Efficient Markets and the Sharpe Ratio Raleigh Deering John Granahan Professor Doremus Econ 464 Fall 2019 Deering & Granahan 2 1 Introduction: Investors are often faced with a choice: they can invest in the market benchmark, or they can select different investment vehicles or strategies. Investing in the market guarantees a relatively stable return over a long investing horizon, but investing with other strategies could open the possibility to outlier returns. These returns may be substantially higher or lower than the market return, and the claims about the upside potential may be an attractive alternative to the market. Over time, these underperforming investment vehicles could dramatically reduce the future value of an investor’s balance if they cannot outperform the market on a consistent basis. Furthermore, exchanges, brokers, and hedge funds directly benefit from people believing that they can beat the market through collecting fees. Therefore, our research question seeks to address the issue of whether a given asset class or option strategy can outperform the market on a risk-adjusted basis. In essence, this research question seeks to test the efficient market hypothesis, which posits that all stocks and options accurately reflect all information, making it impossible to outperform the market or achieve alpha. Alpha is defined as a financial performance metric that equates to a portfolio’s excess return over a market benchmark. If an asset class has a statistically significant alpha, investors could benefit by purchasing those funds. To test the efficient market hypothesis, we sought to test whether any popular asset class or option strategy has an alpha that is statistically significant from zero. Previous literature addresses the efficient market hypothesis, but no literature exists with respect to portfolio performance over the past 15 years for stocks, bonds, and option strategies. For example, one of the most commonly cited research papers on option strategies does not include data from the 2008 Financial Crisis and their paper concluded that option strategies can Deering & Granahan 3 outperform the market on a risk-adjusted basis. Therefore, our research intends to supplement existing literature with a 15 year time frame between 2004 to 2018 for equity, fixed income, commodity, and option returns. Although there are no public policy implications pertaining to this specific research question, there are still ethical concerns regarding active fund managers. If investors are aware of the data surrounding the efficient market hypothesis, they may be less willing to invest in various ETFs instead of the S&P 500. Over the past 15 years, throughout periods of bull and bear markets, our research indicates that asset classes have been unable to outperform the market on a risk-adjusted basis. The remainder of the paper will be structured between a review of existing academic literature, followed by a description of our methodology, relevant results from our data, and concluding remarks. 2 Full Literature Review: The main goal of financial economics is to be able to provide investors with a framework on how to make investment decisions. Markowitz (1952) founded what we now refer to as Modern Portfolio Theory (MPT) in his paper titled, “Portfolio Selection.” His theory stated that rational risk-averse investors will create portfolios that maximize expected return based on the level of market risk. Thus, in order to receive a higher rate of return, an investor must be exposed to more risk. Additionally, Markowitz’s theory concluded a portfolio of assets that has a higher rate of return for a given level of risk is more efficient or optimal. Several years later, Sharpe (1966) added on to the work of Markowitz and developed what is referred to as the Sharpe ratio. The Sharpe ratio can be calculated by taking the return of a given portfolio and subtracting the risk-free interest rate, then dividing that outcome by the standard deviation of the portfolio. Deering & Granahan 4 Annualized Sharpe ratios are standard for reporting purposes, and since references within our literature review report sharpe ratios on a yearly basis, we maintained consistency by analyzing the ratios along the same horizon. Therefore, maximizing the Sharpe ratio of a given portfolio will lead to more desirable outcomes for the investor. Since its introduction, the Sharpe ratio has been used as a benchmark to compare different asset returns along with the performance of active investment strategies. Additionally, Sharpe (1964) helped develop the Capital Asset Pricing Model, which does not allow for risk-adjusted returns over the market portfolio. In financial literature, the market portfolio has been largely defined as the S&P 500 because it captures the return of the top 500 U.S. publicly traded companies by market capitalization. Thus, the financial literature began to conclude that, under the assumptions of the model, rational investors will not be able to predictively beat the risk-adjusted returns of the S&P 500. Starting in the early 1970’s, the financial literature started to test the findings of Sharpe (1964) and Markowitz (1952) to see if the majority of actively managed funds did underperform, merely holding the market portfolio. For example, Frino and Gallagher (2001) took a sample of 343 active mutual funds over an 8-year period and found that the overwhelming majority were not able to outperform the S&P 500 after fees. At the same time, there has been an ongoing concern about other asset classes possibly being able to outperform the S&P 500 after adjusting for risk. For instance, Merk and Osborne (2012) analyzed historical data from 2002 to 2012 and found that during that period gold had a Sharpe ratio of 0.85 compared to 0.30 of the S&P 500. Also, Hodges, Taylor, and Yoder (1997) found that the investment horizon changes the optimal portfolio, which many prior research papers failed to take into consideration. Given this point, Deering & Granahan 5 their data concluded that when looking at longer time horizons, long-term corporate bonds had higher Sharpe ratios compared to common stocks. This is contrary to the prior conclusion in financial literature that the optimal portfolio is the S&P 500. Since the creation of liquid financial exchanges, there have been academics that assert it is possible to consistently achieve risk-adjusted returns through “day trading” in financial markets. More specifically, these academics argue that there are behavioral biases reflected in the markets that rational investors can exploit. Although this notion usually runs contrary to the conclusions reached by the majority of academia in financial economics, it is important to stress ​ ​ this point in order to move forward in our discussion. We will do this by showing what has been concluded from the past literature pertaining to efficient markets and rule out the possibility of achieving risk-adjusted returns through day trading. Most notably, Barber et al. (2011) took the transaction history of 360,000 individuals who participated in day trading from 1992 to 2006 to determine whether retail investors could outperform a buy-and-hold strategy in the S&P 500. Their research found that only 1,000 out of the 360,000 day traders were able to achieve a risk-adjusted return for a given year, which was not statistically significant. Furthermore, the top 500 day traders were only able to achieve a risk adjusted return of 5% per year after fees and the day traders who were ranked below 10,000 lost on average 15% per year. These results are consistent with the vast majority of financial literature that have concluded that investors will be better off not attempting to actively manage their money through day trading while trying to achieve a non-existent risk-adjusted return. In recent years, there has been an expanding literature regarding the use of options as a means to increase the Sharpe ratio of the simple buy-and-hold strategy of the S&P 500. Guasoni, Deering & Granahan 6 Huberman, and Wang (2011) concluded that, even if there is no ability of the investor to predict future returns, holding options on indices will likely result in a higher risk-adjusted return. A strategy known as a covered call has been shown to be one straightforward way for investors to achieve a volatility risk premium, which would result in a higher Sharpe ratio. Put simply, a covered call is where you own shares in a stock and make an agreement with another party to sell those shares at a future date at a certain price. In return for making this agreement, you collect a premium today, which effectively reduces the cost basis for the shares purchased. Israelov and Nielsen (2015) backtested a variety of different covered call strategies on the S&P 500 and found that all of them outperformed buying the S&P 500 outright on a Sharpe ratio basis. A traditional notion in finance surrounds the standard normal distribution of returns, where annualized returns follow an approximate frequency “bell curve.” However, recent empirical studies reject the traditional notion of a symmetrical return distribution, instead favoring the "fat-tailed” distribution or kurtosis, meaning that large losses and gains are too frequent to fit within a standard normal model. For instance, Ivanovski, Stojanovski, and Narasanov (2015) looked at stock market data from 2001 to 2011 and found that asset prices tend to often exhibit skewness and can be characterized at leptokurtic. This means that asset price movements tend to have a slight bias towards the upside and have a higher frequency concentrated around the mean. As a result, rational investors should account for the performance of an asset over a time horizon that includes skewness and kurtosis during both peaks and troughs of the economic cycles.