Lesson 3: Risk and Return Flashcards by Emil Melchor

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

Holding Period

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the return for the period of investment

Holding Period Return

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Formula of HPR

HPR = ending value of investment/ beginning value of investment

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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?

HPR = 550/500
= 1.10

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

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Percentage Return

Holding Period Yield

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Formula of Annual HPR

Annual HPR = HPR^1/n

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Formula of Holding Period Yield

HPY = HPR - 1

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

HPR = Php 800/Php 1,000
= 0.8

Annual HPR = 0.8^1/1
= 0.8

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

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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.

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%

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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.

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%

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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.

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%

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Mean Historical Rate of Return (Single Investment)

Arithmetic Mean
Geometric Mean

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the sum of HPYs divided by the number of years

Arithmetic Mean

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

Geometric Mean

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Formula of Arithmetic Mean

AM = Sum of HPY / n

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Formula of Geometric Mean

={[(HPR1)(HPR2)…(HPRn)]^1/n} - 1

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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

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%

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

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

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%

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

Mean Historical Rate of Return (Portfolio)

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

Mean Historical Rate of Return (Portfolio)

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Expectation from an investment

Expected Rate of Return

Point of estimate

Expected Rate of Return

Statistical measure of return

Expected Rate of Return

formula of ERR

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

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

~ E(Ri ) = ∑ (Pi)( Ri)

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

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

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

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

statistical measurement of the spread between numbers in a data

Variance

determine the volatility and market security

Variance

– the square root of the variance

Standard Deviation

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

Standard Deviation

Risk of Expected Rates of Return

1. Variance 2. Standard Deviation

Formula of Variance

Variance = ∑(Probability)x (Possible return – Expected Return)^2 Variance = =[(P1)(PR1 -ER)2 + (P2)(PR2 -ER)2 + …….(Pn)(PRn -ER)2 ]

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

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

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%

=[(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

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%

o^2 = 0.0141 σ = Square root 0.0141 σ = 0.11874 or 11.87%

Formula of Coefficient Of Variation

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

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%

CV = 0.11874 ÷ 0.07 = 1.696

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

Required Rates of Return

Components of Required Rates of Return

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

published rate and the growth rate of your money

Nominal Interest Rate

growth rate of your purchasing power.

Real Interest Rate

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

Real Interest Rate

Formula of Approximated Real Interest Rate

R ≈ 𝑛𝑟 − 𝑖

Formula of Exact Real Rate

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

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.

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%

difference between the holding period return and risk- free rate

Risk Premium

rate you earn by investing in risk-free instruments

Risk-free rate

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

Excess return

Major Sources of Risk

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

Formula of Risk Premium

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