Slide Investment 2020 (Đầu tư tài chính)

Chapter 1 Introduction to Investment Investment • Lecturer Nguyen Thanh Huong • Email huongntdue edu vn 1 mailto huongntdue edu vn 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 Course outline • Chapter 1 Introduction to Investment • Chapter.

Investment

• Lecturer: Nguyen Thanh Huong

• Email: huongnt@due.edu.vn

1

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

Materials and 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

INTRODUCTION TO INVESTMENT

Chapter 1

6

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

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

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

2 Real Assets versus Financial Assets

 Claims to the income generated by real assets: stocks, bonds…

 Define the allocation of income or wealth among investors

10

 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

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

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

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

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

5.1 Arithmetic Mean vs Geometric Mean

− 1

19

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?

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

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

5.1 Expected return and Risk

23

 Risky Investment with three possible returns

5.1 Expected return and Risk

24

 The return that investment is expected to earn on average

𝑤ℎ𝑒𝑟𝑒 𝑝𝑖 is the probability of scenario i,

𝑅𝑖 is the return of investment A in scenario i

5.1 Expected Return

25

5.1 Expected Return

Example 5.6: Calculate the expected return of stock ABC

given the following data

26

 Risk-free Investment

𝐸(𝑅𝐹) = 𝑅𝐹= 5%

5.1 Expected return and Risk

27

 Measuring the risk of an individual investment

Var RA = σA2 = 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

 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

Possible Rate Expected

of Return (R i ) Return E(R i )

Using historical rate of return

Calculate return and risk over time:

 𝐸 𝑅𝐴 = 1

𝑛 𝑛𝑖=1 𝑅𝑖,

 𝜎𝐴 = 1

𝑛−1 𝑛𝑖=1 𝑅𝑖 − 𝐸 𝑅𝐴 2,

where n is the number of observations,

𝑅𝑖 is return during the period i

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?

32

 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 = ni=1 wiE Ri

5.3.1 Return on a Portfolio

33

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)

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

Portfolio Weight

35

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

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 = ni=1 pi R𝐴,i − E RA [RB,i−E RB ]

A measure of the degree to which two variables “move

together” relative to their individual mean values over time

37

5.3.2 Risk of a Portfolio

38

 Example 5.10

Security Weight Boom Normal Recession E(R) σ

 The negative covariance between B and A, C helps lower

the volatility of the portfolio

 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

 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

 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

 Standard deviation of a portfolio

 Standard deviation of a portfolio

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

5.3.2 Risk of a Portfolio

47

5.3.2 Risk of a Portfolio

48

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

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

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

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

6 Utility, Risk aversion, and Portfolio selection

 Investor’s Utility function:

U = E RP − 0.005AσP2

 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

6 Utility, Risk aversion, and Portfolio selection

𝐔 = 𝐄 𝐑𝐏 − 𝟎 𝟎𝟎𝟓𝐀𝛔𝐏𝟐

54

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

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

Utility and Indifference Curves

 Represent an investor’s willingness to trade-off return and

 Indifference curve:

 The set of all portfolios that have the same level of utility

6 Utility, Risk aversion, and Portfolio selection

 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

High Risk Aversion

Low Risk Aversion

E(R)

σ

6 Utility, Risk aversion, and Portfolio selection

59

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

Exercise

1 Calculate the expected return and standard deviation of

the following portfolio

Chapter 2

PORTFOLIO THEORY

1

2

Chapter 2: Portfolio management

 How to allocate capital between risky and risk free assets?

 What is optimal risky portfolio? And how to construct it?

3

 It’s possible to split investment funds between safe and

risky assets

 Risk free asset: T-bills

 Risky asset: stock (or a portfolio)

Allocating Capital Between Risky Risk Free

Assets

4

Issues

will affect allocations between risky and risk free

assets

Allocating Capital Between

Risky & Risk Free Assets (cont.)

Allocating Capital Between

Risky & Risk Free Assets (cont.)

 Example: Portfolio (C) consists of a risk-free asset (F)

and a risky asset (P)

Allocating Capital Between

Risky & Risk Free Assets (cont.)

 E(RC) = yE(RP) + (1 – y)RF

Allocating Capital Between

Risky & Risk Free Assets (cont.)

• If y = 1 then C = 1 x 0.22 = 0.22 = 22%, E(RC) = 15% = E(RP)

• If y = 0 then C = 0 x 0.22 = 0, E(RC) = 7% = E(RF)

7

Borrow at the Risk-Free Rate and invest in stock Using 50% Leverage,

Allocating Capital Between

Risky & Risk Free Assets (cont.)

• The risk premium of portfolio P per unit of risk (σ)

• Higher Sharpe ratio = Higher return per unit of risk

9

Allocating Capital Between

Risky & Risk Free Assets (cont.)

