Asset Allocation, Security Selection And Market Timing in Mutual Funds Master Thesis in Economic Analysis (ECO) Bjarte Espedal Advisor: Knut Kristian Aase NORGES HANDELSHØYSKOLE Bergen, spring 2011 This thesis was written as a part of the Master of Science in Economics and Business Administration at NHH. Neither the institution, the advisor, nor the sensors are - through the approval of this thesis - responsible for neither the theories and methods used, nor results and conclusions drawn in this work. ii I. PREFACE As the title indicates, this thesis is about asset allocation, security selection and market timing in mutual funds. This is a topic that should be of interest for most people that let mutual funds handle their personal wealth or pension liabilities. Natural questions to ask in this matter are “What asset classes is my wealth/pension exposed to?” and “How is the performance of my manager?” This thesis will enable investors to answer such questions, and more. When I was on exchange at Johnson School at Cornell University, I was introduced to these exciting topics in a course called “Investments” taught by Professor G. Saar. During this course I was also introduced to many interesting academic papers. Among these, were two papers which have an important part in this thesis; namely “Asset Allocation: Management Style and Performance Measurement” by Nobel laureate W. Sharpe (1992) and “Determinants of Portfolio Performance” by Brinson, Hood, and Beebower (1986). Both these papers combine mathematics and econometrics into elegant and pedagogical models. Basically, this thesis combines the insight from these papers to answer a set of questions that are relevant for people investing in mutual funds. The process of writing this thesis has been interesting and challenging at the same time. I have had the possibility to be both creative and to use accumulated knowledge. Most importantly, the process of writing this thesis has enabled me to learn much more about topics that I find very interesting. Having taken courses such as “Financial Theory”, “Econometric Techniques”, “Times Series Analysis and Prediction” and “Empirical Analysis of Financial and Commodity Markets” has been vital in order to write this thesis. II. ACKNOWLEDGEMENT I would like to thank my advisor Knut K. Aase for the helpful discussions I had with him, and all his comments. I am grateful to Petter Slyngstadli in Holberg Forvaltning for giving me updated Norwegian mutual fund data. I am also thankful to Andreas Steiner, whom made the MATLAB code for Return Based Style Analysis available through the MATLAB Central. My lecturer in “Time Series Analysis and Prediction”, Jonas Anderson, has also been helpful when I have had questions. Lastly, I am grateful for all the encouragement and help from family and friends. Bjarte Espedal Bergen, June 2011 iii III. ABSTRACT CHAPTER 1: Estimating Determinants of a Mutual Fund’s Risk and Managerial Performance In this chapter, we construct a framework that can be used by investors to independently estimate a mutual fund’s actual and policy weights in a set of predefined asset classes, and to estimate a mutual fund’s security selection and market timing. Our framework has its foundation in a paper by Brinson, Hood and Beebower (1986). By generalizing the ideas in their paper, we see that we can measure a fund’s security selection and market timing only if we have the actual and policy weights. We argue that weights that reflect the fund’s short- term and long-term behavior are good estimates of a fund’s actual and policy weights respectively. In this matter, we can get estimates of the actual and policy weights by using Return Based Style Analysis (Sharp, 1992) in two steps. These estimates can in turn be used to estimate the fund’s security selection and market timing. CHAPTER 2: An Empirical Study of Norwegian Mutual Fund Managers In this chapter, we use the framework developed in chapter 1 to answer 3 important questions related to Norwegian mutual fund managers: 1) How much of the total variation in mutual fund return is explained by asset allocation, security selection and market timing respectively? 2) Is the average managerial performance positive? 3) Ceteris paribus, does a change in a mutual fund’s management cause a change in managerial performance? We find that a fund’s respective asset allocation, security selection and market timing explain 90.6%, 4.5% and 4.9% of the variation over time. Moreover, we find that the mutual funds are good in picking stocks, but loose by timing the market. In sum, the managerial performance is not significantly different from 0. We also find that when poor performing managers are replaced, excess return increases significantly. The opposite result holds when the very best managers are replaced. JEL Classification: C32; C61; G20; G23 Keywords: Asset Allocation; Security Selection; Market Timing; Return Based Style Analysis iv TABLE OF CONTENT: INTRODUCTION ................................................................................................................................. 1 CHAPTER 1: Estimating Determinants of a Mutual Fund’s Risk and Managerial Performance ......... 7 1.1. Introduction ................................................................................................................................. 7 1.2. Determinants of Mutual Fund Performance ................................................................................ 9 1.3. The Asset Classes Constituting our Benchmark........................................................................ 17 1.3.1. Style Investing ....................................................................................................................... 17 1.3.2. Asset Classes for Norwegian Mutual Funds ......................................................................... 20 1.3.3. Section Summary .................................................................................................................. 