Luca Ghezzi

Financial Modelling and Management – Part II concerns the application of scientific tools to investment and funding activities that are also represented in terms of random cash flows. More precisely, it deals with some validated models and procedures that support decisions on the appraisal of companies; the management of portfolios according to the requirements in terms of liquidity, diversification, income/growth, risk/return. The presentation is both qualitative and quantitative. Emphasis is placed on data and procedures that are used or taken into consideration by financial advisors, financial analysts, and portfolio managers, e.g. of mutual or pension funds. Although coverage is neither exhaustive nor entirely up-to-date, it is rigorous; a broad set of useful and consistent notions is explained in the clearest possible form. Accordingly, students will learn which data to analyse and how to go about financial analysis and discretionary portfolio management, especially in connection with stocks, bonds, and exchange-traded funds. After outlining the stages and tasks of a portfolio management process, students will learn how to choose a strategic asset allocation in line with household age, goals, and risk tolerance; spot social, technical, economic/ecological, or political trends by following a top-down approach; look for mispriced stocks by relying on fundamental analysis, a bottom-up approach. As for equity research and value investing, students will focus on whether a listed company benefits from a sustainable competitive advantage and whether stock price and fundamental value are consistent. In doing so, Benjamin Graham’s, Philip Fisher’s, and Warren Buffett’s guidelines will be mentioned. A problem-oriented and hence multidisciplinary approach is adopted so that reference is made to the theoretical principles and practical notions of other related subjects such as business economics and applied statistics; due attention is paid to economic science, the main findings of selected empirical studies being summarised in the simplest possible form. Different anomalies and regularities of US financial markets are taken into consideration, as they lay the foundations for proficient portfolio management by both individual and institutional investors. In other words, stress is put on a business practice that is consistent with empirical evidence; the informational and fundamental efficiency of US financial markets is examined, with attendant neoclassical and behavioural interpretations being contrasted. As investment decisions are both rational and emotional, emphasis is placed on bounded rationality and cognitive biases leading to irrational exuberance and speculative bubbles. The author shares the belief with other Italian colleagues that a fruitful theory rests on a solid and practical basis, and vice versa. Accordingly, learning and retaining Financial Modelling and Management – Part II should be made easier by a twofold course of reading the theoretical one, concerned with analytical processes or statistical inquiries and their peculiarities; the operational one, focused on financial contracts, financial transactions, and business practice.

This study focuses on efficient asset allocations that properly include T-bills, T-bonds, and the S&P 500 stock index. It checks that their annual real rates of linear return are both normal and almost lognormal. It reexamines how efficient portfolios based on the rates of linear return may turn into efficient portfolios based on the rates of logarithmic return. It finds that each efficient asset allocation has the lowest possible standard deviation as well as the highest possible arithmetic and geometric means. It eventually reconsiders the relationship between the confidence interval of a geometric mean and an expected long-run capital accumulation. As a consequence, it bridges a gap in the scientific literature by enabling financial advisors to trade off the mean rate of return on a portfolio more rigorously against the value at risk.

This study makes use of a very long time series of the S&P Composite Index, checking once more that the rates of return benefit from aggregational normality. It performs unit root tests as well as elementary statistical tests that take advantage of normality. It finds that mean blur is not consistent with the hypothesis of random walk with constant parameters, because the means of the annual real rates of linear return can be estimated as usual. It gives further evidence that the rates of return on the S&P Composite Index are mean‐reverting.

This statistical study refines and updates Sharpe’s empirical paper (1975, Financial Analysts Journal) on switching between US common stocks and cash equivalents. According to the original conclusion, profitable market timing relies on a representative portfolio manager who can correctly forecast the next year at least 7 times out of 10. Four changes are made to the original setting. The new data set begins and ends with similar price-earnings ratios; a more accurate approximation of commissions is given; the rationality of assumptions is examined; a prospective and basic Monte Carlo analysis is carried out so as to consider the heterogeneous performance of a number of portfolio managers with the same forecasting accuracy. Although the first three changes improve retrospectively the odds of profitable market timing, the original conclusion is corroborated once more.

The stage of strategic asset allocation is the most important one in a process of portfolio management: asset classes are selected and target weights are set. Careful decision-making benefits from the computation of an efficient frontier. In this work, weights are nonnegative and rebalanced once a year; portfolio returns are time uncorrelated and lognormal. A novel sufficient condition is obtained, whereby efficient portfolios based on linear returns may turn into efficient portfolios based on logarithmic returns. If that is met, the efficient frontier based on logarithmic returns is upward sloping, stretching from a corner portfolio with global minimum-variance to a corner portfolio with global maximum-variance. Such a complementary efficient frontier allows a decision maker to forecast the long-term portfolio value. The null hypothesis of lognormal portfolio returns is also tested by using two different data sets. It is always rejected in the latter; it is either accepted or rejected in the former, depending on the specific efficient portfolio.

