1. Investment
• Lecturer: Nguyen Thanh Huong
• Email: huongnt@due.edu.vn
1

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

6. INTRODUCTION TO INVESTMENT
Chapter 1
6

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

15. 5.1. Measuring Return
 Holding-Period Return (single period):
HPR =
P1 + D1
P0
− 1
 P0 = Beginning price
 P1 = Ending price
 D1 = Dividend during period one
15

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

27.  Risk-free Investment
𝐸(𝑅𝐹) = 𝑅𝐹= 5%
5.1. Expected return and Risk
27

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

38. 5.3.2. Risk of a Portfolio
38
 Example 5.10

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

47. 5.3.2. Risk of a Portfolio
47

48. 5.3.2. Risk of a Portfolio
48

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

54. 6. Utility, Risk aversion, and Portfolio selection
𝐔 = 𝐄 𝐑𝐏 − 𝟎. 𝟎𝟎𝟓𝐀𝛔𝐏
𝟐
54

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