22 1.4. Estimating a Mutual Fund’s Weights using Return Based Style Analysis ................................ 23 1.4.1. Multifactor-Models ............................................................................................................... 23 1.4.2. From Linear Regression to Quadratic Programming ............................................................ 26 1.4.3. Return Based Style Analysis ................................................................................................. 28 1.4.4. The Duck Theorem ................................................................................................................ 32 1.4.5. Evaluating the Asset Classes ................................................................................................. 34 1.4.6. An Investor’s Effective Asset Mix ........................................................................................ 34 1.4.7. Approximating the Confidence Intervals for the Style-Weights ........................................... 35 1.4.8. Section Summary .................................................................................................................. 37 1.5. Combining Style-Analysis and the BHB-framework ................................................................ 38 1.5.1. A Two-Step Approach using RBSA ...................................................................................... 38 1.5.2. Finding the Optimal Time Length for Describing a Mutual Fund’s Short-Term Movements ………………………………………………………………………………………………41 1.5.3. Section Summary .................................................................................................................. 42 1.6. Estimating Determinants of Risk and Managerial Performance using Norwegian Mutual-Fund Data ........................................................................................................................................... 43 1.6.1. Mutual Fund Data .................................................................................................................. 43 1.6.2. Finding for Norwegian Mutual Funds ............................................................................... 43 1.6.3. Estimating a Mutual Fund’s Determinants Risk ................................................................... 46 1.6.4. Estimating a Mutual Fund’s Determinants of Managerial Performance ............................... 51 1.6.5. Section Summary .................................................................................................................. 56 1.7. Weaknesses in Framework and Future Research ...................................................................... 57 1.8. Conclusion ................................................................................................................................. 58 CHAPTER 2: An Empirical Study of Norwegian Mutual Fund Managers ......................................... 61 2.1. Introduction ............................................................................................................................... 61 2.1.1. Problem Statement 1: ............................................................................................................ 61 v 2.1.2. Problem Statement 2 ............................................................................................................. 63 2.1.3. Problem Statement 3 ............................................................................................................. 63 2.1.4. Disposal ................................................................................................................................. 65 2.2. Methodology and Data .............................................................................................................. 66 2.2.1. Methodology and Data in Problem Statement 1 .................................................................... 67 2.2.2. Methodology and Data in Problem Statement 2 .................................................................... 68 2.2.3. Methodology and Data in Problem Statement 3 .................................................................... 69 2.3. Results and Analysis ................................................................................................................. 73 2.3.1. Problem Statement 1 ............................................................................................................. 73 2.3.2. Problem Statement 2 ............................................................................................................. 74 2.3.3. Problem Statement 3 ............................................................................................................. 75 2.4. Weaknesses of Study ................................................................................................................. 82 2.4.1. Sample Size ........................................................................................................................... 82 2.4.2. Survivorship Bias .................................................................................................................. 82 2.5. Conclusion ................................................................................................................................. 83 2.5.1. Problem statement 1: ............................................................................................................. 83 2.5.2. Problem statement 2: ............................................................................................................. 83 2.5.3. Problem statement 3: ............................................................................................................. 83 2.5.4. Implication of Results – and Lessons to be drawn ................................................................ 