- Email: [email protected]
The econometric analysis of time series
92
Rook R~vtews
for several multinational firms. He presents his experiences in this little book, which must be of interest to both those who are working on cash management models and those who have an interest in international financial management. Soenen's book concerns the optimal hedging of international capital transactions. This means to determine the optimal amount of future exchange contracts ('forward cover') that should be signed on a certain date in advance. He forms a portfolio model where the total variance of currency exposure can be minimized subject to a given level of the expected value of the currency transactions (Chapter II). With that as a reference point he analyses the problems of measuring exposure (Chapter III), of predicting exchange rates (Chapter IV) and of determining the costs of hedging (Chapter V) and the costs of taxation (Chapter VI). The final portfolio model (Chapter VII) is one of quadratic programming. One of the most interesting chapters concerns the potential application of the model seen in view of the current practice of exposure management (Chapters VIII and IX). Finally Soenen presents his conclusions (Chapter X). The classical approach to international cash management is to assume the use of two objectives - - o n e concerns maximizing the expected value of the outcome and the other the minimization of risk in terms of the variance. There has been a long line of reports about how to make the best trade-off between them. Soenen's model (pp. 58-67) allows for different alternative ways by iteratively minimizing the quadratic function of the variance subject to different levels of the expected value for the outcome. In addition to this he requires linear constraints on each hedging alternative as well as on the total amount of exposure that can be hedged. The model is applied to a U.S. multinational firm called the "Exa" Company. Over a quarter of a year as a single planning period capital will be exposed in sixteen currencies. This means a quadratic programming model with the size of fortyfive variables (exchanges between fifteen currencies and the U.S. dollar X three alternative methods of hedging) and sixty-one constraints. He solves this model by using an algorithm devised by Prof. J. Bishop of the Harvard Business School. Then he finds out that the variance of the company's foreign exchange portfolio can be substan-
tially reduced at a very low cost. This also means that hedging should be used much more extensively than now. I like this book. I have some critical comments on it but they are not too serious. For example, the model is limited to 'bilateral' transactions between foreign currencies and the 'home currency'. If multi-lateral hedging is introduced (i.e. from pounds to francs) the model will expand rapidly in size and the quadratic programming might become rather expensive. And there are reasons to believe that one must use such a currency-to-currency hedging, as in many countries currency exchanges are restricted to situations where there is a trade of commodities or services. Another critical comment is that very few companies will be able to estimate variances and covariances for future exchange rates even if they are as close as three months from now. In those cases the quadratic programming model will be of little help. I have not found any important printing errors in this book. However, I miss the use of brackets in some mathematical formulations (see pages 10 and 44). I also miss the definition of K (on page 67). This book presents the use of portfolio models on international financial transactions. Personally I like its financial sections more than those of mathematical modelling. I think that the field research on the current practice (Chapter VIII) as well as the practical implementation of the model (Chapter IX) are just excellent. I strongly recommend this book to management scientists working in firms which have international flow of capital.
Grran BERGENDAHL University of Gothenburg Gothenburg, Sweden Andrew C. HARVEY
The Econometric Analysis of Time Series Philip Allan, Oxford, 1981, xi + 384 pages, £17.50 The book gives a comprehensive introduction to econometric model building. It is intended for readers (students) who already are familiar with mathematical and statistical topics, such as matrix algebra, calculus and statistical inference. How-
93
Book Reviews
ever, the author does pay attention to some advanced topics usually not covered by low or medium level statistical courses (for instance asymptotic theory and the Cramer-Rao inequality). The contents of the book are arranged as follows Preface !. Introduction 2. Regression 3. The Method of Maximum Likelihood 4. Numerical Optimisation 5. Test Procedures and Model Selection 6. Regression Models with Serially Correlated Disturbances 7. Dynamic Models I 8. Dynamic Models II: Stochastic Difference Equations 9. Simultaneous Equation Models Appendix on Matrix algebra (Differentiation and Kronecker Products), Tables, Answers to Selected Exercises, References, Subject Index
p. p. p. p. p.
1 36 82 119 144
p. 189 p. 221 p. 262 p. 309
discussed. The interesting question of model selection is discussed extensively. Attention is paid to the consequences of misspecification (i.e. adopting the wrong model) and to tests of specification and misspecification (Wald, LM and LR procedures). Also, a strategy for model selection is presented. Furthermore, it is worth stressing that a very good chapter dealing with Numerical Optimisation has been included. The material presented about this subject will give the reader a good insight in several optimisation procedures and their shortcomings. Among others, the Gauss-Newton and the Newton-Raphson procedure, the Method of Scoring and Two-step estimators are explained. Concluding, I can recommend this book warmly to everyone who is interested in statistical (and computational) aspects of econometric models. Cornelis BONGEBS Erasmus University Rotterdam, Netherlands
Each chapter contains about 8 exercises; answers to selected exercises have been included.
