## How to use Sharpe Ratio?

#### The Sharpe Ratio is well known measure of portfolio performance. It is a ratio which allows to compare various portfolios and allows to measure theirs profitability. The mathematical definition is described as a division between expected rate of return subtracted by risk free rate of return and standard deviation of rates of return [6].

In practice the ratio is calculated annually:

The ratio describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset ([1]). In simple words, the higher Sharpe Ratio is, the portfolio is more profitable.

Why it is so popular?

Most traders are still using the Sharpe Ratio because of its simplicity and ease of interpretation. It was proposed by Sharpe in 1966 and became credible to most users due to Nobel Prize in Economics for his works on Capital Asset Pricing Model ([5]).

Properties of the Sharpe Ratio

With reference to [1], the ratio has several properties. It is immune to manipulation by leverage. It can be interpreted as a T-statistics to test the hypothesis (see [8]) that the return on the portfolio is equal to the risk free rate of return.  The higher ratio is consistent with a higher probability that the portfolio return will exceed the risk- free return. The investor who is using the ratio has a utility (see [7]) whose only arguments are expectation and variance of returns.

Forgotten assumptions

Unfortunately, most traders forget that the Sharpe Ratio doesn’t apply for every set of data. The main assumption of the ratio is that the distribution of the returns is normal. The financial market should be frictionless (without financial costs) and the risk free rate of return should be constant and identical for lending and borrowing. Also data used for computation should contain initial capital of the portfolio.

Consequences of the ratio

Despite the fact that it is really hard to obtain normality of returns on every possible data, the Sharpe Ratio has other disadvantages which are represented from [1].

The ratio does not quantify the value added and it’s only a ranking criterion. It has hard interpretation when the value is negative. The Sharpe ratio does not make any distinction between upside risk and downside risk.

In case of aggregation of portfolios, the correlation between volatilities is not included in the ratio. It is suitable for investors who invest in only one fund.

It doesn’t refer to a benchmark. The choice of risk free rate is rather important, though the impact is rather week. The result highly depends on the initial capital of the portfolio.

The sampling error of standard deviation is embedded in the values of the ratio. By using standard deviation of returns, the Sharpe measure puts both positive and negative variations from the average on the same level. But most investors are only afraid of negative variations.

As a consequence, the Sharpe Ratio leads to inappropriate results on particular sets of data.

When the ratio fails

To be aware of how important are the assumptions, consider the following example [*]:

In the case when the expected return is negative, the Sharpe Ratio gives inappropriate answer. The Sharpe Ratio from Instrument A should be greater than the Sharpe Ratio from Instrument B.

 INVESTMENT A SHARPE RATIO TOTAL RETURN -10.00% -1.5 RISK FREE RATE 5.00% NUMERATOR -15.00% STANDATD DEVIATION 10.00% DENOMINATOR 10.00% INVESTMENT B SHARPE RATIO TOTAL RETURN -10.00% -0.92 RISK FREE RATE 5.00% NUMERATOR -15.00% STANDATD DEVIATION 16.25% DENOMINATOR 16.25%

Solution to Negative Returns

In the case of negative returns, the Israelsen modification of a Sharpe Ratio gives appropriate results. This ratio could be used as a verifying measure of a standard Sharpe Ratio (the values are meaningless but the order remains accurate).

The Israelsen modification of the Sharpe Ratio from a previous example provides that Instrument A is greater than the Sharpe Ratio from Instrument B.

 INVESTMENT A SHARPE RATIO ISRAELSEN TOTAL RETURN -10.00% -0.015 RISK FREE RATE 5.00% NUMERATOR -15.00% STANDATD DEVIATION 10.00% DENOMINATOR 10.00% INVESTMENT B SHARPE RATIO ISRAELSEN TOTAL RETURN -10.00% -0.024 RISK FREE RATE 5.00% NUMERATOR -15.00% STANDATD DEVIATION 16.25% DENOMINATOR 16.25%

As a conclusion, in the case when the negative returns occurred, the investor should also check the value of the Israelsen modification before making the decision.

