Efficient Markets and the Sharpe Ratio · 2020-02-04 · portfolio is enough to draw strong...

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


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.


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,


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,


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. Richard Casanitas (1978) assigned time periods to

macroeconomic subsets and analyzed this variability within equity markets, but his findings are

outdated for applicability in the current market.


Currently, there is not extensive academic research on this topic, and most financial

models do not consider the effects of skewness and kurtosis. The majority of academic papers in

the financial literature do not properly account for risk when backtesting different asset classes

and strategies. Most financial research incorrectly assumes that maximizing the Sharpe ratio of a

portfolio is enough to draw strong conclusions about the excess return that portfolio has

generated. However, the Sharpe ratio does not accurately reflect the true risk-adjusted returns of

a given portfolio. At this moment, we would argue that there is limited knowledge spreading to

finance professionals, academia, and retail investors. Therefore, our goal of this project is to test

the hypothesis that different asset classes and options strategies can consistently beat the S&P

500 on a true risk-adjusted basis.

3 Data Description and Methodology:

The main goal of our research is to identify if there are investing strategies that have been

overlooked by academia and whether it is reasonable to assume that individual investors are

unable to predictably beat the market. Therefore, individual investors will not spend money on

active strategies and ETFs that underperform the S&P 500. As previously mentioned, the

overwhelming majority of financial economists have concluded that there is no predictable way

to outperform the market on a risk-adjusted basis, and any rational investor should hold the

market portfolio. In order to test these claims, we began by selecting 11 different

exchange-traded funds.

We selected exchange-traded funds for several reasons. First, there is easily accessible

historical data on Yahoo Finance and the Chicago Board of Option Exchange website. Second,


exchange-traded funds are highly liquid, meaning that there are a significant amount of volume

or trades placed in the products. Therefore, the data provided allowed us the liquidity to assume

there were no significant spreads associated with buying the assets. Third, exchange-traded funds

track an underlying asset class, which allowed us to directly compare the different asset classes

in a fair manner.

As for exchange-traded funds, we selected funds that were the most heavily traded and

had the appropriate data needed to conduct our analysis. We choose to analyze 15 years of data

starting on January 1, 2004, and ending on December 31, 2018. We did this in order to capture

market cycles and sufficient variance of the Sharpe ratios in both bull and bear markets.

Additionally, we pulled data pertaining to the risk-free rates from Macrotrends.com in order to

calculate each investment vehicles’ Sharpe ratio for the given years.

Two assumptions were made when conducting our analysis. First, when calculating the

Sharpe ratios for the exchange-traded funds, we found the risk-free rates on a daily basis and

averaged them as a marker for the yearly rate. However, this is not an extremely strong

assumption and it will not impact our conclusions because we are analyzing Sharpe ratios of

different asset classes and strategies on a relative basis. This means that the actual Sharpe ratio

numbers could be slightly off, but the order of the performance will still be correct. Second, as

mentioned in the previous paragraph, we selected the investment vehicles and did not take a

random sample for each asset class. Nevertheless, this assumption will not make our conclusions

unreasonable because often times investors are likely to invest in products that are highly liquid.

Lastly, it is important to point out that just because a strategy or asset class has worked in the

past, does not mean that it will perform exactly the same moving forward into the future.


When conducting our analysis, we looked at data from 2004 to 2018, which included a

section of the post-Dotcom bubble bull run, the 2008 Financial Crisis, and the expansion of the

United States’ market from 2010 onward. This is extremely important because many papers in

financial economics will not look at data with outliers because they do not fit inside the

traditional models. Thus, there are people reaching erroneous conclusions that need to be

corrected because it is only fair to include larger changes in each asset’s standard deviation.

From our research, we wanted to see if there were any strategies that tended to do

significantly better during a systematic decline in asset values. Therefore, if you, as an investor,

believe that asset prices are going to decline in the near future, then investing in assets that had

higher Sharpe ratios in the 2008 recession may be a profitable strategy during a future economic

downturn. As mentioned previously, Merk and Osborne (2012) and many others have found that,

during bear markets, gold tends to perform well compared to the overall stock market. For that

reason, we wanted to test if that claim reflected reality.

To conclude, there is extremely limited current research on option strategies and how

they perform during bull and bear markets on a risk-adjusted basis. For example, Ungar and

Morgan (2009) tested option strategies from July 1986 and ending in September 2008; their data

did not include the 2008 Financial Crisis, and this could have led them to draw unreasonable

conclusions. Our analysis will look into all of these questions more thoroughly.


