
E and F has the same utility.
𝑈 𝐴 > 𝑈 𝐷 > 𝑈(𝐸)
58
59. High Risk Aversion
Low Risk Aversion
E(R)
σ
6. Utility, Risk aversion, and Portfolio selection
59
60. 6. Utility, Risk aversion, and Portfolio selection
Portfolio selection:
How does an investor choose the best portfolio to invest in?
Given a set of portfolios that an investor can invest in,
the investor should choose the portfolio that provides
the investor with the highest utility.
60
61. Exercise
1. Calculate the expected return and standard deviation of
the following portfolio
Portfolio 1:
Security Weight Boom Normal Recession E(R) σ
0.2 0.6 0.2
A 0.30 14.0% 8.0% -8.0% 6.0% 7.38%
B 0.70 4.0% 12.0% 10.0% 10.0% 3.10%
P 7.0% 10.8% 4.6% 8.8% 2.56%
61