Essentials Of Investment Analysis And Portfolio Management
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Essentials of Investment Analysis and Portfolio Management by Frank K. Reilly & Keith C. Brown
Chapter 1 The Investment Setting
2
Why Do Individuals Invest ? By saving money (instead of spending it), individuals tradeoff present consumption for a larger future consumption. (consumption choice) 3
How Do We Measure the Rate Of Return On An Investment ?
The pure rate of interest is the exchange rate between future consumption and present consumption. Market forces determine this rate. 4
How Do We Measure the Rate Of Return On An Investment ?
People’s willingness to pay the difference for borrowing today and their desire to receive a surplus on their savings give rise to an interest rate referred to as the pure
5
How Do We Measure the Rate Of Return On An Investment ?
If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense.
6
If the future payment from the investment is not certain (uncertainty), the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover
7
Defining an Investment A current commitment of $ for a period of time in order to derive future payments that will compensate for: – the time the funds are committed – the expected rate of inflation – uncertainty of future flow of funds.
8
• A central question in investments: How investors select investments that will give them their required rate of return. 9
Measures of return and risk We have to know: • Historical rate of return for an individual investment over one period of time • Average historical return for an individual investment over a number of time periods • Average return for a portfolio
10
Measures of Historical Rates of Return Holding Period Return
Ending Value of Investment HPR = Beginning Value of Investment $220 for example : = 1.10 $200 11
Holding Period Yield HPY = HPR - 1 Prior example: 1.10 - 1 = 0.10 = 10% 12
Annual Holding Period Return •Annual HPR = HPR
1/n
n = number of years the investment is held
Annual Holding Period Yield
13
For instance (page 7) • A two-year HPR=$350/$250=1.4 • Annual HPR=1.4 (1/2) =1.1832 • Annual HPY=1.1832-1=18.32% (Annual HPY is thus assumed constant for each year)
14
• However, if the prior example is for a time period of 6 months, what (Try it out!) is the annual HPR?
15
Computing mean historical returns Arithmetic Mean (AM) for an investment over a number of time HPY ∑ periods AM = n
where:
∑ HPY
= the sum of annual holding period yields 16
Geometric Mean (GM) GM = [ π HPR ] where:
1
n
−1
π = the product operator π HPR = ( HPR1 ) × ( HPR2 ) × × ( HPRn )
17
HPY for a portfolio The mean historical rate of return for a portfolio is measured as the weighted average of the HPYs for the individual investments.
18
• You can also consider the mean historical rate of return of a portfolio as the overall change in value of the original portfolio.
19
Computation example of HPY for a portfolio Exhibit 1.1 Stock A B C Total
# Shares 100,000 200,000 500,000
HPY =
Begin Price $ 10 $ 20 $ 30
Beginning Mkt. Value $ 1,000,000 $ 4,000,000 $ 15,000,000 $ 20,000,000
Ending Ending Price Mkt. Value $ 12 $ 1,200,000 $ 21 $ 4,200,000 $ 33 $ 16,500,000 $ 21,900,000
HPR =
$ 21,900,000 $ 20,000,000
=
1.095
1.095
-1
=
0.095
=
9.5%
Market HPR HPY Wt. 1.20 20% 0.05 1.05 5% 0.20 1.10 10% 0.75
Wtd. HPY 0.010 0.010 0.075 0.095
20
Expected Rates of Return • Risk: uncertainty that an investment will earn its expected rate of return (historical return=realized return) • Point estimate: He/she expects to earns 10% over a year. 21
Computing expected return Expected Return = E(Ri ) n
= ∑ (Probability of Return) × (Possible Return) i =1
= P1 R1 + P2 R2 + ... + Pn Rn n
= ∑ Pi Ri i =1
See the detailed computation shown on page 12. 22
Probability Distributions 1.00
Risk-free Investment (perfect certainty)
0.80
0.60
0.40
0.20
0.00 -5%
0%
5%
10%
15% 23
Probability Distributions Risky investment with 3 possible rates of returns 1.00 0.80
0.60
0.40
0.20
0.00 -30%
-20%
-10%
0%
10%
20%
30%
24
Probability Distributions Risky investment with 10 possible rates of return 1.00 0.80
0.60
0.40
0.20
0.00 -40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
25
Risk Aversion Most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return.
Compare the perfect certainty case and the risky investment case on page 12.