Avoiding invalid distribution

The most dangerous usage of the ratio is when the distribution of the returns isn’t normal. It seems that the best idea is to check normality of the returns before use of the Sharpe Ratio. There are several statistical test that can validate data’s distribution such us: Sharpiro Wilk, Anderson Darling, Cramer von Misses, Dagostino Pearson, Jarque Berra, Kolmogorov Smirnov, Kolmogorov Lilliefors, Shapiro Francia (see [9]).

Generalizing Sharpe Ratio

On the other hand there are different extensions of the Sharpe Ratio, which gives more accurate results by extending different assumptions. There are plenty of them described in [1], but only these which contain skewness and kurtosis will be presented.

Skewness describes asymmetry of the probability distribution. If there are more extreme returns extending to the right tail of a distribution it is said to be positively skewed and if they are more returns extending to the left it is said to be negatively skewed [2].

Kurtosis provides additional information about the shape of a return distribution. Formally it measures the weight of returns in the tails of the distribution relative to standard deviation but is more often associated as a measure of flatness or peakedness of the return distribution [2].

Skewness and Kustosis are normalized forms of 3rd and 4th central moments respectively (see [10]). Its combination with the Sharpe Ratio allows to approximate the ratio when the distribution is not normal. This method leads to the proposition from [4], where skewness divided by kurtosis is added to the Sharpe Ratio which results a new performance measure.

In the case when the owner of the portfolio has different preference (different utility – see [7]), there are other ratios to measure the performance. The Adjusted for Skewness Sharpe Ratios, gives the opportunity to measure the performance using hyperbolic absolute risk aversion (HARA), constant relative risk aversion (CARA) or constant absolute risk aversion (CRRA). More details can be found in [3].

Conclusion

The Sharpe Ratio is a standard measure for portfolio performance. Due to simplicity and ease of interpretation, it is one of the most popular indexes. Unfortunately, most users forget the assumptions what results inappropriate outcome. They should consider checking the distribution of the returns or validating the results with other performance measures before making a decision on the market.

References

[1] Cogneau P., Hübner G., The 101 ways to measure portfolio performance, Université de Liège

[2] Bacon C., How Sharp is The Sharpe Ratio? – Risk-Adjusted Performance Measures, StatPro Group

[3] Zakamouline V., Koekebakker S., Portfolio Performance Evaluation with Generalized

Sharpe Ratios: Beyond the Mean and Variance, University of Agder, 2008

[4] Watanabe Y., Is Sharpe Ratio Still Effective?, Journal of Performance Measurement, 2006

[*] The original example is taken from the site:

[5] http://www.investopedia.com/articles/07/sharpe_ratio.asp

[10] https://en.wikipedia.org/wiki/Central_moment

## VWAP Algorithm

### Volume-Weighted Average Price known as VWAP is one the most basic and commonly used market indicators by traders around the world. In a book “Algorithmic & Trading DMA” we can read about VWAP that  “As a benchmark, it rapidly became ubiquitous since it gives a fair reflection of market conditions throughout the day and is simple to calculate. This led to algorithms that tracked the VWAP benchmark becoming extremely popular.”

Calculations

Calculation of VWAP it’s relatively simple and it can be done even on piece of paper for small amount of data. In mathematical approach VWAP is represented by equation below:

where P is the price of i-th trade and V is the size related to i-th trade. In fact it takes five steps to calculate your first VWAP. First, only if we use intraday data for examination, we need to calculate typical price for our intervals. Then multiply the price by period’s volume and create running total of these values for future trades. Fourthly we create cumulative volume and in the end we divide cumulative multiplication of price and volume by running total of volume to obtain VWAP. Even simpler, VWAP is a turnover divided by total volume.

