CHAPTER 5 Risk and Rates of Return
description
Transcript of CHAPTER 5 Risk and Rates of Return
![Page 1: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/1.jpg)
5-1
CHAPTER 5Risk and Rates of Return
![Page 2: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/2.jpg)
5-2
5.1 Rates of Return Holding Period Return: Rates of Return over a given
period
Suppose the price of a share is currently $100, and your time horizon is one year. You expect the cash dividend during the year to be $4. Your best guess about the price of the share is to be $110 after one year from now. So,
priceBeginningdividendCashpriceBeginningpriceEndingHPR
%14100$
4$100$110$
HPR
![Page 3: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/3.jpg)
5-3
Measuring Investment Return over Multiple Period
Year Annual Holding Period Return
2000 0.2
2001 0.05
2002 -0.05
2003 0.15
2004 0.3
Arithmetic Mean (20+5-5+15+30)/5 =0.13
Geometric Mean (1.2*1.05*.95*1.15*1.3)1/5-1 =0.1
![Page 4: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/4.jpg)
5-4
5.2 Risk and Return Risk is the concept of fluctuations. This fluctuations
can be (i) a deviation of the actual return from the expected return, or (ii) a deviation of average return from the year to year return. Higher the fluctuations, higher is the risk.
Measures of risk are: i. Standard Deviation ii. Coefficient of Variance iii. Beta
![Page 5: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/5.jpg)
5-5
Calculation of Risk-Return
)()()(
)(1
)(
)*()(
2
2
ondistributiyprobabilitforRRPRisk
dataseriestimeForn
RRRisk
PRnR
RREeturnRExpected
ii
i
iii
![Page 6: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/6.jpg)
5-6
Calculation of Risk-Return (Historical Data)
Year Return (%) Dev. (Ri-E(R)) Dev. Square2000 20 7 492001 5 -8 642002 -5 -18 3242003 15 2 42004 30 17 289
Mean Return= 13% Sum of Dev sq= 730Stand.Deviation2 730/(5-1)= 182.5Stand.Deviation= Square root (182.5)= 13.5%
![Page 7: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/7.jpg)
5-7
Calculation of Risk-Return: Scenario Analysis (Probability Distribution)
State ofEconomy
Probability (Pi)
Return (Ri) (%)
Exp. Value (Pi*Ri)
Deviation (Ri-E(R))
DeviationSquare Dev sq* Pi
Boom 0.25 25 6.25(25-13.25)
=11.75(11.25)2
=138.0625(138*.25)=34.52
Normal 0.5 14 7(14-13.25)
=0.75(0.75)2
=0.5625(.56*.5)=0.28
Recession 0.25 0 0(0-13.25)=-13.25
(-13.25)2
=175.5625(175*.25)=43.89
13.25% 78.69
Return =13.25% Risk=8.9% Stand Dev 8.87
m
iiiRPRE
1
)(
m
iiii RERp
1
22 })]({[(
![Page 8: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/8.jpg)
5-8
Figure:5.3:Normal DistributionA normal distribution looks like a bell-shaped curve.
Probability
99.74%
– 3 – 13.36%
– 2 – 4.5%
– 1 4.4%
013.25%
+ 1 22.12%
+ 2 31%
+ 3 39.86%
Mean=13.25%Standard Deviation=8.87%
68.26%
95.44%
![Page 9: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/9.jpg)
5-9
5.3 THE HISTORICAL RECORDBills, Bonds, and Stocks:1926-2006
![Page 10: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/10.jpg)
5-10
Figure 5.1 Frequency Distributions of Holding Period Returns
![Page 11: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/11.jpg)
5-11
Probability distributions With the same average return more standard
deviation means more risk. Shown graphically. Note that as risk increases height goes down and width increases.
Expected Rate of Return
Rate ofReturn (%)100150-70
Firm X
Firm Y
%40%10
y
x
![Page 12: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/12.jpg)
5-12
Effectiveness of Diversification of Portfolio
Climate Probability Return of Umbrella
ReturnIce-cream
PortfolioReturn
Rainy 0.25 25 -5 10
Moderate 0.5 14 10 12
Dry 0.25 0 15 7.5
E(R) = 13.3% 7.5% 10.4%
Risk
8.9% 7.5% 1.9%
ii PR *
ii PRR 2)(
![Page 13: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/13.jpg)
5-13
Portfolio Effects on Risk and Return
0
2
4
6
8
10
12
14
0 2 4 6 8 10
Risk
Retu
rn Series1
![Page 14: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/14.jpg)
5-14
Optimum portfolio and CML: Given the feasible set highest possible utility function gives us O.P. and the tangency is CML
.Re
turn
Risk (σ)
CML
Feasible set
Lending
BorrowingU1
O.P
![Page 15: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/15.jpg)
5-15
Investor attitude towards risk Risk aversion – assumes investors dislike
risk and require higher rates of return to encourage them to hold riskier securities.
Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.
![Page 16: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/16.jpg)
5-16
Risk Premiums and Risk Aversion If T-Bill denotes the risk-free rate, rf, and variance, ,
denotes volatility of returns then:The risk premium of a portfolio is:
2P
2P
2
To quantify the degree of risk aversion with parameter A:
If the risk premium of a portfolio is 8%, and the standard deviation is 20%, then risk aversion of the investor is: A=.08/(.5x.22)=4.
Compare this with risk premium of 10%, and A=.1/(.5x.22)=5
![Page 17: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/17.jpg)
5-17
The Sharpe (Reward-to-Volatility) Measure
![Page 18: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/18.jpg)
5-18
Coefficient of Variation (CV)
A standardized measure of dispersion about the expected value, that shows the risk per unit of return. When, both return and risk increase then coefficient of variance (CV) should be used.