Table 1: ETF Descriptions within Equity Sectors

Equity Sectors Ticker Description*

Technology XLK The Fund seeks to provide investment results that, before expenses, correspond generally to the price and yield performance of the Technology Select Sector Index.

Financial Services XLF The Fund seeks to provide investment results that, before expenses, correspond generally to the price and yield performance of the Financial Services Select Sector Index.

Health Care XLV The Fund seeks to provide investment results that, before expenses, correspond generally to the price and yield performance of the Health Care Select Sector Index.

Energy XLE The Fund seeks to provide investment results that, before expenses, correspond generally to the price and yield performance of the Energy Select Sector Index.

Utilities XLU The Fund seeks to provide investment results that, before expenses, correspond generally to the price and yield performance of the Utilities Select Sector Index.

Real Estate IYR The Fund seeks investment results that correspond generally to the price and yield performance, before fees and expenses, of the Dow Jones US Real Estate Index.

* Description from www.cnbc.com/sector-etfs

Table 2: ETF Description within Commodity Sector

Commodity Ticker Description*

Gold GLD The Fund seeks to achieve the performance of gold bullion less the expenses of the Fund. The Fund is designed as a cost effective way for investors to access the gold bullion market.

* Description from www.cnbc.com/sector-etfs

Table 3: ETF Descriptions for Option Strategies

Option Strategy Ticker Description*

Put Option on S&P 500

PUT PUT is an award-winning benchmark index that measures the performance of a hypothetical portfolio that sells S&P 500 Index (SPX) put options against collateralized cash reserves held in a money market account.

http://www.cboe.com/spx


30 Delta Covered Call on S&P 500

BXMD The Cboe S&P 500 30-Delta BuyWrite Index is designed to track the performance of a hypothetical covered call strategy that holds a long position indexed to the S&P 500 Index and sells a monthly out-of-the-money (OTM) S&P 500 Index (SPX) call option. The call option written is the strike nearest to the 30 Delta at 10:00 a.m. CT on the Roll Date.

* Description from www.cboe.com

Table 4: ETF Descriptions within Fixed Income Categories

Bonds Ticker Description*

Investment Grade Corporate Bonds

LQD The Fund seeks investment results that correspond generally to the price and yield performance of a segment of the U.S. investment grade corporate bond market as defined by the GS $ InvesTop Index.

BlackRock High Yield Bonds

BHYIX The Fund seeks to maximize total return, consistent with income generation and prudent investment management. The fund normally invests at least 80% of its assets in high yield bonds, including convertible and preferred securities.

* Description from www.cnbc.com/sector-etfs (The tables above display the exchange-traded funds we analyzed)

4 Empirical Analysis of Sharpe Ratios:

Our 15 year analysis of the Sharpe ratios led to several conclusions (see Exhibit 1). First,

BHYIX (BlackRock High Yield Bonds) had the highest average Sharpe ratio among all asset

classes over the 15 year period. Additionally, the risk-adjusted return of BHYIX performed

worst among all asset classes in 2008 but performed best in 2009. The downturn in BHYIX’s

Sharpe ratio in 2008 can be primarily explained by the systematic risk of the overall economy.

We hypothesize the drastic increase in BHYIX’s 2009 Sharpe ratio can be explained by multiple

factors: As a function of the government’s Troubled Asset Relief Program (TARP), the Federal

Reserve purchased a significant number of high yield bonds in 2009, which artificially led to an

increase in demand, and therefore price, among toxic asset ETFs. Additionally, the Federal


Reserve reduced the Federal Funds Rate during this period. Bond prices and interest rates follow

an inverse relationship, therefore lowering interest rates leads to price appreciation. This finding

mimics a conclusion made by Hodges, Taylor, and Yoder (1997), in which they found corporate

bonds had higher Sharpe ratios compared to common stocks when looking at longer time frames.

When we restrict our sample to 2008, we found that GLD (Gold ETF) had the highest

Sharpe ratio. This may be explained by consumer behavior during economic downturns, in

which we generally see a preference shift from risky assets to comparatively secure assets. As

the demand for gold increases, price appreciation occurs and the return increases. Unlike other

asset classes, return on gold is not strongly correlated with the return of the market. As a

consequence of these factors, GLD’s 2008 return is comparatively higher than most asset classes,

while its standard deviation is comparatively lower than most asset classes. This coupling

explains why GLD had the highest Sharpe ratio during the 2008 period of the recession.

