Raphael TRAEN

Volume-Weighted Average Price (VWAP)

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Volume-Weighted Average Price (VWAP)

Raphael TRAEN

In this article , Raphael TRAEN (ESSEC Business School, Global BBA, 2023-2024) explains about the Volume-Weighted Average Price (abbreviated as VWAP), a statistic used by traders to determine the average trading taking into account transaction volume.

Definition

The volume-weighted average price (VWAP) is a measurement that shows the average price of a security, adjusted for its volume. It is calculated during a specific trading session by taking the total dollar value of trading in the security (sum of the products of the price by the quantity of each trade during the trading session) and dividing it by the total volume of trades (sum of the quantities of each trade during the trading session). The formula for calculating VWAP is given by

Formula VWAP

Where N is the number of transactions during the trading session (trading day).

VWAP can also be computed for consecutive time intervals during the trading sessions.

Sometimes, the price is replaced by a “typical price” computed as the average of the minimal price, maximal price, and closing price observe over a time interval.

Typical price

Interpreting the VWAP indicator / Key takeaways

Volume-weighted average price (VWAP) is a popular technical indicator used by traders and investors to identify trends, support and resistance levels, and potential entry and exit points. It can also be used for example to assess the liquidity and market depth of a security. If the VWAP is closely clustered around the current price, it suggests that there is a lot of liquidity and that the market is well-balanced. If the VWAP is spread out over a wide range of prices, it suggests that the market is less liquid and that there is a higher risk of wide price swings.

Breakout above the VWAP line suggests a bullish trend

A breakout above VWAP suggests that the price has momentum and is moving upwards. This could be due to increased buying pressure from investors, indicating a shift in sentiment towards the security. Once the price breaks above VWAP, it can act as a support level, making it more difficult for the price to fall below that level.

This could be an opportunity to enter a long position, anticipating the price to continue rising.

Breakdown below the VWAP line suggests a bearish trend

If the price of a security breaks below the VWAP line, it may signal a potential bearish trend. This could be an opportunity to enter a short position, anticipating the price to continue falling.

VWAP line can act as support or resistance level

The VWAP line can also function as a support or resistance level, representing a price range where the price of the security may tend to bounce off.

VWAP to identify trends

If the VWAP line is trending upwards, it suggests an overall upward trend in the price of the security. This could indicate favorable conditions for long-term investments. Conversely, if the VWAP line is trending downwards, it suggests an overall downward trend in the price of the security. This could indicate caution for long-term investments.

Conclusion

It is important to note that VWAP is just one indicator, and it should not be used in isolation. It is always a good idea to consider other technical indicators, such as the moving average convergence divergence (MACD) and the relative strength index (RSI), before making any trading decisions.

Often, multiple interpretations are possible and because of this, it is important to use the VWAP in combination with other indicators.

As I said, a breakdown below the VWAP may suggest a bearish trend. But it can also be interpreted as the following: Stocks with prices below the VWAP are considered as undervalued and those with prices above it, overvalued.

So while some institutions may prefer to buy when the price of the security is below the VWAP or sell when it is above, VWAP is not the only factor to consider. In strong uptrends, the price may continue to move higher for many days without dropping below the VWAP at all. Therefore, waiting for the price to fall below the VWAP could mean a missed opportunity if prices are rising quickly.

Why should I be interested in this post?

This article will provide students interested in business and finance a comprehensive overview of VWAP and how it is used by traders and investors. By understanding this fundamental concept in technical analysis, students will gain a valuable tool for making informed investment decisions.

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   ▶ Giovanni PAGLIARDI Tail relation between return and volume

Useful resources

Academic articles

Menkhoff, L. (2010) The use of technical analysis by fund managers: International evidence, Journal of Banking & Finance 34(11): 2573-2586.

Kirkpatrick II, C. D., and J.R. Dahlquist (2010) Technical Analysis: The Complete Resource for Financial Market Technicians. FT press.

Videos

Humbled Trader VWAP Trading Strategy Crash Course (YouTube video)

MHFIN VWAP Explained For Beginners In Under 5 Minutes (YouTube video)

About the author

The article was written in December 2023 by Raphael TRAEN (ESSEC Business School, Global BBA, 2023-2024).

