Portfolio Optimization With or Without Safe Assets? An idea…
Portfolio optimization is one of the most common and essential techniques in measuring the plausibility of the designated combinations of the assets. Optimal portfolios are well diversified to decrease the non-price risk and the unsystematic risk of the assets, which maximizes the returns of the stocks and protects the investors from the underperformance of certain assets.
There is a long history of investing when the Code of Hammurabi in 1700 BC provided an official structure for investing: “an approach for the pledge of collateral by codifying debtor and creditor rights regarding pledge land”. Such behavior can be viewed as a tradeoff between “immediate consumption” and “deferred consumption”, where investors compared the instantaneous benefits of consuming today against the future payoffs of the equity they invested into [1]. In recent decades, as the exchanges and acquisition of information has never been easier, people have engaged in investment behavior more frequently, and to maximize their utility in investment, they would choose assets with the optimal balance between returns and risks: they are trying to find the investment that brought them huge returns and moderate risks.
As Somerville states in his paper, risk aversion is a vital factor in financial investment, which depicts a trade off between risk and return in financial activities [2]. In light of this, the focus of this paper is about portfolio optimization in investing behavior; that is, by using empirical studying and incorporating historical data, the researchers will be able to generate an optimal portfolio for the rational investors.
During the recent decades, research about optimal returns and portfolio optimization is abundant, but most of them are focused on single-type asset; for example, La Porta investigated the expectations and cross-sections of stock returns, or Leim Chin analyzed the portfolio optimization of specific types of stocks returns with the reference of index LQ45[3][4]. Other paper, on the other hand, focused on applying multifactor model in the real life situation; for example, Fama and French discussed the anomalies of multifactorial models in empirical data for their three-factor and five-factor models in investing, and Griffin demonstrated the difference between country-specific and global versions of FF3F model through time series analysis[5][6]. Shedding lights on the optimization problem not only on specific types of stocks or just the model itself, but in a broader context such as a combination of various asset types might bring new innovations to the research of this field. The importance of the study can be articulated in various aspects.
Firstly, portfolio optimization provides a rather comprehensive and accurate measure of the returns of the stocks and risks, which benefits those investors who would like to maximize risk and returns trade-off. The optimization process uses ordinary least squares regression (OLS) and multiple factors to precisely predict the expected returns for the portfolio; thus, the investing managers can combine risky assets with a risk-free asset to discover balance between those two factors [7].
Secondly, although there are papers focusing on portfolio optimization, there are few papers concentrating on diversified assets using mutual funds, ETF and stocks. By incorporating different types of assets into the portfolio, one can manage the risk by diversifying the types of assets and lower the correlations between different sorts of equities.
The process of conducting this study can be summarized as follows. First, the researcher gathers the data of five distinct ETFs, mutual funds and stocks from Yahoo Finance from January 1, 2017, to January l 1, 2022; Second, by applying the correlation function, the researcher is able to see the relationship between different assets and adjust the data set if one sees a very high correlation coefficient.
Thirdly, as the Fama-French three factor (FF3F) coefficients are added into the model. One can then calculate the betas and expected returns for different assets.
Fourthly, using expectation-variance analysis, the conductor can optimize the Sharpe ratio for the portfolio using the Solver function. Fifth, comparing the Sharpe ratio for different portfolios can help generate an optimal portfolio under some constraints. The betas of the stocks are generated via ordinary least squares regression (OLS), and the optimal Sharpe ratio’s portfolio using the OLS data will help the researcher to generate more accurate results.