84 APPENDIX .......................................................................................................................................... 85 3.1. APPENDIX A: Definitions ....................................................................................................... 85 3.2. APPENDIX B: Testing for Unit-Root ....................................................................................... 87 3.3. APPENDIX C: Confidence Interval of Style-Weights .............................................................. 89 3.4. APPENDIX D: Current Mutual Funds ...................................................................................... 92 3.5. APPENDIX E: Testing for Unit-Root ....................................................................................... 93 3.6. APPENDIX F: Mutual funds in Problem Statement 2 .............................................................. 94 3.7. APPENDIX G: Mutual funds in Problem Statement 3 ............................................................. 95 3.8. APPENDIX H: Average return ................................................................................................. 95 REFERENCES .................................................................................................................................... 96 4.1. Academic Papers ....................................................................................................................... 96 4.2. Academic Papers without Direct References ............................................................................ 98 4.3. Books ......................................................................................................................................... 98 4.4. Data Sources .............................................................................................................................. 99 4.5. Internet....................................................................................................................................... 99 4.6. Other Sources .......................................................................................................................... 100 vi “Next, where the Sirens dwells, you plough the seas; Their song is death, and makes destruction please. Unblest the man, whom music wins to stay Nigh the cursed shore and listen to the lay. No more that wretch shall view the joys of life His blooming offspring, or his beauteous wife! In verdant meads they sport; and wide around Lie human bones that whiten all the ground: The ground polluted floats with human gore, And human carnage taints the dreadful shore Fly swift the dangerous coast: let every ear Be stopp‟d against the song! „tis death to hear! Firm to the mast with chains thyself be bound, Nor trust thy virtue to the enchanting sound. If, mad with transport, freedom thou demand, Be every fetter strain‟d, and added band to band.” The Odyssey XII, by Homer INTRODUCTION Asset allocation, Security Selection and Market Timing in Mutual Funds In the epic poem Odyssey, Homer writes that Odysseus wanted to reassert his place as the rightful king of Ithaca. In this matter, he had to sail the perilous route from Circe’s Island to Ithaca. Equivalently, mutual funds and their managers have to guide themselves through a sea of risky investments in order to reach their goals of becoming the kings of the financial industry. Circe advised Odysseus to sail a specific route in order to get to Ithaca. Hence, Odysseus had a pre-defined route with some expected dangers, much like mutual funds have a pre-defined asset allocation with a given level of expected risk. Asset allocation refers to the long-term decision regarding the proportions of total assets that an investor chooses to place in particular classes of investments (Swensen, 2005). We call these long-term proportions policy weights. These weights are often based on an underlying investment philosophy, which is a coherent way of thinking about how financial markets work. New information and events happening along the pre-defined route made it tempting for Odysseys to deviate from Circe’s advice. One such situation occurred when Odysseys had to pass the Sirens. The sirens were creatures that sung so beautiful that sailors were lured to sail into a deathly shore. Odysseus was curious as to what the Sirens sounded like. Therefore, on 1 Circe’s advice, he had all his sailors plug their ears with beeswax and tie him to the mast. He ordered his men to leave him tied to the mast no matter how much he would beg them to untie him. When Odysseus heard the sirens’ beautiful song, he ordered the sailors to untie him, but they bound him just tighter. When the ship had passed the Sirens out of earshot, Odysseus signalized with his frowns to be released. Although Odysseus found it tempting to deviate from his pre-defined route as he passed the Sirens, this would have ended his journey. Hence, he well in listening to Circe’s advice and stick to the pre-defined route. Just as Odysseus had the possibility to deviate from his pre-defined route, your mutual fund manager can choose to deviate from the policy weights by strategic under- or overweighting the asset classes. We call this market timing. Market timers hope to underweight prospectively poorly performing asset classes and overweight prospectively strongly performing asset classes to enhance portfolio returns (Swensen, 2005). Due to market timing, the short-term risk will deviate from normal levels, and the short-term proportions placed in particular classes of investments will deviate from the policy weights. We call the mutual fund’s proportions placed in particular classes of investments in the beginning of the current period (hence short-term) for actual weights. These weights constitute the mutual fund’s current allocation. Economists have for long questioned what a mutual fund’s optimal portfolio choice should be. Mossin (1968), Merton (1969, 1971) and Samuelson (1969) (hereafter MMS) were