26
Measuring the risk of expected rates of return Variance n
= ∑ (Probability) × (Possible Return - Expected Return) 2 i =1 n
= ∑ Pi × [ Ri − E ( Ri )]2 i =1
27
Measuring the risk of expected rates of return Standard deviation is the square root of the variance = n 2 P [R E(R )] ∑ i i i i =1
28
Measuring the risk of expected rates of return Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return.C.V. = σ i
E(R)
29
1.10
Measuring the risk of historical rates of return n
σ = ∑ [HPYi − E(HPY)] /n 2
2
i =1
30
Determinants of required rates of return • Time value of money • Expected rate of inflation • Risk involved 31
• Required rate of return: the minimum rate of return to compensate for deferring consumption. Find out the characteristics of the yield data in Exhibit 1.5: 2. Cross-section 3. Time series 4. Yield spread 32
The components that determine the required rate of return The Real Risk Free Rate (RRFR) • The basic interest rate • Assumes no inflation • Assumes no uncertainty about future cash flows. • Pure time value of money • Influenced by time preference for consumption of income (subjective) and investment opportunities in the economy (objective) 33
Factors for nominal risk-free rate (NRFR) 1+Nominal RFR =(1+Real RFR)(1+Rate of Inflation) (1 + Nominal RFR) −1 Real RFR = (1 + Rate of Inflation) 34
• Real RFR is quite stable over time. • Nominal RFR can be affected by – The relative ease or tightness in the capital markets – Expected rate of inflation
35
Risk Premium • We demand a higher return on an investment if we perceive that its uncertainty about expected return is higher. • The increase in required return over the NRFR is called risk premium. 36
The major sources of uncertainty (fundamental risk) • • • • •
Business risk Financial risk Liquidity risk Exchange rate risk Country risk
37
Business Risk • Uncertainty of income flows • Sales or earnings volatility leverage affects the level of business risk.
38
Financial Risk (financial leverage) • Uncertainty caused by the use of debt financing. • Borrowing requires fixed payments which must be paid ahead of payments to stockholders. • The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium. 39
Liquidity Risk • Uncertainty is introduced by the secondary market for an investment. – How long will it take to convert an investment into cash? – How certain is the price that will be received?
• US T-bills has almost no liquidity risk. 40
Exchange Rate Risk •
Uncertainty of return is introduced by acquiring securities denominated in a foreign currency. • To measure exchange rate risk: Use absolute variability of exchange rate relative to a composite exchange rate. 41
Country Risk • Political risk is the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country.
42
Risk Premium Basically, Risk premium= f (Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk)
43
Pages 22-27 •Risk premium and portfolio theory •Fundamental risk vs systematic risk •Relationship between risk and return →Will be further discussed in the later chapters
44
Exercises • Do Problem 1, 5, 7, 9. • Read Appendix of Chapter 1 (This is extra reading. Of course you need to read the contents of all chapters we discuss!)
45
• Fundamental risk comprises business risk, financial risk, liquidity risk, exchange rate risk, and country risk • Systematic risk refers to the portion of an individual asset’s total variance attributable to the variability of the total market portfolio 46
Chapter 1 The Investment Setting
2
Why Do Individuals Invest ? By saving money (instead of spending it), individuals tradeoff present consumption for a larger future consumption. (consumption choice) 3
How Do We Measure the Rate Of Return On An Investment ?
The pure rate of interest is the exchange rate between future consumption and present consumption. Market forces determine this rate. 4
How Do We Measure the Rate Of Return On An Investment ?
People’s willingness to pay the difference for borrowing today and their desire to receive a surplus on their savings give rise to an interest rate referred to as the pure
5
How Do We Measure the Rate Of Return On An Investment ?
If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense.
6
If the future payment from the investment is not certain (uncertainty), the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover
7
Defining an Investment A current commitment of $ for a period of time in order to derive future payments that will compensate for: – the time the funds are committed – the expected rate of inflation – uncertainty of future flow of funds.
8
• A central question in investments: How investors select investments that will give them their required rate of return. 9
Measures of return and risk We have to know: • Historical rate of return for an individual investment over one period of time • Average historical return for an individual investment over a number of time periods • Average return for a portfolio
10
Measures of Historical Rates of Return Holding Period Return
Ending Value of Investment HPR = Beginning Value of Investment $220 for example : = 1.10 $200 11
Holding Period Yield HPY = HPR - 1 Prior example: 1.10 - 1 = 0.10 = 10% 12
Annual Holding Period Return •Annual HPR = HPR
1/n
n = number of years the investment is held
Annual Holding Period Yield
13
For instance (page 7) • A two-year HPR=$350/$250=1.4 • Annual HPR=1.4 (1/2) =1.1832 • Annual HPY=1.1832-1=18.32% (Annual HPY is thus assumed constant for each year)
14
• However, if the prior example is for a time period of 6 months, what (Try it out!) is the annual HPR?
15
Computing mean historical returns Arithmetic Mean (AM) for an investment over a number of time HPY ∑ periods AM = n
where:
∑ HPY
= the sum of annual holding period yields 16
Geometric Mean (GM) GM = [ π HPR ] where:
1
n
−1
π = the product operator π HPR = ( HPR1 ) × ( HPR2 ) × × ( HPRn )
17
HPY for a portfolio The mean historical rate of return for a portfolio is measured as the weighted average of the HPYs for the individual investments.
18
• You can also consider the mean historical rate of return of a portfolio as the overall change in value of the original portfolio.
