**Portfolio Tilting: Hunt For Positive Alpha Through Style Tilts**

__Muhammad Wajid Raza __

Shaheed Benazir Bhutto University

__Hassan Mohammad Mohsin __

Quaid-i-Azam University – Pakistan Institute of Development Economics (PIDE)

April 11, 2016

*Raza, M. W., & MOHSIN, H. M. (2015). Portfolio Tilting: Hunt For Positive Alpha Through Style Tilts. VFAST Transactions on Education and Social Sciences, 6(2).*

**Abstract: **

A long discussion in literature exist to answer the question how a fund manager can generate extra returns? In order to answer the question this study is concerned with two aspects of this problem. First it discusses the portfolio construction process from separation theorem to modern style tilts. And in second step it provides imperial evidence for superior performance of style tilts. First of all active and passive style of management are compared. Data on returns is taken from KSE for five years and two sets of style based portfolios are constructed. Strong evidence is found in favor of active style of management. Actively managed funds are used as proxy for tilted portfolios. Data of Net asset value is taken from MUFAP. Tilted portfolios are tested for Size and value tilts. This study confirms higher performance of portfolio with style tilts.

### Portfolio Tilting: Hunt For Positive Alpha Through Style Tilts – Introduction

Studies conducted by Basu [1983], keim [1983] and Fama & French [1992] have shown that stocks with smaller size “market capitalization” and high B/M value have generated higher returns for investors. Similar results can be observed for stocks selling at low multiples of their sales. The superior performance of value stocks and small cap stocks has provided new direction for portfolio tilting. This study is concerned with two aspect of this issue. First at discusses the portfolio construction process from separation theorem to modern style tilts. And in second step it provides empirical evidence for superior performance of style tilts.

### Journey from separation theorem to style tilts

It is very difficult to allocate proper assets mix when the investors have multiple options for investment. In earlier ages investors were limited to investment decisions that pertain to a specific security only. Concept of diversificat ion with statistical measures by Markowitz [1952, 1959] opens a new era in portfolio theory. In contrast to single asset he introduce concept of large numbers. With large number in mind best available tilting option was to tilt the portfolio to maximum possible securities. Most prominent drawback of portfolio tilting based on large number is that it ignores risk factors associated with each security. Moreover, the underlying assumption of his work mean variance efficiency is of importance only if returns from securities are uncorrelated. Otherwise manager must tilt his portfolio to stocks with minimum correlation. Another problem arises when managers have to deal with multiple time period data. In order to address the issue researchers address the problem with different set of assumptions Fama [1970], Hakansson [1970, 1974] and Merton [1990]. These studies found that, portfolios that are constructed on the basis of mult i period data are significantly different from single period portfolios. The difference arises because of the utility function “time series data”.

Another important aspect of portfolio theory is the separation theorem. That is, if an investor has access to riskless asset, he will tilt his portfolio to mix of risky assets and risk free assets. The separation theorem thus proposed has three implications. First of all it provides ease in calculation. Problem faced by portfolio manager has been solved by constructing a portfolio with combination of riskless assets and expected standard deviation spread. The two set of securities are joined by a tangent line from riskless asset. This tilting strategy can maximize the ratio of expected future returns with somewhat unknown probability minus the return on the difference of riskless assets and return on assets with defined standard deviation.

Another important implication is the mutual fund theorem. It this particular time period, an important question was raised by Rose [1978]. The basic assumption of constant lending and borrowing risk free rate was very crucial. It is not always available to each and every individual. If we relax this assumption the tilting decision toward mutual fund theorem lose it significance up to 30% [Fama & French, 2004]. For now let us discuss with a simple example. Keeping our discussion limited to Markowitz efficient frontier, if there is different lending and borrowing rate for riskless assets then four mutual funds must be created. Thus investor will create his portfolio by tilting his decision toward two funds of risk free assets and two funds of risky assets that lies on efficient frontier. Third implication of separation theorem is it helps in explaining the estimation of the inputs that needs to be included in a portfolio.

Another point of concern is the calculation of correlation matrix. Moreover estimation of efficient portfolios through quadratic equation programming and difficulty of educating portfolio managers to calculate risk and return tradeoffs as well as the relation of covariance matrix to returns and standard deviation makes the theory more complex.

Most important of these areas is the first one that is the computational efficiency. That is to provide such inputs that can maximize the overall returns of portfolio. If portfolio manager solve this problem they will be able to overcome the next two problems in the long run Elton [1976]. In order to solve the problem of efficient inputs calculation of covariance matrix was required. The principal technique develop to solve the covariance problem was index models. Single and multiple index models were developed with the passage of time. The first and simplest single index model was first discussed by Markowitz [1952] and was developed by Sharpe [1967]. This model was based on single index that is why called market index.

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