Let’s take a look at example results calculated using these five steps on 1-minute interval intraday Morgan Stanley’s data.

 Time Close High Low Open Volume Typical Price Price*Volume Total PV Total Volume VWAP 09:30:00 38.90 38.96 38.90 38.96 69550 38.93 2707581.50 2707581.50 69550.00 38.930 09:31:00 38.94 38.97 38.86 38.92 27617 38.92 1074922.68 3782504.18 97167.00 38.928 09:32:00 38.91 38.96 38.91 38.94 11441 38.93 445398.13 4227902.31 108608.00 38.928 09:33:00 38.89 38.94 38.88 38.92 23587 38.91 917710.61 5145612.93 132195.00 38.924 09:34:00 38.90 38.94 38.90 38.90 10771 38.91 419099.61 5564712.54 142966.00 38.923 09:35:00 38.97 38.97 38.90 38.90 12721 38.93 495276.23 6059988.77 155687.00 38.924 09:36:00 38.92 38.96 38.92 38.96 16471 38.94 641384.86 6701373.63 172158.00 38.926 09:37:00 38.90 38.93 38.86 38.93 23788 38.91 925472.14 7626845.77 195946.00 38.923 09:38:00 38.90 38.92 38.89 38.89 9170 38.90 356701.54 7983547.30 205116.00 38.922 09:39:00 38.92 38.92 38.88 38.91 4644 38.91 180682.02 8164229.32 209760.00 38.922 09:40:00 38.90 38.92 38.88 38.91 4917 38.90 191283.59 8355512.92 214677.00 38.921

All calculations are pretty straightforward, but let us take a look at one interesting element. When you look at typical prices more than half of them (7/11) is below the last VWAP At the same time mean equals 38.917. So where does the difference come from? Volume is the culprit. In our case, period with higher typical price also has bigger Volume, thus bigger market impact and VWAP calculations indicate that.

The most classical VWAP approach is based on tick-by-tick data. But as the market grows and frequency of trades increases more resources are required to keep all calculations up-to-date. Nowadays it is nothing extraordinary for stock to have over hundred trades per minute (true or false?). When multiplied by minutes in a trading day and number of stocks it develops into numbers that might cause some performance troubles.

With help arrives intraday data, i.e. tick-by-tick data aggregated in time periods e.g. 1-minute, 5-minute or 15-minute that contains close, high, low and open price. As in VWAP calculations only one price is required we have to somehow average available prices. For this task exist typical price:

Also there is a second version of typical price that includes Open Price and it’s divided by 4.

Strategy

Most likely we can point out two different strategies of reading VWAP. First one used especially by short-term traders relies on waiting for VWAP to cross above the market price and then enter long position as they interpret price to be bullish. On the other hand are Institutions looking to sell at this moment because they consider it as good opportunity for that day’s price.

When the price goes below VWAP value, the trend seems to be down. Institutions recognize it as good moment to buy, but short-term trader will look to short that stock.

Surely it’s basic approach to VWAP interpretation. For your strategy you would like to scrutinize e.g. influence of price deviation from VWAP value. You should consider that VWAP behaves differently based on period of trading day. It’s because of VWAP cumulative nature. VWAP value is very sensitive for price changes at the beginning of day, but insensitive at the end of trading day.

Big Fish

VWAP is surely commonly used between traders with strategies described above, but on the market there is a bunch of various indicators like VWAP that can suggest when to buy or sell shares. But there is other side of the fence.

Let’s say you want to buy 5 million shares of Morgan Stanley that is 37% of average daily volume in 2014. You cannot buy them at once, because that will impact significantly the market and the market will start to go against you. What you want to do is split the order in small pieces and execute them without impacting the market. Doing it by hand would be backbreaking, that’s what trading application has been made for.

Using trading application and VWAP Strategy, utilizing historical minute intraday files, you can easily generate average volume period profiles that will steadily buy proper number of shares without impacting the market.

