Portfolio rebalancing
著者
書誌事項
Portfolio rebalancing
（Chapman & Hall/CRC financial mathematics series）（A Chapman & Hall book）
CRC Press, c2019
- : hardback
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注記
Includes bibliographical references (p. 243-244) and index
内容説明・目次
内容説明
The goal of Portfolio Rebalancing is to provide mathematical and empirical analysis of the effects of portfolio rebalancing on portfolio returns and risks. The mathematical analysis answers the question of when and why fixed-weight portfolios might outperform buy-and-hold portfolios based on volatilities and returns. The empirical analysis, aided by mathematical insights, will examine the effects of portfolio rebalancing in capital markets for asset allocation portfolios and portfolios of stocks, bonds, and commodities.
目次
Contents
Preface, vii
Chapter 1 Introduction 1
1.1 RISK MANAGEMENT 1
1.2 REBALANCING ALPHA 2
1.3 DIVERSIFICATION RETURN, VOLATILITY EFFECT 3
1.4 SERIAL CORRELATION AND REBALANCING ALPHA 5
1.5 NEW TOPICS IN PORTFOLIO REBALANCING 6
1.6 OUTLINE OF THE BOOK 7
Chapter 2 A Brief Review of Portfolio Theory 9
2.1 ARITHMETIC AND GEOMETRIC MEANS 9
2.2 RETURN VOLATILITIES 11
2.3 RELATIONSHIPS BETWEEN ARITHMETIC AND
GEOMETRIC MEANS 13
2.3.1 Analytic Approximation 13
2.3.2 Empirical Examination 15
2.4 PORTFOLIO RETURN AND VOLATILITY 19
2.5 SERIAL CORRELATION AND VOLATILITY OF MULTIPERIOD
RETURNS 23
2.5.1 Single Asset Multi-Period Volatility 24
2.5.2 Portfolio Multi-Period Volatility 26
PROBLEMS 27
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Chapter 3 Portfolio Rebalancing 29
3.1 SIMPLE EXAMPLES 29
3.2 REBALANCING LONG-ONLY PORTFOLIOS 32
3.3 REBALANCING LONG-SHORT PORTFOLIOS 36
3.4 REBALANCING ALPHA 41
3.4.1 Rebalancing Alpha of Asset Allocation Portfolios 42
3.4.2 Periodic Rebalancing versus Threshold Rebalancing 46
PROBLEMS 47
Chapter 4 Volatility Effect and Return Effect 49
4.1 DEFINITIONS OF TWO EFFECTS 50
4.2 POSITIVE RETURN EFFECT OF LONG-ONLY
PORTFOLIOS 52
4.2.1 Jensen's Inequality 52
4.2.2 Return Effect of Long-Only Portfolios 53
4.3 POSITIVE VOLATILITY EFFECT OF LONG-ONLY
PORTFOLIOS 53
4.3.1 Cauchy's Inequality 54
4.3.2 A Two-Asset Two-Period Case 54
4.3.3 An M-Asset Two-Period Case 57
4.3.4 The General Case 58
4.4 CASES OF POSITIVE AND NEGATIVE REBALANCING
ALPHAS 61
4.4.1 The Case of Positive Rebalancing Alpha 61
4.4.2 The Case of Negative Rebalancing Alpha 62
4.5 TWO-ASSET LONG-SHORT PORTFOLIOS 63
4.5.1 Negative Return Effect of Two-Asset Long-Short
Portfolios 63
4.5.2 Negative Volatility Effect of Two-Asset Long-Short
Portfolios 65
PROBLEMS 66
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Chapter 5 Analysis of Volatility Effect 69
5.1 "DIVERSIFICATION RETURN" 69
5.1.1 Two-Asset "Diversification Return" 71
5.1.2 Pairwise Decomposition of "Diversification Return" 72