I consider the book to be a valuable contribution to econometric literature. However, a few critical remarks have to be made. First, the book (inevitably) contains some printing errors (e.g. in (2-6) on p. 127). Second, the author does not discuss Partial and Part Correlation. A good treatment of this subject usually deepens insight in the regression problem considerably. Two other critical remarks are related to the fact that the book is intended to be used by students. The first is that the author has been extremely thrifty with chapterindices; these are contained neither in formula numbers nor in page titles. As a result tracing back a formula in another chapter than the one that is being studied becomes a cumbersome process. Second, in view of the rather large number of abbreviations used (i.e. BLUE, SURE, MAD, NID, etc.), it is a pity that these are neither listed in an appendix (with a reference to the relevant chapter) nor mentioned in the index. Apart from these minor blemishes, the book is certainly worth reading or studying. It is well written, up to date and most topics are self containing. What I particularly like is the attention the author pays to a practical question such as "What constitutes a good model". Related to this question five criteria a model should satisfy are
M.M~',,GUPTA, R.K. RAGADE and R.R. YAGER (Eds.)
Advances in Fuzzy Set Theory and Applications North-Holland, Amsterdam, 1979, xvi + 754 pages, Dfl. 150.00 This book is a follow up on the first volume in this series published by North-Holland in 1977. It consists of 36 papers written by 49 authors from 11 different countries. The book gives a fairly true indication of the rapid and far-reaching advances in Fuzzy Set Theory and its numerous applications over the past few years. From a purely mathematical point of view this theory has advanced both in terms of formal rigour and in its application to new topics, e.g., fuzzy numbers, fuzzy statistics, possibilities, fuzzy mathematical programming, etc. its scope has been widened and at the same time axiomatic advances have been made. As far as its applications are concerned, fuzzy mathematics has moved into a range of subjects as varied as engineering, medicine, linguistics, the social sciences, etc. In his foreword, Peter N. Nikiforuk most appropriately summarizes this simultaneous move-
Rook R~vtews
for several multinational firms. He presents his experiences in this little book, which must be of interest to both those who are working on cash management models and those who have an interest in international financial management. Soenen's book concerns the optimal hedging of international capital transactions. This means to determine the optimal amount of future exchange contracts ('forward cover') that should be signed on a certain date in advance. He forms a portfolio model where the total variance of currency exposure can be minimized subject to a given level of the expected value of the currency transactions (Chapter II). With that as a reference point he analyses the problems of measuring exposure (Chapter III), of predicting exchange rates (Chapter IV) and of determining the costs of hedging (Chapter V) and the costs of taxation (Chapter VI). The final portfolio model (Chapter VII) is one of quadratic programming. One of the most interesting chapters concerns the potential application of the model seen in view of the current practice of exposure management (Chapters VIII and IX). Finally Soenen presents his conclusions (Chapter X). The classical approach to international cash management is to assume the use of two objectives - - o n e concerns maximizing the expected value of the outcome and the other the minimization of risk in terms of the variance. There has been a long line of reports about how to make the best trade-off between them. Soenen's model (pp. 58-67) allows for different alternative ways by iteratively minimizing the quadratic function of the variance subject to different levels of the expected value for the outcome. In addition to this he requires linear constraints on each hedging alternative as well as on the total amount of exposure that can be hedged. The model is applied to a U.S. multinational firm called the "Exa" Company. Over a quarter of a year as a single planning period capital will be exposed in sixteen currencies. This means a quadratic programming model with the size of fortyfive variables (exchanges between fifteen currencies and the U.S. dollar X three alternative methods of hedging) and sixty-one constraints. He solves this model by using an algorithm devised by Prof. J. Bishop of the Harvard Business School. Then he finds out that the variance of the company's foreign exchange portfolio can be substan-
tially reduced at a very low cost. This also means that hedging should be used much more extensively than now. I like this book. I have some critical comments on it but they are not too serious. For example, the model is limited to 'bilateral' transactions between foreign currencies and the 'home currency'. If multi-lateral hedging is introduced (i.e. from pounds to francs) the model will expand rapidly in size and the quadratic programming might become rather expensive. And there are reasons to believe that one must use such a currency-to-currency hedging, as in many countries currency exchanges are restricted to situations where there is a trade of commodities or services. Another critical comment is that very few companies will be able to estimate variances and covariances for future exchange rates even if they are as close as three months from now. In those cases the quadratic programming model will be of little help. I have not found any important printing errors in this book. However, I miss the use of brackets in some mathematical formulations (see pages 10 and 44). I also miss the definition of K (on page 67). This book presents the use of portfolio models on international financial transactions. Personally I like its financial sections more than those of mathematical modelling. I think that the field research on the current practice (Chapter VIII) as well as the practical implementation of the model (Chapter IX) are just excellent. I strongly recommend this book to management scientists working in firms which have international flow of capital.