With regard to the equity classes, XLU (Utilities ETF) had the highest average Sharpe

ratio for the 15 year period. In addition, XLU had the lowest variability among equity Sharpe

ratios. This may be explained by the relative demand inelasticity within the utilities industry.

Consumers demand electricity, water, and gas services regardless of the state of the economy.

Stable demand is a particularly attractive quality for investors, and since the utilities industry

pays the highest dividend yield among all equity classes, investor demand for utility companies

props up the return for the industry’s ETF.

As for option strategies, we tested the two best performing option strategies that Ungar

and Morgan (2009) found which included the put and call option strategy (see Table 3). Contrary

to Ungar and Morgan (2009), our data included the 2008 Financial Crisis. In short, the option


strategies had not performed as well as previously mentioned in past literature. More

specifically, we found that the Sharpe ratio over the 15 years of the S&P 500 was 0.629, the call

option strategy of writing a 30 delta call every month was 0.612, and the put option strategy of

writing an at-the-money put option was 0.682. This is contrary to what Ungar and Morgan

(2009) found looking at data from 1986 to 2008 where the same put option strategy led to a

sharpe ratio of 0.69 whereas the S&P 500 was 0.37. To quote Ungar and Morgan (2009: 55),

“Over the studied period of more than 22 years, the CBOE S&P 500 PutWrite Index (PUT): 1)

generated compound annualized returns in excess of the S&P 500 Index, 2) had 39% less

volatility than the S&P 500 Index, and 3) had better risk-adjusted returns than the other seven

indexes studied.” However, we would argue that there are problems assuming that the Sharpe

ratio is a perfect metric for quantifying risk. This point will be highlighted and explained more

extensively in the Limitations of The Sharpe Ratio Metric section. Thus, Ungar and Morgan

(2009) did not account for all the relevant factors when adjusting for risk in their study. Given

these points, it is difficult to firmly state that those options strategies will predictably outperform

the market over long periods of time.


Exhibit 1: Sharpe Ratios for all Asset Classes: 2004-2018


4.1 Empirical Analysis of Alpha and Beta:

quation (1) Ŷ x E i = α + β i + ε i

here Ŷ expected daily asset return, x aily market return, and subscript i designatesw = = d

the asset class tested in the regression.

In order to get a better understanding of our results, we performed a regression analysis to

determine the alpha and beta coefficients (see Exhibit 2). In this context, alpha represents the

excess return relative to the market and beta is the sensitivity of a portfolio’s exposure to

systematic factors in the overall market. This means that, all else equal, a higher alpha is more

advantageous for investors. Furthermore, we calculated confidence intervals for alpha to test for

statistical significance among the different asset classes and strategies.

After conducting a 95% confidence interval, we found all of the asset classes and option

strategies, with the exception of BHYIX and LQD, did not have statistically significant

risk-adjusted returns over the S&P 500. With respect to BHYIX and LQD, the alpha values were

only 0.0241% and 0.0175%, respectively. These values are inconsequential for a given portfolio,

even if the portfolio is held for a long period of time. Additionally, we believe the alpha values

can be explained away by the previous factors mentioned pertaining to the 2008 Financial Crisis.

Consequently, none of the asset classes or strategies that we tested seem to suggest that there is a

predictable away to outperform the S&P 500 on a risk-adjusted basis.


Asset Classes and Strategies

Ticker Alpha Beta Lower 95% Confidence (Alpha)

Higher 95% Confidence (Alpha)

Statistical Significance (Alpha, Beta)

