Upload
robert-hamilton
View
214
Download
0
Embed Size (px)
Citation preview
Bodi Kane Marcus Ch 5
1
Learning about Return and Risk from The Historical Record
Chapter 5
Bodi Kane Marcus Ch 5
2
Determinants of the level of Interests
•Real and Nominal rates of Interest•The equilibrium Real Rate of Interest•The equilibrium Nominal Rate of Interest•Taxes and Real Rate of Interest
more…
Real vs. Nominal Rates
Fisher effect: Approximationnominal rate = real rate + inflation premium
R = r + i or r = R - iExample r = 3%, i = 6%
R = 9% = 3% + 6% or 3% = 9% - 6%Fisher effect: Exact
r = (R - i) / (1 + i) 2.83% = (9%-6%) / (1.06)
Empirical Relationship:Inflation and interest rates move closely together
3
Bodi Kane Marcus Ch 5
Bodi Kane Marcus Ch 5
Factors Influencing Rates
•Supply▫Households
•Demand▫Businesses
•Government’s Net Supply and/or Demand▫Federal Reserve Actions
4
Bodi Kane Marcus Ch 5
The equilibrium Real Rate of Interest
Q0 Q1
r0
r1
Funds
Inte
rest
R
ate
s
Supply
Demand
5Pergeseran kurva Demand ke kanan dapat terjadi karena pemerintah menerapkan budget deficit permintaan akan uang meningkat interest rate naik
Bodi Kane Marcus Ch 5
6
Risk and Risks Premium
•Holding Period Returns•Expected Return and Standard Deviation•Excess Returns and Risk Premiums
more……
Bodi Kane Marcus Ch 5
Rates of Return: Single Period
7
PDPPHPR
0
101
HPR = Holding Period Return
P0 = Beginning price
P1 = Ending price
D1 = Dividend during period one
Holding Period Returns
Bodi Kane Marcus Ch 5
Rates of Return: Single Period Example
Ending Price ($) = 48Beginning Price ($) =
40Dividend ($) = 2
HPR = (48 - 40 + 2 )/ (40) = 25%8
Bodi Kane Marcus Ch 5
Characteristics of Probability Distributions
1) Mean: most likely value2) Variance or standard deviation3) Skewness
* If a distribution is approximately normal, the distribution is described by characteristics 1 and 2
9
Bodi Kane Marcus Ch 5
10
Characteristics of Probability Distributions
1) Mean:The simple mathematical average of a set of two or more numbers
2) Variance : A measure of the dispersion of a set of data points around their mean value. ▫Variance is a mathematical expectation of the
average squared deviations from the mean.
3) Skewness : an asymmetry in the distribution of
the data values
Bodi Kane Marcus Ch 5
11
The Coefficient of Variation (CV)•A statistical measure of the dispersion of data
points in a data series around the mean. It is calculated as follows:
The coefficient of variation represents the ratio of the standard deviation to the mean.
In the investing world, CV determine how much volatility (risk) in comparison to the amount of return you can expect from your investment.
Source: Investopedia
Bodi Kane Marcus Ch 5
Symmetric distributionr
s.d. s.d.
