Lesson 3: Risk and Return

Question 1

the time period an investment is held
or is the period in which you own an investment

Answer 1

Holding Period

Question 2

the return for the period of investment

Answer 2

Holding Period Return

Question 3

Formula of HPR

Answer 3

HPR = ending value of investment/ beginning value of investment

Question 4

If you commit to invest Php 500 at the beginning of the year and get back Php 550 at the end of the year, what is your return for the period?

Answer 4

HPR = 550/500
= 1.10

HPY = HPR - 1
=1.10 -1
= 0.10 or 10%

Question 5

Percentage Return

Answer 5

Holding Period Yield

Question 6

Formula of Annual HPR

Answer 6

Annual HPR = HPR^1/n

Question 7

Formula of Holding Period Yield

Answer 7

HPY = HPR - 1

Question 8

Consider an investment that cost Php 1,000 and is worth Php 800 after a year. Calculate for the HPR and the HPY.

Answer 8

HPR = Php 800/Php 1,000
= 0.8

Annual HPR = 0.8^1/1
= 0.8

Annual HPY = 0.8 - 1
= -0.20 / -20%

Question 9

Consider an investment that cost Php 2, 500 and is worth Php 3,500 after being held for 2 years. Calculate for the HPR and the HPY.

Answer 9

HPR = Php 3,500/Php 2,500
= 1.40

Annual HPR = 1.4^1/2
= 1.1832

Annual HPY = 1.1832 - 1
= 0.1832 or 18.32%

Question 10

You have an investment of Php 1,000 held for 6 months and this investment earned Php 1,120. Calculate for the HPR and the HPY.

Answer 10

HPR = Php 1,120/Php 1,000
= 1.12

Annual HPR = 1.12 1/0.5
= 1.2554

Annual HPY = 1.2554 - 1
= 0.2554 / 25.54%

Question 11

Consider an investment that cost Php 1,000 and is worth Php 750 after being held for 2 years. Calculate for the HPR and the HPY.

Answer 11

HPR = Php 750.00/Php 1,000
= 0.75

Annual HPR = 0.75^1/2
= 0.8660

Annual HPY = 0.8660 - 1
= -0.1339 or -13.4%

Question 12

Mean Historical Rate of Return (Single Investment)

Answer 12

1. Arithmetic Mean
2. Geometric Mean

Question 13

the sum of HPYs divided by the number of years

Answer 13

Arithmetic Mean

Question 14

the nth root of the product of the HPRs for the number of years minus one

Answer 14

Geometric Mean

Question 15

Formula of Arithmetic Mean

Answer 15

AM = Sum of HPY / n

Question 16

Formula of Geometric Mean

Answer 16

={[(HPR1)(HPR2)…(HPRn)]^1/n} - 1

Question 17

Find AM and GM

Year 1:
Beginning Value = 100
Ending Value = 115
HPR = 1.15
HPY = 0.15

Year 2:
Beginning Value = 115
Ending Value = 138
HPR = 1.2
HPY = 0.20

Year 3:
Beginning Value = 138
Ending Value = 110.4
HPR = .8
HPY = -0.20

Answer 17

AM = [(0.15)+(0.20)+(-0.20)] / 3
= 0.15 / 3
= 0.05 = 5%

GM = [(1.15) X (1.20) X (0.80)] 1/3 - 1
= (1.04) 1/3 - 1
= 1.03353- 1
= 0.03353 = 3.353%

Question 18

Year 1:
Beginning Value = 50
Ending Value = 110
HPR = 2
HPY = 1

Year 2:
Beginning Value = 100
Ending Value = 50
HPR = .50
HPY = -.50

Answer 18

AM = [(1) + (-0.50] / 2
= 0.50 / 2
= 0.25 = 25%

GM = [(2) X (0.50)] 1/2 - 1
= (1) 1/2 - 1
= 1 - 1
= 0%

Question 19

Measured as the weighted average of the HPYs for the individual investments in the portfolio

Answer 19

Mean Historical Rate of Return (Portfolio)

Question 20

Weights used in computing are the relative beginning market values for each investment (dollar-weighted or value weighted)

Answer 20

Mean Historical Rate of Return (Portfolio)

Question 21

Expectation from an investment

Answer 21

Expected Rate of Return

Question 22

Point of estimate

Answer 22

Expected Rate of Return

Question 23

Statistical measure of return

Answer 23

Expected Rate of Return

Question 24

formula of ERR

Answer 24

~ ERR = ∑ (Probability of Return) X ( Possible return)

~ E(Ri) = [P1 R 1 + P 2R 2 + P3 R3 + …+P nRn]

~ E(Ri ) = ∑ (Pi)( Ri)

Question 25

An investor is absolutely certain of a return of 20%.