As we mentioned in previous paragraph there is a way to improve VWAP performance by creating volume profiles based on historical data. According to Kissel, Malamut and Glantz optimal trading strategy to meet VWAP benchmark can obtained by using equation:

where X is the total volume traded,  is percentage of daily volume traded and  is target quantity for each j-th period. Hence, VWAP can be calculated as below:

where is the average price level in each period.

Summary

VWAP is really simple indicator although it can be interpreted in various ways depending on goal and approach of the trader. It is mainly used by mutual and pension funds, but also by short-term traders. Aside from buying/selling small amount of shares, VWAP might be used as strategy for trading  huge number of shares without impacting the market. “Simplicity leads to popularity.”

References

1. Berkowitz, S., D. Logue, and E. Noser. “The Total Cost of Transactions on the NYSE.”Journal of Finance,41 (1988), pp.97-112.
2. H. Kent Baker, Greg Filbeck. “Portfolio Theory of Management” (2013) , pp.421
3. Barry Johnson “Algorithmic & Trading DMA – An introduction to direct access trading strategies” (2010), pp. 123-126

## Who is moving FinTech forward in continental Europe? Thoughts after FinTech Forum on Tour.

By Michal Rozanski, CEO at Empirica.

In the very centre of Canary Wharf, London’s financial district, in a brand new EY building, a very interesting FinTech conference took place – FinTech Forum on Tour. The invitation-only conference targeted the most interesting startups from the investment area (InvestTech) from mainland Europe. The event had representative stakeholders from the entire financial ecosystem. As Efi Pylarinou noted – the regulator, the incumbents, the insurgents, and investors, were all represented.

Empirica was invited to present its flagship product – Algorithmic Trading Platform, which is a tool professional investors use for building, testing and executing of algorithmic strategies. However, it was amazing to see what is happening in other areas of the investment industry. There were a lot of interesting presentations of companies transforming the FinTech industry in the areas of asset and wealth management, social trading and analytics.

The conference was opened with a keynote speech by Anna Wallace from FCA. Anna talked about the mission of FCA’s Innovation Hub; that is to promote innovation and competition in the financial technology field and to ensure that rules and regulations are respected. Whilst listening to Anna it became clear to me what the real advantage of London holds in the race to become the global FinTech capital – London has Wall Street, Silicon Valley and the Government in one place – and what’s most important, they cooperate trying to push things forward in one direction.

A short look at the companies presenting themselves at the event leads to the conclusion that the hottest sector of FinTech right now is robo-advisory. It’s so hot, that one of the panellists noted it’s getting harder and harder to differentiate for robo-advisory startups. On FinTech on Tour this sector was represented by AdviseOnly from Italy, In2experience,  Niiio, Vaamo and Fincite – all from Germany. Ralf Heim from Fincite presented an interesting toolkit ‘algo as a service’ and white label robo-advisory solutions. Marko Modsching from niiio revealed the motivation of retail customers, that “they do not want to be rich, they do not want to be poor”. Scalable Capital stressed the role of risk management in its offering of robo advisory services.

Social analysis/Sentiment/ Big Data

The social or sentiment analysis area, keeps growing and gains traction. Every day there’s more data and more trust in the results of backtesting as that data builds up over the years. The social media space is gaining ground. Investment funds as well as FinTech startups are finding new ways to use sentiment data for trading. And, it’s inseparably related with the analysis of huge amounts of data, so technically the systems behind it? are not trivial.

Anders Bally gave an interesting presentation about how to deal with sentiment data and showed  how his company Sentifi is identifying and ranking financial market influencers in social channels, and what they discuss.

Sentitrade showed its sentiment engine for opinion mining that is using proprietary sentiment indicator and trend reversal signals. Sentitrade is concentrated on German-speaking markets.