Normal Distribution
12
Bodi Kane Marcus Ch 5
Subjective returns
p(s) = probability of a stater(s) = return if a state occurs1 to s states
E(r) = p(s) r(s)s
Measuring Mean: Scenario or Subjective Returns
13
Bodi Kane Marcus Ch 5
State Prob. of State r in State1 .1 -.052 .2 .053 .4 .154 .2 .255 .1 .35
E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35)E(r) = .15
Numerical Example: Subjective or Scenario Distributions
14
Bodi Kane Marcus Ch 5
Standard deviation = [variance]1/2
Measuring Variance or Dispersion of Returns
Subjective or Scenario
15
Variance = s
p(s) [rs - E(r)]2
Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2...+ .1(.35-.15)2]Var= .01199
S.D.= [ .01199] 1/2 = .1095
Using Our Example:
Bodi Kane Marcus Ch 5
Annual Holding Period Returns
Geom. Arith. Stan.Series Mean% Mean% Dev.%
Large Stock10.5 12.5 20.4Small Stock12.6 19.0 40.4LongT Gov 5.0 5.3 8.0
T-Bills 3.7 3.8 3.3
Inflation 3.1 3.2 4.5 16
Bodi Kane Marcus Ch 5
17
Expected Return and Standard Deviation
•Spreadsheet 5.1
Purchase Price 100$ T-Bill Rate 6%
ProbabilityEnding Price($)
Dividends HPR p* HPR Dev2 p*Dev2
Excess Returns
Boom 0.3 129.5 4.5 0.34 0.10 0.04 0.012 0.28Normal growth 0.5 110 4 0.14 0.07 0 0 0.08Recession 0.2 80.5 3.5 -0.16 -0.03 0.09 0.018 -0.22Expected value (mean) 0.14Standard Deviations 0.1732
Bodi Kane Marcus Ch 5
18
Teknis Penghitungan
• Expected Value▫ Jumlahkan hasil perkalian probabilitas dengan HPR
• Standard Deviation of HPR▫ Deviasi= HPR dikurangi mean▫ Kuadratkan Deviasi▫ Kalikan probabilitas dg Dev2
▫ Jumlahkan (p* Dev2 ), kemudian pangkat-kan (0.5) atau diakar• Excess Return
▫ HPR dikurangi RFR• Squared Deviations (Dev2 ) Excess Return
▫ Excess Return dikurangi risk premium, kemudian dikuadratkan
• Standard Deviation of Excess Return▫ Kalikan probabilitas dg Dev2 Excess Return ▫ Jumlahkan (p* Dev2 ), kemudian pangkat-kan (0.5) atau diakar
Bodi Kane Marcus Ch 5
19
Expected Return and Standard Deviation
•Problem 5-7 page 151
ProbabilityEnding Price($)
HPR (incl Dividends) p* HPR Dev2
Boom 0.35 140 44.50% 0.16 0.093025Normal growth 0.3 110 14% 0.04 0Recession 0.35 80 -16.50% -0.06 0.093025Expected value (mean) 0.14
Bodi Kane Marcus Ch 5
20
Excess Returns and Risk Premiums
• Excess Returns : Returns in excess of the risk-free rate or in excess of a market measure, such as an index fund. ▫ When you have excess returns you are making more
money than if you put your money into an index fund like the Dow Jones Industrial Average (DJIA).
• Risk Premiums : The return in excess of the risk-free rate of return that an investment is expected to yield. ▫An asset's risk premium is a form of compensation for
investors who tolerate the extra risk - compared to that of a risk-free asset - in a given investment.
Source: Investopedia
Bodi Kane Marcus Ch 5
21
Time Series Analysis of Past Rates of Return
•Time Series versus Scenario Analysis•Expected Returns and the arithmetic
Average•The Geometric (Time Weighted) Average
Return•The Reward to Volatility (Sharpe) Ratio
Bodi Kane Marcus Ch 5
22
Time Series Analysis of Past Rates of Return• Time Series versus Scenario Analysis• Time Series Analysis
▫useful to see how a given asset, security or economic variable changes over time or how it changes compared to other variables over the same time period
• Scenario Analysis: The process of estimating the expected value of a portfolio after a given period of time, assuming specific changes in the values of the portfolio's securities or key factors that would affect security values, such as changes in the interest rate.
Source: Investopedia
Bodi Kane Marcus Ch 5
23
• The arithmetic Average: A mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series.
Source: Investopedia
Time Series Analysis of Past Rates of Return
Day 1 2 3 4 5 Sum
Closing Price
$14.50 $14.80 $15.20 $14.00 $15.50 $74.00
the arithmetic mean of a stock's closing price = $ 74.00 / 5 = $14.80.