^k
Mean
dev Std CV
![Page 19: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/19.jpg)
5-19
Use of coefficient of variance Example: We have 2 alternatives to invest.
Security A has a mean return of 10% and a standard deviation of 6%, and security B has a mean return of 13% with a standard deviation of 8%. Which investment is better.
%5.61100*%13%8
%60100*%10%6
B
A
CV
CV
So, security A is better as the Coefficient of variance of A is less than the that of B.
![Page 20: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/20.jpg)
5-20
5.4 INFLATION AND REAL RATES OF RETURN
![Page 21: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/21.jpg)
5-21
Real vs. Nominal Rates Fisher effect: ApproximationLet, nominal rate=R
Real rate=rInflation rate (CPI)=i
nominal rate = real rate + inflation rate: R ≈ r + i or r = R - i
Example r = 3%, i = 6%R = 9% = 3% + 6% or 3% = 9% - 6%
Fisher Effect:
2.83% = (9%-6%) / (1.06)
![Page 22: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/22.jpg)
5-22
5.5 ASSET ALLOCATION ACROSS RISKY AND RISK-FREE PORTFOLIOS
![Page 23: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/23.jpg)
5-23
Risk tolerance: Slope of Indifference curves Return
ConservativeNormal
Aggressive
Risk (σ)
15%
10%7%6%
![Page 24: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/24.jpg)
5-24
Optimum portfolio with different risk tolerance Return
Conservative
Normal
Aggressive
Risk (σ)
CML
Efficient Frontier
σm
Rm
![Page 25: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/25.jpg)
5-25
Risk Aversion and Allocation 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
![Page 26: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/26.jpg)
5-26
Possible to split investment funds between safe and risky assets
Risk free asset: proxy; T-bills Risky asset: stock (or a portfolio)
Issues Examine risk/ return tradeoff Demonstrate how different degrees of risk aversion will
affect allocations between risky and risk free assets
Allocating Capital
![Page 27: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/27.jpg)
5-27
The Risky Asset:Text Example (Page 149)
Total portfolio value = $300,000Risk-free value = 90,000 Risky (Vanguard and Fidelity) = 210,000Vanguard (V) = 54% =$113,400 Fidelity (F) = 46% = $96,600Total =$210,000y=210,000/300,000 =0.7 (portfolio in risky assets)1-y=90,000/300,000 =0.3 (proportion of Risk-free investment)Vanguard 113,400/300,000 = 0.378Fidelity 96,600/300,000 = 0.322Portfolio P 210,000/300,000 = 0.700Risk-Free Assets F 90,000/300,000 = 0.300Portfolio C 300,000/300,000 = 1.000
![Page 28: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/28.jpg)
5-28
Change in risk exposure (p.150) Suppose, the investor decides to decrease the risk
exposure from 0.7 to 0.56. Now, the risky portfolio would be=0.56*300,000=$168,000 This requires a sale of (210,000-168,000)=$42,000 of risky
holdings, and use the sale proceeds to purchase risk-free asset
How would the investment of risky asset change? Sale of Vanguard=42,000*.54=$22,680;
New Vanguard holding=113,400-22,680=$90,720 Sale of Fidelity=42,000*.46=$19,320
New Fidelity holding=96,600-19,320=$77,280 Total Vanguard & Fidelity=90,720+77,280=$168,000 y=168,000/300,000=.56
![Page 29: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/29.jpg)
5-29
Capital Allocation Line (CAL)(Test of linearity)
036.33.
07.19.;33.22.*5.1;19.)07.*5.()15.*5.1()(;5.1
:%50,;
36.011.
07.11.;11.)22.*5.0(*,11.)07.*5(.)15.*5.0()(;5.
50:50:
36.022.
07.15.)(;22.22.*1%,15)(;1,
,
)(;.;)1()(.)(
%)1(;%
%22%15)(
%0%7
sloperEy
leverageIfcaseBorrowing
slopeyrEy
caseLending
rrEsloperEyIf
Example
rrEslopeyryrEyportfoliocompleteofreturnExpectedrE
rinyportfolioriskyiny
rE
r
cc
pcc
p
fpcc
c
fcpcfpc
f
pp
rff
![Page 30: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/30.jpg)
5-30
Figure 5.5 Investment Opportunity Set with a Risk-Free Investment
![Page 31: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/31.jpg)
5-31
CAL and CMLre
turn
P
rf
CML CAL 1
CAL 2
CAL 3
CAL4
Efficient Frontier
Rm
m CAL1 is dominant over CAL2, CAL2 is dominant over
CAL3. CML is dominant over CAL1.
![Page 32: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/32.jpg)
5-32
5.6 PASSIVE STRATEGIES AND THE CAPITAL MARKET LINE
![Page 33: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/33.jpg)
5-33
Table 5.5 Average Rates of Return, Standard Deviation and Reward to Variability
![Page 34: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/34.jpg)
5-34
Use of historical data to predict CML Use of old data is popular Old data may not be representative for future Weight of old data keeps changing Correction of old data for future is largely
subjective, but customary.
![Page 35: CHAPTER 5 Risk and Rates of Return](https://reader030.fdocuments.us/reader030/viewer/2022013012/56815bac550346895dc9adf9/html5/thumbnails/35.jpg)
5-35
Costs and Benefits of Passive Investing Active strategy entails costs Free-rider benefit Involves investment in two passive
portfolios Short-term T-bills Fund of common stocks that follows a
broad market index. Diversification can be based on asset allocation like industry classification, large and small firms, local and foreign firms