Lesson 3: Risk and Return Flashcards
the time period an investment is held
or is the period in which you own an investment
Holding Period
the return for the period of investment
Holding Period Return
Formula of HPR
HPR = ending value of investment/ beginning value of investment
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%
Percentage Return
Holding Period Yield
Formula of Annual HPR
Annual HPR = HPR^1/n
Formula of Holding Period Yield
HPY = HPR - 1
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%
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%
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%
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%
Mean Historical Rate of Return (Single Investment)
- Arithmetic Mean
- Geometric Mean
the sum of HPYs divided by the number of years
Arithmetic Mean
the nth root of the product of the HPRs for the number of years minus one
Geometric Mean
Formula of Arithmetic Mean
AM = Sum of HPY / n
Formula of Geometric Mean
={[(HPR1)(HPR2)…(HPRn)]^1/n} - 1
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%
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%
Measured as the weighted average of the HPYs for the individual investments in the portfolio
Mean Historical Rate of Return (Portfolio)
Weights used in computing are the relative beginning market values for each investment (dollar-weighted or value weighted)
Mean Historical Rate of Return (Portfolio)
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
- Variance
- 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)