Asset management

From the area of asset management an interesting pitch was given by Cashboard, offering alternative asset classes and preparing now for a  huge TV marketing campaign . StockPluse showed how to combine information derived from social networks and base investment decisions on the overall sentiment. United Signals allows for social investing by making it possible to trade by copying transactions of chosen trading gurus with a proven track record, all in an automated way. And, finally BondIT, an Israeli company, presented tools for fixed income portfolio construction, optimization and rebalancing with use of algorithms.

Bitcoin and Blockchain

An interesting remark was given   by one of the panelist: ‘we have nearly scratched the surface for what blockchain technology can be applied to in financial industry’. Looking at the latest news reports that are saying that big financial institutions are heavily investing in blockchain startups and their own research in this field, there is definitely something in it.

A company from this sector of FinTech – Crypto Facilities, represented by its CEO Timo Schaefer, showed  the functionalities of its bitcoin derivatives trading platform.

Other fields

Hervé Bonazzi, CEO of Scaled Risk, presented its technologically advanced Big Data platform for financial institutions for risk management, compliance, analytics and fraud detection. Using Hadoop under the hood and low latency processing. Ambitious as it sounds.

Analysis of financial data for company  valuations, Valutico presented a tool that’s using big data, AI and swarm intelligence. Dorothee Fuhrmann from Prophis Technologies (UK) presented a generic tool for financial institutions to derive value and insights from data, interestingly describing indirect exposures and a hidden transmission mechanism.

Stephen Dubois showed  what Xignite (US) has to offer to financial institutions and other FinTech startups in the area of real-time and historical data that is stored in the cloud and accessible by proprietary API.

Qumram, in an energetic presentation delivered by Mathias Wegmueller, described technology for recording online sessions on web, mobile and social channels, allowing for the analysis of user behaviour and strengthening internal security policy.

Conclusion

London is the place to be for FinTech startups. No city in Europe gives such possibilities. Tax deductions for investors. Direct help from the UK regulator FCA. Great choice of incubators and bootcamps for startups. No place gives such a kick. Maybe Silicon Valley is the best place for finding investor for a startup, maybe the Wall Street is the centre of the financial world, but London is the place that combines both the tech and the finance. It has a real chance of becoming the FinTech capital of the world.

The people responsible for creating both a great and professional atmosphere at the event were Samarth Shekhar and Michael Mellinghoff. Michael was a great mentor of mine who transformed my pitch from a long and quite boring list of functionalities of our product to something that was bearable for the audience. Michael let me thank you once more for the time and energy you have devoted to Empirica’s pitch!

And because the FinTech scene in our region is not well organized yet, I sincerely advise all FinTech startups from Central and Eastern Europe to attend cyclic events of FinTech Forum in Frankfurt organized by Techfluence professionals!

## Empirica has been nominated for Best Fintech Startup at CESA 2015

Empirica has been nominated for the Best Fintech Startup in Poland at the CESA festival. CESA (Central European Startup Award) is the biggest no-pitch, no-conference start-up festival in the Central-Eastern European region. The festival brings together nearly 4.000 start-ups from 10 countries and it will be held in Vienna this year.

We are in good company, as other companies nominated in FinTech category are:

• Zencard
• Billon
• WealthArc
• our friends from FriendlyScore

The Central European Startup Awards is a series of events in the CEE countries, that aims to recognize and celebrate the entrepreneurial spirit and startup ecosystems of the region. This year eight categories will be awarded in:

• Startup Of The Year
• Best Investor
• Best FinTech startup
• Best Cloud/Data Application
• Best User Experience
• Best Social Impact Startup
• Most Influential Woman
• Best Coworking Space

CESA regognized FinTech as separate category this year reflecting that financial technologies are now the fastest growing technology sector worldwide. Incumbents in the financial industry – big banks and other financial institutions – are witnessing the emergence of new players that are profoundly changing the way individuals and business conduct their financial operations. Global investment in financial-technology (fintech) ventures tripled from \$4.05 billion in 2013 to \$12.2 billion in 2014, with Europe being the fastest growing region in the world, according to a report by Accenture.  Last year, fintech investment increased at more than three times the rate of overall venture capital investment. While it remains to be seen whether the burgeoning fintech industry will actually pose a threat to established institutions, it is clear that the sector is rapidly growing and many of these entrants are here to stay. Investors in the nascent sector are taking notice, profitable exits are on the horizon, and big banks are investing in new technologies to strengthen their competitive positions.