Answer 25

Expected Rate of Return = ∑ (1) X ( 0.20)
= 0.20 / 20%

Question 26

Economic Conditions:

Strong Economy
Probability = 0.15
Rate of Return = 0.20

Weak Economy
Probability = 0.15
Rate of Return = -0.20

No Change
Probability = 0.70
Rate of Return = 0.10

Answer 26

E(Ri) = {(0.15)(0.20)} + {(0.15)(-0.20)} + {(0.70)(0.10)}
= (0.03) + (-0.03) + (0.07)
= 0.07

Question 27

statistical measurement of the spread between numbers in a data

Answer 27

Variance

Question 28

determine the volatility and market security

Answer 28

Variance

Question 29

– the square root of the variance

Answer 29

Standard Deviation

Question 30

• determines the consistency of the investment’s
  return over a period of time

Answer 30

Standard Deviation

Question 31

Risk of Expected Rates of Return

Answer 31

1. Variance
2. Standard Deviation

Question 32

Formula of Variance

Answer 32

Variance = ∑(Probability)x (Possible return – Expected Return)^2

Variance = =[(P1)(PR1 -ER)2 + (P2)(PR2 -ER)2 + …….(Pn)(PRn -ER)2 ]

Question 33

Find the variance

An investor is absolutely certain of a return of 20%. Expected Rate of Return = ∑ (1) X ( 0.20) = 20%

Answer 33

Variance = 1 x (0.20 – 0.20)
= 1(0) = 0

Question 34

Find the Variance

Economic Conditions:

Strong Economy
Probability = 0.15
Rate of Return = 0.20

Weak Economy
Probability = 0.15
Rate of Return = -0.20

No Change
Probability = 0.70
Rate of Return = 0.10

ERR = 7%

Answer 34

=[(0.15)(0.20-0.07)2 + (0.15)(-0.20-0.07)2 +
(0.70)(0.10-0.07)2 }
={0.010935+ 0.002535 + 0.00063}
= 0.0141

Question 35

Find the Standard Deviation

Economic Conditions:

Strong Economy
Probability = 0.15
Rate of Return = 0.20

Weak Economy
Probability = 0.15
Rate of Return = -0.20

No Change
Probability = 0.70
Rate of Return = 0.10

ERR = 7%

Answer 35

o^2 = 0.0141

σ = Square root 0.0141

σ = 0.11874 or 11.87%

Question 36

Formula of Coefficient Of Variation

Answer 36

Coefficient of Variation =Standard Deviation of Returns / Expected Rate of Return

Question 37

Find the Coefficient of Variance

Economic Conditions:

Strong Economy
Probability = 0.15
Rate of Return = 0.20

Weak Economy
Probability = 0.15
Rate of Return = -0.20

No Change
Probability = 0.70
Rate of Return = 0.10

ERR = 7%

Answer 37

CV = 0.11874 ÷ 0.07

    = 1.696

Question 38

This is the minimum rate of return that you should accept from an investment in order to compensate you for deferring consumption.

Answer 38

Required Rates of Return

Question 39

Components of Required Rates of Return

Answer 39

> time value of money during the investment period
Expected rate of inflation
Risk involved

Question 40

published rate and the growth rate of your money

Answer 40

Nominal Interest Rate

Question 41

growth rate of your purchasing power.

Answer 41

Real Interest Rate

Question 42

This is the nominal rate reduced by the the loss of the purchasing power resulting from inflation.

Answer 42

Real Interest Rate

Question 43

Formula of Approximated Real Interest Rate

Answer 43

R ≈ 𝑛𝑟 − 𝑖

Question 44

Formula of Exact Real Rate

Answer 44

RR = (nr-i) / (1+i)

Question 45

The nominal interest rate on a 1-year time deposit is at 18% and inflation rate is expected to be 15% over the coming year.

Answer 45

Approximated real rate
R ≈ 𝑛𝑟 − 𝑖
≈ 0.18 – 0.15 = 0.03 or 3%

Exact real rate
rr = (nr-i) / (1+i)
= (0.18 – 0.15) / (1.15)
= 0.03 / 1.15 = 2.60%

Question 46

difference between the holding period return and risk- free rate

Answer 46

Risk Premium

Question 47

rate you earn by investing in risk-free instruments

Answer 47

Risk-free rate

Question 48

difference in any particular period between actual rate of return on risky assets and actual risk-free rate

Answer 48

Excess return

Question 49

Major Sources of Risk

Answer 49

• Business Risk
• Financial Risk
• Liquidity risk
• Exchange rate risk
• Political Risk

Question 50

Formula of Risk Premium

Answer 50

= f(business risk, financial risk, liquidity risk, exchange rate risk, political risk)