first to find an answer. To exemplify MMS’ findings, say we have a mutual fund that wants to maximize its expected utility of assets under management (final wealth) with respect to its allocation between equity and bonds. MMS show that the multiperiod problem is degenerated into several one-period problems under the following assumptions (Aase, 2009): i) The returns of the asset classes are independently and identically distributed with jointly normally distributions (i.e., returns of equity and bonds have constant expectation and standard deviation) ii) The mutual fund has a additively separable constant relative risk-aversion (i.e., risk aversion is independent of the assets under management) iii) The mutual fund has no non-tradable assets (i.e., only investment income is considered) 2 iv) Financial markets (i.e., stock and bond market) are frictionless and complete1 Under these assumptions, the solution to the problem satisfying the assumptions can be shown to give a constant allocation between equity and bonds, which is independent of both investment horizon and the mutual fund’s assets under management. Presumably, this constant allocation is the same as the mutual fund’s policy weights for equity and bonds. This implies that when the stock market boosts, it is optimal to sell equity and buy bonds, whereas when the stock market falls, the fund should sell bonds and buy equity. This argument can be generalized to n asset classes, making it optimal to stick to the policy weights which are found by solving MMS’ problem. Of course, for practical purposes, mutual funds just pick some subjective policy weights that they feel are according to their desired level of risk. Based on the above arguments, the discretionary policy of market timing is not optimal. Just like Circe advised Odysseus to bind himself to the mast and stick to his pre-defined route, the economists advise mutual fund managers to stick to their predefined policy-weights. In effect, this is an argument for rules rather than discretion; mutual funds that do this have policy weights that are equal to their actual weights. Although economists have long advised investors not to time the market, buying equity in a bear market and selling equity in a bull market is contrary to human nature. Humans go in crowds and engage in counterproductive performance by buying yesterday’s winners and selling yesterday’s losers. Interestingly, the most frequent variant of market timing comes not in the form of explicit bets for or against asset classes, but in the form of a passive drift away from target allocations (Swensen, 2005). If investors fail to counter market moves by rebalancing their portfolio, the allocation inevitably moves away from the policy weights. A simple buy and hold portfolio is an example of a strategy that passively drifts away from the policy weights in the long run. Based on MMS’s arguments, we can expect that successful mutual funds are able to act in a contrarian way, and that they rebalance their portfolios as often as possible. However, if MMS’s assumptions are too strict, market timing might be valuable. For example, if a mutual 1 A complete market is a system of market in which every agent (here: mutual fund) is able to exchange every good (here: bonds and equity), either directly or indirectly, with every other agent (Flood, 1991) 3 fund finds that past returns of a specific asset class can be used to predict future returns, this is clearly something they should take advantage of by timing the market. By improving the sailing along the pre-defined route, Odysseus could get to Ithaca quicker. Equivalently in the capital markets, your mutual fund manager will try to pick the stocks that boost the mutual fund’s return. This tool is called security selection, and is the active selection of investments within an asset class (Brinson, Hood and Beebower, 1986). The amount of security selection that is generated by a mutual fund is dependent on the market’s efficiency. Roberts (1967) and Fama (1970) define three levels of market efficiency: weak form, semi- strong form, and strong form market efficiency. The weak form market efficiency claims that stock prices reflect all past public information and that it is not possible to earn positive security selection based on historical information. Semi-strong form market efficiency says that stock prices reflect all publicly available information. Hence, new public information will instantly be absorbed into the price. Strong form market efficiency claims that all public and private information are reflected in the stock price; this implies that inside information is baked into the price. Beating the market by security selection and not luck is dependent on information or skills. This implies that a market with successful active management cannot be efficient in the semi-strong form. A benchmark is the standard in which the mutual fund’s return is evaluated against. A passive mutual fund tries to track a given benchmark whereas an active mutual fund attempts to generate return in excess of the benchmark. Sharpe (1991) argues that over any specified time period, the market return must equal a weighted average of the return on the passive and active segments of the market. Since each passive manager obtains exactly the market return, before costs, it follows that the return on the average actively managed dollar must equal the market return. Since the cost of the actively managed dollar is larger than the passively managed dollar, it implies that after cost, the return on the average actively managed dollar will be less than the return on the average passively managed dollar. This can have two implications: 1) the average active return of mutual funds is negative after cost, or 2) active return is positive at the expense of investors outside the mutual funds. If mutual funds do indeed have skills or have information, they will be in the second category. 4