More on this year’s nominees:

## Free version of Algorithmic Trading Platform for retail investors

 We have just released beta of Empirica – Algorithmic Trading Paltform for retail investors! It’s lifetime free for development, testing and optimizing of trading algorithms. Our development team (exactly this team who implemented the entire system) also provides full support in algorithms development as well as connectivity to brokers. If you need help just contact us. Among many features what is unique is our exchange simulation where you can influence market conditions under which you test your algorithms. No others software offers such a realistic level of simulation. In paid versions we offer the execution of algorithms in robust server side architecture. We strive for your feedback! Best regards, Michal Rozanski Founder and CEO at Empirica twitter: @MichalRoza http://empirica.io Empirica Trading Platform – http://empirica.io

## Empirica joins advisory board of London’s FinTech Connect

Michal Rozanski, CEO of Empirica, was invited to join advisory board of FinTech Connect. The main purpose of the board would be to share knowledge and experiences with new fintech ventures looking for support.

FinTech Connect is a new initiative for the global community of financial technology stakeholders – investors, financial institutions, fintech startups and solution providers.

Empirica definitely sees a need for one place where people interested in advancement of financial technologies could exchange ideas, experiences and good practices. We are already taking part in similar initiative but on different field – IT Corner association for local software companies – and advantages of such an initiative are obvious to us. When such an idea gets critical mass of people involved that want to be active, then the effect is much more than the sum of its parts. IT Corner is living evidence of that. Therefore we are great fans and we will happily support the development of FinTech Connect.

FinTech Connect provides a digital hub and meeting place for the fintech sector. It allows start-ups, tech providers, investors and financial institutions to connect and do business through community platform. FinTech Connect has already thousands of members and the count is growing daily. In addition to start up events, FinTech Connect provides global seminars and conferences on subjects such as banking security, cash management and commercial payment strategies for corporate treasurers, and cloud IT platforms for financial institutions.

Steve Clarke, the founder and CEO of FinTech Connect says: ‘We launched FinTech Connect because we wanted to provide a global platform and community for  the fintech industry. With the incredible amount of innovation going on within many different technology hubs around the World, there is a natural element of fragmentation between stakeholders and it can at times, seem like innovation is taking place within micro-communities; either in certain geographies, sub sectors or on a smaller scale again within accelerator or incubator programmes.’

FinTech Connect is also organizing Europe’s most exciting exhibition of fintech startup innovation – FinTech Connect Live. This conference will gather over 2000 fintech professionals, over 100 exhibitors and over 100 speakers and visionaries all in one place for two days in London in December 2015.

and about FinTech Connect Live at: www.fintechconnectlive.com .

## Our platform implemented by large brokerage house!

Empirica has successfuly finished the implementation of its Algorithmic Trading Platform in one of the largest brokerage houses in Poland.

Brokerage house will use our software to:

• aid its internal trading operations, like market making of derivatives on Warsaw Stock Exchange
• offer functionalities of our platform to its institutional clients, which will be able to build, test and execute their own algorithmic trading strategies

Implementation included connecting of our software system directly to the system of Warsaw Stock Exchange (Universal Trading Platform delivered by NYSE Technologies), as well as the integration with transaction systems of brokerage house. Additionally we have fulfilled and successfuly passed tests regarding the highest security, stability and performance requirements.

This implementation is an important milestone for our system. The usage by team of market makers is a proof that our system is capable of performing high-throughput and low latency operations on level required by most sophisticated traders on the capital marketets.