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Table 27.2
Make up a view and replace the one in spreadsheet 27.2. Recalculate the optimal asset allocation and portfolio expected performance.
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
)()( MM RVarARE
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
),()()( , SBSBBMB RRCovwRVarwRRCov
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
%40.1%46.5018186.0
00466.0)(
)(
)()( , M
M
MBB RE
RVar
RRCovRE
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
Table 27.2
%41.581.640.1'
%)81.6%,40.1())(),((
)1,1(
EE
SBE
PRQ
RERER
P
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
Table 27.2
))()(()(2SB
E REREVarQ ))(),((2)( 2
)(2
)(2
SBREREE RERECovQ
SB
0002714.00000408.02000289.0000064.0)(2 EQ
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
2
2)( )(),(
)|(D
SBREBB
RERECovDREPRE B
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
%40.1%46.5018186.0
00466.0)(
)(
)()( , M
M
MBB RE
RVar
RRCovRE
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
2
2)( )(),(
)|(D
SBREBB
RERECovDREPRE B
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
2
2)( )(),(
)|(D
SBREBB
RERECovDREPRE B
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
)()()( 222 EQD
Table 27.2
)()()( 222 EQD
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
)()()( 10 ttaaatu f
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
2
2)()(),(
)|(D
RESBSS
SRERECovD
REPRE
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
2
2)()(),(
)|(D
RESBSS
SRERECovD
REPRE
Table 27.2
Table 1: Bordered Covariance Matrix based on Historical Excess Returnsand Market-Value Weights and Calculation of Baseline Forecasts
Bonds StocksWeights 0.25 0.75
Bonds 0.25 0.006400 0.004080Stocks 0.75 0.004080 0.028900
sumproduct 0.001165 0.017021 Market portfolio variance V(M) = sum(c11:d11) = 0.018186 Coefficient of risk aversion of representative investor = 3 Baseline market portfolio risk premium = A x V(M) = 0.0546
Covariance with RM 0.00466 0.022695
Baseline risk premiums 0.01 0.07
Proportion of covariance attributed to expected returns: 0.01Covariance matrix of expected returns
Bonds StocksBonds 0.000064 0.0000408Stocks 0.0000408 0.000289
Table 27.2
Table 2: Views, Confidence and Revised (Posterior) Expectations
View: Difference between returns on bonds and stocks, Q = 0.0050View embedded in baseline forecasts QE = -0.0541Variance of QE = Var(RB – RS) 0.000271
Var[E(RB)] – Cov[E(RB),E(RS)] = 0.000023
Cov[E(RB),E(RS)] – Var[E(RS)] = -0.000248
Difference between view and baseline data, D = 0.0591Confidence measured by standard deviation of view QPossible SD 0 0.0100 0.0173 0.0300 0.0600Variance 0 0.0015 0.0003 0.0009 0.0036 BaselineE(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143 0.0140E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643 0.0681
Exercise 27.4
Make up a view and replace the one in spreadsheet 27.2. Recalculate the optimal asset allocation and portfolio expected performance.