19
Computation example of HPY for a portfolio Exhibit 1.1 Stock A B C Total
# Shares 100,000 200,000 500,000
HPY =
Begin Price $ 10 $ 20 $ 30
Beginning Mkt. Value $ 1,000,000 $ 4,000,000 $ 15,000,000 $ 20,000,000
Ending Ending Price Mkt. Value $ 12 $ 1,200,000 $ 21 $ 4,200,000 $ 33 $ 16,500,000 $ 21,900,000
HPR =
$ 21,900,000 $ 20,000,000
=
1.095
1.095
-1
=
0.095
=
9.5%
Market HPR HPY Wt. 1.20 20% 0.05 1.05 5% 0.20 1.10 10% 0.75
Wtd. HPY 0.010 0.010 0.075 0.095
20
Expected Rates of Return • Risk: uncertainty that an investment will earn its expected rate of return (historical return=realized return) • Point estimate: He/she expects to earns 10% over a year. 21
Computing expected return Expected Return = E(Ri ) n
= ∑ (Probability of Return) × (Possible Return) i =1
= P1 R1 + P2 R2 + ... + Pn Rn n
= ∑ Pi Ri i =1
See the detailed computation shown on page 12. 22
Probability Distributions 1.00
Risk-free Investment (perfect certainty)
0.80
0.60
0.40
0.20
0.00 -5%
0%
5%
10%
15% 23
Probability Distributions Risky investment with 3 possible rates of returns 1.00 0.80
0.60
0.40
0.20
0.00 -30%
-20%
-10%
0%
10%
20%
30%
24
Probability Distributions Risky investment with 10 possible rates of return 1.00 0.80
0.60
0.40
0.20
0.00 -40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
25
Risk Aversion Most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return.
Compare the perfect certainty case and the risky investment case on page 12.
26
Measuring the risk of expected rates of return Variance n
= ∑ (Probability) × (Possible Return - Expected Return) 2 i =1 n
= ∑ Pi × [ Ri − E ( Ri )]2 i =1
27
Measuring the risk of expected rates of return Standard deviation is the square root of the variance = n 2 P [R E(R )] ∑ i i i i =1
28
Measuring the risk of expected rates of return Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return.C.V. = σ i
E(R)
29
1.10
Measuring the risk of historical rates of return n
σ = ∑ [HPYi − E(HPY)] /n 2
2
i =1
30
Determinants of required rates of return • Time value of money • Expected rate of inflation • Risk involved 31
• Required rate of return: the minimum rate of return to compensate for deferring consumption. Find out the characteristics of the yield data in Exhibit 1.5: 2. Cross-section 3. Time series 4. Yield spread 32
The components that determine the required rate of return The Real Risk Free Rate (RRFR) • The basic interest rate • Assumes no inflation • Assumes no uncertainty about future cash flows. • Pure time value of money • Influenced by time preference for consumption of income (subjective) and investment opportunities in the economy (objective) 33
Factors for nominal risk-free rate (NRFR) 1+Nominal RFR =(1+Real RFR)(1+Rate of Inflation) (1 + Nominal RFR) −1 Real RFR = (1 + Rate of Inflation) 34
• Real RFR is quite stable over time. • Nominal RFR can be affected by – The relative ease or tightness in the capital markets – Expected rate of inflation
35
Risk Premium • We demand a higher return on an investment if we perceive that its uncertainty about expected return is higher. • The increase in required return over the NRFR is called risk premium. 36
The major sources of uncertainty (fundamental risk) • • • • •
Business risk Financial risk Liquidity risk Exchange rate risk Country risk
37
Business Risk • Uncertainty of income flows • Sales or earnings volatility leverage affects the level of business risk.
38
Financial Risk (financial leverage) • Uncertainty caused by the use of debt financing. • Borrowing requires fixed payments which must be paid ahead of payments to stockholders. • The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium. 39
Liquidity Risk • Uncertainty is introduced by the secondary market for an investment. – How long will it take to convert an investment into cash? – How certain is the price that will be received?
• US T-bills has almost no liquidity risk. 40
Exchange Rate Risk •
Uncertainty of return is introduced by acquiring securities denominated in a foreign currency. • To measure exchange rate risk: Use absolute variability of exchange rate relative to a composite exchange rate. 41
Country Risk • Political risk is the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country.
42
Risk Premium Basically, Risk premium= f (Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk)
43
Pages 22-27 •Risk premium and portfolio theory •Fundamental risk vs systematic risk •Relationship between risk and return →Will be further discussed in the later chapters
44
Exercises • Do Problem 1, 5, 7, 9. • Read Appendix of Chapter 1 (This is extra reading. Of course you need to read the contents of all chapters we discuss!)
45
• Fundamental risk comprises business risk, financial risk, liquidity risk, exchange rate risk, and country risk • Systematic risk refers to the portion of an individual asset’s total variance attributable to the variability of the total market portfolio 46
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