The arithmetic mean of a stock's closing price = $ 74.00 / 5 = $14.80.
Bodi Kane Marcus Ch 5
24
Time Series Analysis of Past Rates of Return
• The Geometric (Time Weighted) Average Return: The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.
• The Geometric = {(1+ r1)*(1+r2)*…*(1+rn)} 1/n -1
Average Return
more……
25
Illustration Geometric Mean
Year Return
1 0.15
2 0.20
3 -0.20
•Geometric Mean•[(1.15) x(1.20) x (0.80)]1/3 – 1 •= (1.104) 1/3 -1 =0.03353 =
3.353%
Bodi Kane Marcus Ch 5
26
Time Series Analysis of Past Rates of Return
• The Reward to Volatility (Sharpe) Ratio: A ratio developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. ▫ The Sharpe ratio is calculated by subtracting the
risk-free rate from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns
(5.18) Return Excess of SD
PremiumRisk Ratio Sharpe
Source: Investopedia
Bodi Kane Marcus Ch 5
27
The Normal Distribution
State ofEconomy
Probability ofEconomic State
Stock Performance
Probability of Stock Performance in Given Economic
Joint Probability
Good 0.3 Good 0.6 0.18Neutral 0.3 0.09Poor 0.1 0.03
Neutral 0.5 Good 0.4 0.20Neutral 0.3 0.15Poor 0.3 0.15
Poor 0.2 Good 0.2 0.04Neutral 0.3 0.06Poor 0.5 0.10
1
Jawaban: Probabilitas perekonomian dalam keadaan neutral dan saham pada kondisi kinerja poor=
0.15
Problem 5.6/ CFA Problem/p.153
Bodi Kane Marcus Ch 5
28
Deviations from Normality
(5.19) E(r)] -E[r(s)
Skew3
3
Positively skewed
Negatively skewed
Bodi Kane Marcus Ch 5
29
The Historical Record of Returns on Equities and Long Term Bonds•Average Returns and Standard Deviations•Other statistics of Risky Portfolios•Sharpe Ratios•Serial Correlation•Skewness and Kurtosis•Estimates of Historical Risk Premiums•A Global View of the Historical Record
more……
Bodi Kane Marcus Ch 5
30
Average Returns and Standard Deviation
Answer CFA Problem 3 dan 4/ p.153
Probabilitystock X Exp Return Dev Dev2 Dev2*p
Bull market 0.3 50% 15.00%30.00% 0.090 0.0270
Normal Market
0.5 18% 9.00%-2.00% 0.000 0.0002
Bear Market 0.2 -20% -4.00% -40.00% 0.160 0.0320Exp Return 20.00%
Variance 0.0592St Dev 0.2433
Bodi Kane Marcus Ch 5
31
Measurement of Risk with non Normal Distributions
• Value at Risk (VaR) : A technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities.
• Conditional Tail Expectation (CTE) : an important actuarial risk measure and a useful tool in financial risk assessment.
• Lower Partial Standard Deviation (LPSD) : Compute expected lower partial moments for normal asset returns
Bodi Kane Marcus Ch 5
32
Lower Partial Standard Deviation (LPSD)•Measure of risk non normal distributions•The LPSD for the large and small stock
portfolios are not very different from value from the normal distributions because the skews are similar to those from the normal (see Table 5.5)Large US Stocks Small US Stocks
Lower Partial Standard Deviation (%)
History Normal History Normal
LPSD for 25 year HPR 4.34 4.23 7.09 7.14
LPSD for 1 year HPR 21.71 21.16 35.45 35.72
Average 1 –year HPR 12.13 12.15 17.97 17.95
Bodi Kane Marcus Ch 5
Annual Holding Period Risk Premiums and Real Returns
Risk RealSeriesPremiums% Returns%Lg Stk 8.7 9.3Sm Stk 15.2 15.8LT Gov 1.5 2.1T-Bills 0 0.6Inflation 0.6
33