 Capital Allocation Line (CAL):

CAL : 𝐸 𝑅𝐶 = 𝑅𝑓 + 𝜎𝐶 𝐸 𝑅𝑃 − 𝑅𝑓

𝜎𝑃

 The slope of CAL = The Sharpe Ratio of portfolio P (or 𝑆 )

 All portfolios on the CAL has the same reward-to-risk, the

difference is their total risk and return

10

11

CAL (Capital Allocation Line)

14

16

 Greater levels of risk aversion lead to larger proportions of the risk

free rate

 Lower levels of risk aversion lead to larger proportions of the

portfolio of risky assets

 Willingness to accept high levels of risk for high levels of returns

would result in leveraged combinations

Risk Aversion and Allocation

 Stock A

 Stock B

Diversification and Portfolio Risk

17

What risk does an asset have?

 Firm-specific factors: management, R&D, strategy, etc

 The risk that affect 1 or a small group of firms

Diversification and Portfolio Risk

 What type of risk can be eliminated through diversification?

 Firm-specific risks

 What type of risk should investors be compensated for?

 Systematic risk, Market risk

 𝑅𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑓(𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑅𝑖𝑠𝑘)

19

Number of Securities Systematic Risk

Specific Risk

Diversification and Portfolio Risk

Std Deviation

20

Correlation and Portfolio Risk:

The case of 2 assets

𝐸 𝑅𝑃 = 𝑤𝐴𝐸 𝑅𝐴 + 𝑤𝐵𝐸 𝑅𝐵𝑉𝑎𝑟 𝑅𝑃 = 𝑤𝐴2𝜎𝐴2 + 𝑤𝐵2𝜎𝐵2 + 2𝑤𝐴𝑤𝐵𝐶𝑜𝑣 𝑅𝐴, 𝑅𝐵

 Portfolio (P) consists of two stocks (A) and (B)

• E(RA) = 5%, A = 4%, E(RB) = 8%, B = 10%

• 𝜎𝑃 = 𝑤𝐴𝜎𝐴 + 𝑤𝐵𝜎𝐵

• 𝒘𝑨 𝒘𝑩 E(R P ) 𝝈𝑷

Correlation and Portfolio Risk:

The case of 2 assets ( 𝜌𝐴,𝐵 = 1 )

22

It is only possible to create

a two asset portfolio with risk-return along a line between either single asset

• 𝜎𝑃2 = 𝑤𝐴2𝜎𝐴2 + 𝑤𝐵2𝜎𝐵2

• 𝒘𝑨 𝒘𝑩 E(R P ) 𝝈𝑷

Correlation and Portfolio Risk:

The case of 2 assets ( 𝜌𝐴,𝐵 = 0 )

23

It is possible to create a two asset portfolio with lower risk than either single asset

• 𝜎𝑃 = ±(𝑤𝐴𝜎𝐴 − 𝑤𝐵𝜎𝐵)

• 𝒘𝑨 𝒘𝑩 E(R P ) 𝝈𝑷

Correlation and Portfolio Risk:

The case of 2 assets ( 𝜌𝐴,𝐵 = −1 )

24

It is possible to create a two asset portfolio with almost no risk

Correlation and Portfolio Risk:

The case of 2 assets

25

 When 𝜌𝐴𝐵 = 1, diversification doesn’t reduce portfolio risk

 When 𝜌𝐴𝐵 < 1, diversification can reduce portfolio risk

 The risk reduction potential increases as the correlation

decreases

Benefits of Diversification ↑↓ Assets Correlation (𝜌𝑖𝑗)

 Is there a limit to the benefits of diversification?

 Undiversifiable or Systematic risk

Correlation and Portfolio Risk:

The case of 2 assets

26

Minimum-Variance portfolio (MIN):

𝜎𝑃2 = 𝑤𝐴2𝜎𝐴2 + 𝑤𝐵2𝜎𝐵2 + 2𝑤𝐴𝑤𝐵𝐶𝑜𝑣 𝑅𝐴, 𝑅𝐵

𝑤𝐴 + 𝑤𝐵 = 1 Find the portfolio that has the smallest variance?

min

𝑤𝐴 𝜎𝑃2 = 𝑤𝐴2𝜎𝐴2 + 1 − 𝑤𝐴 2𝜎𝐵2 + 2𝑤𝐴 1 − 𝑤𝐴 𝐶𝑜𝑣 𝑅𝐴, 𝑅𝐵

Minimum-Variance portfolio (MIN)

27

 Find the portfolio that has the smallest variance?

 Example: Portfolio (P) consists of two stocks (A) and (B)

Efficient diversification:

The general case of many risky assets

 For portfolios with 2 assets:

 𝐸 𝑅𝑃 = 𝑤1𝐸 𝑅1 + 𝑤2𝐸 𝑅2

 𝑤1 + 𝑤2 = 1

 Only 1 portfolio can be formed given a value of 𝐸 𝑅𝑃

 When there are more than 2 assets:

 𝐸 𝑅𝑃 = 𝑤1𝐸 𝑅1 + 𝑤2𝐸 𝑅2 + ⋯ + 𝑤𝑛𝐸(𝑅𝑛)

 𝑤1 + 𝑤2 + ⋯ + 𝑤𝑛 = 1

 Many portfolios can be formed given a value of 𝐸 𝑅𝑃

 Which combination is the best (most efficient)?

31