5.1.3 Another Decomposition of "Diversification Return" 74
5.2 MAXIMIZING "DIVERSIFICATION RETURN" 75
5.3 DIVERSIFICATION RETURNS OF LONG-SHORT
PORTFOLIOS 78
5.3.1 Two-Asset Long-Short Portfolios 78
5.3.2 Inverse and Leveraged Exchange-traded Funds 79
5.3.3 Leveraged "Long-Only" Portfolios 81
PROBLEMS 84
Chapter 6 Analysis of Return Effect 87
6.1 RETURN EFFECT OF LONG-ONLY PORTFOLIOS 87
6.1.1 Two-Asset Return Effect 90
6.1.2 Pairwise Decomposition of Return Effect 92
6.2 THE IMPACT OF CROSS-SECTIONAL SERIAL
CORRELATIONS ON RETURN EFFECT 93
6.3 APPROXIMATING RETURN EFFECTS OF LONGSHORT
PORTFOLIOS 96
6.3.1 Two-Asset Long-Short Portfolios 97
6.3.2 General Long-Short Portfolios 99
PROBLEMS 102
Chapter 7 Analysis of Rebalancing Alpha 103
7.1 REBALANCING ALPHA OF TWO-ASSET PORTFOLIOS 103
7.1.1 Pairwise t-Statistics 103
7.1.2 Probability of Positive Rebalancing Alpha 106
7.1.3 Expected Value and Standard Deviation of
Rebalancing Alpha 110
7.1.4 Distribution of Rebalancing Alpha 112
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7.2 REBALANCING ALPHA OF GENERAL PORTFOLIOS 116
7.2.1 Pairwise Decomposition of Rebalancing Alpha 116
7.2.2 An Alternative Decomposition of Rebalancing Alpha 118
7.2.3 Expectation of Portfolio Rebalancing Alpha 118
7.2.4 Rebalancing Alpha-S&P 500 Sector Portfolios 119
7.2.5 Cross-Sectional Serial Correlations of Sector
Portfolios 125
7.2.6 Rebalancing Alpha of Varying Horizons 127
PROBLEMS 130
Chapter 8 Asset Allocation Portfolios 131
8.1 TRADITIONAL 60/40 PORTFOLIOS 131
8.2 RISK PARITY PORTFOLIOS 138
8.2.1 Risk Parity Portfolio without Leverage 138
8.2.2 Risk Parity Portfolio with Leverage 142
Chapter 9 Asset Class Portfolios 147
9.1 STOCK PORTFOLIOS 147
9.2 BOND PORTFOLIOS 156
9.3 COMMODITY PORTFOLIOS 164
Chapter 10 Rebalancing Alpha and Mean Reversion 173
10.1 TWO-ASSET TWO-PERIOD CASE 173
10.2 MULTIPLE-ASSET TWO-PERIOD CASE 176
10.3 TWO-ASSET THREE-PERIOD CASE 177
10.4 MULTIPLE-ASSET THREE-PERIOD CASE 182
10.5 THE GENERAL CASE 183
10.6 INCOMPLETE REBALANCE 187
PROBLEMS 191
Chapter 11 Risk and Return of Rebalancing Effects 193
11.1 TERMINAL WEALTH 193
11.2 EXPECTED TERMINAL WEALTH 195
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11.2.1 Equal Expected Returns 196
11.2.2 General Case 196
11.3 VARIANCE OF TERMINAL WEALTH 198
11.4 COMPARISON OF TWO VARIANCES 201
11.5 A GENERAL TWO-ASSET CASE 209
11.6 THE IMPACT OF SERIAL CORRELATIONS 212
11.7 TERMINAL WEALTH OF LONG-SHORT PORTFOLIOS 218
APPENDIX 11.A RISK-ADJUSTED WEALTH OF TWO-ASSET
LONG-ONLY PORTFOLIOS 225
APPENDIX 11.B EXPECTED TERMINAL WEALTH AND
VARIANCE WITH SERIAL CORRELATIONS 226
PROBLEMS 231
Chapter 12 Threshold Rebalancing 233
12.1 RETURN DISPERSION OR WEIGHT DISPERSION
AS A THRESHOLD 234
12.2 NUMERICAL SIMULATION OF THRESHOLD
REBALANCING 235
BIBLIOGRAPHY, 243
INDEX, 245
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