Kurtosis

Skew

Technology XLK 0.0000179

0.979174912 -0.0001512

0.0001870

(No, Yes) 9.781 0.176

Financial Services

XLF -0.0003155 1.417455578 -0.0006394

8.42131E-06

(No, Yes) 16.832 0.419

Health Care XLV 0.0000725

0.713631046 -0.0001150

0.0002599

(No, Yes) 11.150 -0.075

Energy XLE -0.0000847

1.198979081 -0.0004268

0.0002574

(No, Yes) 10.269

-0.172

Utilities XLU 0.0001925

0.627008788 -0.0000615

0.0004464

(No, Yes) 12.521

0.352

Real Estate IYR -0.0001604

1.233576162 -0.0005465

0.0002257

(No, Yes) 16.973 0.039

Gold GLD 0.0003510

0.032537893 -0.0000351

0.0007371

(No, No) 6.477 -0.154

Put Option on S&P 500

PUT 0.0000522

0.629004873 -0.0000595

0.0001639

(No, Yes) 30.966 -0.271

30 Delta Covered Call on S&P

BXMD 0.0000254

0.834705602 -0.0000598

0.0001107

(No, Yes) 17.532

-0.194

Investment Grade Corporate Bonds

LQD 0.0001749

0.041664757 0.0000215

0.0003282

(Yes, Yes) 98.279 -0.440

BlackRock High Yield Bonds

BHYIX 0.0002407

0.093409122 0.0001447

0.0003368

(Yes, Yes) 15.515 -0.934

S&P 500 SPY N/A N/A N/A N/A N/A 16.737 0.164

Exhibit 2: Alphas, Betas, Kurtosis, and Skew for all Asset Classes: 2004-2018


4.2 Limitations of the Sharpe Ratio Metric:

The goal of rational investors will always be to maximize the rate of return of their

portfolio for a given level of risk. Most financial economists argue that asset prices are

efficiently priced because if an opportunity to achieve a risk-adjusted return exists, then it will

quickly be exploited by investors with sufficient access to information. The Sharpe ratio is

arguably the most popular metric used by finance professionals to compare sets of portfolios.

However, like many economic models, it is difficult to find a model that perfectly

accounts for all variables and does not contain unreasonable assumptions. The Sharpe ratio uses

the standard deviation of returns as a measurement of the total risk of a portfolio and assumes

that the returns are normally distributed. In practice, the returns of financial markets tend to be

skewed because there are a large number of “crashes” and “rallies” that do not conform to a

normal distribution. In other words, there tends to be more outlier movements than a normal

distribution would assume.

This phenomenon is shown Exhibits 3, 4, 5 and 6. Exhibit 3 is the compounded return of

the S&P 500 starting on January 1, 2004 and ending on December 31, 2018. As readers will find,

the stock market tends to move up more often than down and have significant downward moves

in short periods of time. For example, this effect can be seen in both the 2008 Financial Crisis

and the 2018 stock market downturn, as there were significant moves in short periods of time.

This means that financial markets display kurtosis and skew in their distributions of returns. Both

of these factors have to be considered when measuring the risk of a portfolio.

These characteristics can be further understood from Exhibit 4, which is the frequency of

percentage daily returns on S&P 500 in the 15 year time frame. In comparison, Exhibit 5 shows


the theoretical frequency of percentage daily returns on S&P 500 assuming that the stock market

follows a normal distribution. In addition, Exhibit 6 shows the time-weighted returns of each of

the 11 ETFs that we tested from 2004 to 2018. This graph further illustrates our point that price

movements are not normally distributed.

Using the Sharpe ratio as a measurement for risk-adjusted returns can lead to erroneous

results that make certain portfolios appear to be more optimal. For example, the conclusions

previously mentioned by Ungar and Morgan (2009) who tested multiple option strategies that

were based around the S&P 500 index is not representative of the true risk of the strategy. All

else equal, a rational investor would prefer to hold a portfolio that has a lower kurtosis value and

a higher skew value. Therefore, if you find a portfolio that has a higher Sharpe ratio than the

market, then that does not necessarily mean that the portfolio has achieved a risk-adjusted return

over the market. We tested the two best performing strategies from Ungar and Morgan (2009)

which were the PUT and BXMD strategies and found that those strategies had kurtosis values of

30.966 and 17.532, compared to 16.737 for the S&P 500 (see Exhibit 2). This means that there

will be a higher probability of an extreme tail end move for the option strategies compared to

holding the S&P 500. Furthermore, the skew values were -0.271 and -0.194, compared to 0.164

for the S&P 500 (see Exhibit 2).

From our research, the asset classes and strategies that achieved higher Sharpe ratios than

the market, generally speaking had higher kurtosis values and lower skew values. With that said,

XLU had a higher Sharpe ratio, lower kurtosis, and higher skew than the S&P 500. Given that

point, XLU may have achieved a risk-adjusted return over the market over the 15 year period.


However, there currently is no academic literature published that comes up with a model that

takes kurtosis and skew into account when comparing different portfolios.

Additionally, there could be other variables to consider when calculating risk-adjusted

returns that the financial literature has not developed. Nevertheless, there has not been adequate

research in the financial economics space to affirm those claims and that research is beyond the

scope of this paper. In summary, it is difficult to assert a strong conclusion about whether any of

these asset classes or strategies have outperformed the market to any significant degree between

2014 to 2018.