The stage of strategic asset allocationisthe most important one in a process of portfolio management. Asset classes are to be selected and percent target weights are to be set. Careful decision-making benefits from the computation of an efficient frontier. In this work, a single investment is considered with all coupons and dividends being reinvested. Percent weights are supposed to be nonnegative and subject to annual rebalancing. Portfolio returns are assumed to be time uncorrelated and lognormal. Linear quadratic optimization is complemented with a lognormal mapping, resulting in a rigorous procedure, where by efficient portfolios based on linear returns may turn into efficient portfolios based on logarithmic returns. Two data sets are used by way of illustration under the tentative yet usual assumption that forecast moments are the same as historical moments. The former data set includes the annual total returns of three US asset classes for the years 1872-2012. The latter includes the annual total returns offour equity or equity-like asset classes for the years 1972-2017. The efficient frontier based on logarithmic returns is upward sloping in both instances, stretching from a portfolio with global minimum-variance to a portfolio with global maximum-variance. Nonetheless, if short selling and hence negative weights were allowed, the efficient frontier based on logarithmic returns wouldn't be upward sloping in the latter instance. The null hypothesis of lognormal returns is tested. It is always rejected in the latter data set; it is either provisionally accepted or rejected in the former data set, depending on the specific efficient portfolio. An interpretation of the statistical evidence is provided.

In 1971 floating exchanged rates replaced fixed exchange rates, originally agreed upon in 1944 in Bretton Woods. Since then both financial modelling and financial management have undergone an unprecedented development, fed and facilitated by the liberalisation and globalisation of financial markets, the diffusion of information technologies, the progress made by financial information services. This electronic book is consistent with such a development. It allows a twofold course of reading: the theoretical one as well as the operational one. The former is about analytical processes or statistical enquiries, whereas the latter is about financial contracts, financial transaction, and business practice. The approach is rigorous yet both practical and multidisciplinary, reference being made to business economics, industrial economics, and financial economics.

An insightful problem of passive management is considered, where an aggregate portfolio is rebalanced annually to restore the percent weights of its strategic asset allocation. As its annual total returns are assumed to be time uncorrelated and lognormally distributed, multi-period optimization boils down to single period optimization. Expanding on previous theoretical results, it is shown how a minimum-variance set based on linear returns turns into a minimum-variance set based on logarithmic returns. More precisely, it is found that there can be two different qualitative patterns, one of which is unprecedented and striking. Both patterns are tentatively portrayed by using historical data. The resulting efficient frontier is readily complemented by a dynamic shortfall constraint. Each threshold return can be turned into a threshold accumulation that has the same shortfall probability; coeteris paribus, the more distant the time horizon, the smaller the shortfall probability. As our procedure is analytically tractable, it might be operationally useful, especially to financial advisors and individual investors.

An insightfulproblem of passive managementis considered, where an aggregate portfolio is rebalanced annually to restore the percent weights of its strategic asset allocation. Asits annual total returns are assumed to be time uncorrelatedand lognormally distributed, multi-period optimization boils down to single period optimization. Expanding on previous theoretical results, it is shown how a minimum-variance set based on linear returns turns into a minimum-variance set based on logarithmic returns. More precisely, inefficient portfolios based on linear returns cannot turn into efficient portfolios based on logarithmic returns, whereas efficient portfolios based on linear returns can also turn into inefficient portfolios based on logarithmic returns. In the latter instance, there can be two different qualitative patterns, both of which are portrayed by using historical data. Moreover, a dynamic shortfall constraint is introduced. Each threshold return can be turned into a threshold accumulation that has the same shortfall probability; coeteris paribus, the more distant the time horizon, the smaller the shortfall probability. As our procedure is analytically tractable, it might be operationally useful, especially to financial advisors and institutional investors.

A divergence-based procedure is applied to trading in the S&P 500 stock index. Such a procedure has previously and successfully been applied to trading in foreign currencies. Performance is tested against a benchmark, i.e. a passive portfolio replicating the S&P 500 stock index; its robustness is also checked in a few subperiods. According to our numerical evidence, higher annualised mean returns, i.e. higher final portfolio values, as well as lower annualised standard deviations can be obtained in all subperiods. However, basic Montecarlo tests are failed. The on-line extension of the present off-line implementation is taken into consideration, as it is more suited for an operational use.