Grran BERGENDAHL University of Gothenburg Gothenburg, Sweden Andrew C. HARVEY
The Econometric Analysis of Time Series Philip Allan, Oxford, 1981, xi + 384 pages, £17.50 The book gives a comprehensive introduction to econometric model building. It is intended for readers (students) who already are familiar with mathematical and statistical topics, such as matrix algebra, calculus and statistical inference. How-
93
Book Reviews
ever, the author does pay attention to some advanced topics usually not covered by low or medium level statistical courses (for instance asymptotic theory and the Cramer-Rao inequality). The contents of the book are arranged as follows Preface !. Introduction 2. Regression 3. The Method of Maximum Likelihood 4. Numerical Optimisation 5. Test Procedures and Model Selection 6. Regression Models with Serially Correlated Disturbances 7. Dynamic Models I 8. Dynamic Models II: Stochastic Difference Equations 9. Simultaneous Equation Models Appendix on Matrix algebra (Differentiation and Kronecker Products), Tables, Answers to Selected Exercises, References, Subject Index
p. p. p. p. p.
1 36 82 119 144
p. 189 p. 221 p. 262 p. 309
discussed. The interesting question of model selection is discussed extensively. Attention is paid to the consequences of misspecification (i.e. adopting the wrong model) and to tests of specification and misspecification (Wald, LM and LR procedures). Also, a strategy for model selection is presented. Furthermore, it is worth stressing that a very good chapter dealing with Numerical Optimisation has been included. The material presented about this subject will give the reader a good insight in several optimisation procedures and their shortcomings. Among others, the Gauss-Newton and the Newton-Raphson procedure, the Method of Scoring and Two-step estimators are explained. Concluding, I can recommend this book warmly to everyone who is interested in statistical (and computational) aspects of econometric models. Cornelis BONGEBS Erasmus University Rotterdam, Netherlands
Each chapter contains about 8 exercises; answers to selected exercises have been included.
I consider the book to be a valuable contribution to econometric literature. However, a few critical remarks have to be made. First, the book (inevitably) contains some printing errors (e.g. in (2-6) on p. 127). Second, the author does not discuss Partial and Part Correlation. A good treatment of this subject usually deepens insight in the regression problem considerably. Two other critical remarks are related to the fact that the book is intended to be used by students. The first is that the author has been extremely thrifty with chapterindices; these are contained neither in formula numbers nor in page titles. As a result tracing back a formula in another chapter than the one that is being studied becomes a cumbersome process. Second, in view of the rather large number of abbreviations used (i.e. BLUE, SURE, MAD, NID, etc.), it is a pity that these are neither listed in an appendix (with a reference to the relevant chapter) nor mentioned in the index. Apart from these minor blemishes, the book is certainly worth reading or studying. It is well written, up to date and most topics are self containing. What I particularly like is the attention the author pays to a practical question such as "What constitutes a good model". Related to this question five criteria a model should satisfy are
M.M~',,GUPTA, R.K. RAGADE and R.R. YAGER (Eds.)
Advances in Fuzzy Set Theory and Applications North-Holland, Amsterdam, 1979, xvi + 754 pages, Dfl. 150.00 This book is a follow up on the first volume in this series published by North-Holland in 1977. It consists of 36 papers written by 49 authors from 11 different countries. The book gives a fairly true indication of the rapid and far-reaching advances in Fuzzy Set Theory and its numerous applications over the past few years. From a purely mathematical point of view this theory has advanced both in terms of formal rigour and in its application to new topics, e.g., fuzzy numbers, fuzzy statistics, possibilities, fuzzy mathematical programming, etc. its scope has been widened and at the same time axiomatic advances have been made. As far as its applications are concerned, fuzzy mathematics has moved into a range of subjects as varied as engineering, medicine, linguistics, the social sciences, etc. In his foreword, Peter N. Nikiforuk most appropriately summarizes this simultaneous move-