Exhibit 3: S&P 500 Total Return: 2004-2018


Exhibit 4: Frequency of % Daily Returns on S&P 500: 2004-2018


Exhibit 5: Theoretical Frequency of % Daily Returns of S&P 500 Assuming a Normal

Model: 2004-2018


Exhibit 6: Time-Weighted Returns Among Tested Asset Classes


5 Ethical Concerns and Conflicts of Interest:

When it comes to any applied research topic it is always important to understand the

possibility that there will be biases and self interests contained in the research. Again, most

academics within finance conclude that an investor will not be rewarded for risk that they do not

take. For example, Rompotis (2009) and French (2008) both concluded that active strategies

have not been able to outperform the benchmark index after you adjust for risk and management

fees. However, it is worth pointing out that there are conflicts of interest within the finance

industry that would encourage investors to actively trade their money and not be passively

exposed to systematic risk. As previously mentioned, options exchanges, brokers, and hedge

funds benefit from people who believe that outperforming the market is possible by collecting

fees. Therefore, these firms will be more likely to promote false conclusions that active investing

will “outperform” simply holding holding the S&P 500 in an effort to increase revenue from

commissions. Additionally, the Sharpe ratio can be manipulated by ignoring kurtosis and skew.

This can mislead investors and create portfolios that do not reflect true risk-adjusted returns.

Given these points, it is important that investors are fully aware of how to make the best

investment decisions in order to maximize their risk-adjusted returns. Therefore, it is safe to

conclude that placing faith in an active fund manager, ETF, or actively trading your own money,

has a low probability of outperforming the market on a consistent basis.

6 Conclusion:

Due to the unique market conditions over the past 15 years, we were interested in

determining whether any asset classes notably outperformed the market in recent bear and bull


markets. Our primary reason for conducting this analysis was to bring forth new literature

regarding the risk-adjusted returns of asset classes from 2004 onward and take into consideration

the impacts of skewness and kurtosis on portfolio performance. Over the course of this research

paper, we discovered the financial metrics and summary statistics that were missing from the

current literature. Our results prove that no tested asset class or strategy outperformed the market

in a significant manner on a risk-adjusted basis between 2004 and 2018.

If we were to expand upon this research question, we would test alternative asset classes

that were not included in this study. Additionally, we would also test many portfolios holding

several asset classes. Due to the vast number of portfolio combinations, we were unable to test

portfolios with varying weights of each asset class in order to optimize their performance. We

also considered looking at data that spanned for a longer period of time in order to capture more

market cyclicality, but ETFs are a relatively recent investment vehicle, and it was difficult

finding liquid ETFs for these asset classes prior to 2004.

In terms of policy implications, we would not suggest any major changes. However, it is

still important to stress the ethical issues pertaining to active management. Currently, there

seems to be a problem with asymmetric information among investors and active fund managers.

If more investors were aware that the majority of active managers will not be able to outperform

the market on a risk-adjusted basis, then investors will not forgo the cost of high expense ratios

and management fees that effectively reduce the available balance in their portfolio.

Furthermore, exchanges and brokers have an incentive to encourage retail investors to actively

trade because they collect exchange fees and profit off the difference between the bid-ask spread.

Given these points, we would suggest that there needs to be more education spread to the masses


on this topic. For example, this research should be taught in high school curriculum so that

people can know to avoid underperforming ETFs and active fund managers. Additionally, we

would suggest regulations be put into place that show investors the alphas of each ETF before

they purchase the funds. Therefore, investors that hold portfolios can have more money in their

accounts when they retire.

The returns for each ETF bring into question the relevance of the 80/20 rule, where 80%

of results come from 20% of causes. It may be possible that the majority of the returns for each

ETF stem from a small subset of performance outliers. Our analysis did not find that any

industry could outperform the market on a risk-adjusted basis, but we should disclose that it is

theoretically possible to hold a portfolio of high performance companies within a specific

industry that outperform the market, but the probability of finding these companies on a

consistent basis is nearly impossible in practice.

For investors operating over longer time horizons, a portfolio of bonds may outperform

equities on a risk-adjusted basis. This is consistent with the findings of Hodges, Walton, and

Yoder (1997), where they found that the Sharpe ratio for bonds is higher than the Sharpe ratio for

equities over considerable periods of time. Our research indicated that high yield bonds have the

highest Sharpe ratio out of all the ETFs we tested, but our research only spans over a 15 year

period and does not perfectly account for kurtosis and skew. Future researchers should extend

the timeline of our analysis to 45 years, which equates to the investment timeline between early

adulthood and average retirement, in order to offer a definitive conclusion to this research topic.


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Efficient Markets and the Sharpe Ratio · 2020-02-04 · portfolio is enough to draw strong...

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