Understanding Correlation in the Financial Landscape: How It Drives Portfolio Diversification

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Understanding Correlation in the Financial Landscape: How It Drives Portfolio Diversification

Raphael TRAEN

In this article, Raphael TRAEN (ESSEC Business School, Global BBA, 2023-2024) delves into the fascinating world of correlation and its profound impact on diversification strategies in the financial realm. Understanding correlation is crucial for crafting well-diversified investment portfolios that can effectively mitigate risk and enhance overall performance (the famous trade-off between risk and expected return).

Statistical correlation

Definition

Statistical correlation is a quantitative measure of the strength and direction of the linear relationship between two variables. It describes how two variables are related to each other and how one variable changes in response to the other (but remember that correlation is not causality!).

Mathematically (or more precisely statistically), correlation is defined by the following formula:

Correlation formula

where ρ1,2 is the correlation coefficient between the two random variables (say X1 and X2), 𝜎1,2 the covariance between the two random variables, and 𝜎1 and 𝜎2 are the standard deviation of each random variable.

Correlation is measured on a scale from -1 to +1, with -1 representing a perfect negative correlation, +1 representing a perfect positive correlation, and 0 representing no correlation.

Correlation vs Independence

Correlation and independence are two statistical measures that describe the relationship between two variables. As already mentioned, correlation quantifies the strength and direction of the relationship, ranging from perfect negative (one variable decreases as the other increases) to perfect positive (both variables increase or decrease together). Independence on the other hand indicates the absence of any consistent relationship between the variables.

If two random variables are independent, their correlation is equal to zero. But if the correlation between two random variables is equal to zero, it does not necessarily mean that they are independent. This can be illustrated with an example. Let us consider two random variables, X and Y, defined as follows: X is a random variable that takes discrete values from the set {-1, 0, 1} with equal probability (1/3) and Y is defined as Y = X2.

E(X) = 0, as the expected value of X is (1 + 0 + (-1))/3 = 0
E(Y) = E(X2) = (12 + 02 + (-1)2)/3 = 2/3
E(XY) = (-1 * 1 + 0 * 0 + 1 * 1)/3 = 0

Cov(X, Y) = E(XY) – E(X)E(Y) = 0 – 0 * (2/3) = 0

As Corr(X, Y) is equal to Cov(X, Y) / (sqrt(Var(X)) * sqrt(Var(Y))), we find that Corr(X, Y) = 0.

Application in finance

We now consider a financial application : the construction of portfolios. We show that correlation is a key input when building portfolios.

If the concept of portfolios is completely new to you, I recommend first reading through the article by Youssef LOURAOUI about Portfolio.

Portfolio with two assets

In the world of investments, understanding the expected return and variance of a portfolio is crucial for informed decision-making. These two statistical measures provide valuable insights into the potential performance and risk of a collection of assets held together. In what follows, we first focus on a portfolio consisting of two assets.

Return and expected return of a portfolio

The return of a two-asset portfolio P is computed as

Return two assets

where w1 and w2 are the weights of the two assets in the portfolio and R1 and R2 are the returns of the two assets.

The expected return of the two-asset portfolio P is computed as

Expected return two assets

where w1 and w2 are the weights of the two assets in the portfolio and μ1 and μ2 are the expected returns of the two assets.

Risk of a portfolio

The standard deviation (squared root of the variance) of a two-asset portfolio is computed as

Standard deviation of the return of a two-asset portfolio

or

Standard deviation of the return of a two-asset portfolio

where w1 and w2 are the weights of the two assets in the portfolio, 𝜎1 and 𝜎2 are the standard deviations of the returns of the two assets, and 𝜎1,2 and ρ1,2 are the covariance and correlation coefficient between the two assets returns.

The first expression uses the covariance 𝜎1,2 and the second expression the correlation ρ1,2.

Impact of correlation on diversification (the case of two assets)

From the above formulas follows a very interesting theorem called the “Diversification effect” which says the following: with two assets, suppose the weights of both securities are positive. As long as the correlation coefficient is less than 1, the standard deviation of a portfolio of two securities is less than the weighted average of the standard deviation deviations of the individual securities. Investors can obtain the same level of expected return with lower risk.

The figures below illustrate the impact of the correlation between the two assets on portfolio diversification and the efficient portfolio frontier. For a given level of portfolio risk, the lower the correlation, the higher the expected return of the portfolio.

Impact of the correlation on portfolio diversification

Impact of the correlation on portfolio diversification

Impact of the correlation on portfolio diversification

Impact of the correlation on portfolio diversification

Impact of the correlation on portfolio diversification

You can download below an Excel file (from Prof. Longin’s course) that illustrates the impact of correlation on portfolio diversification.

Excel file on impact of correlation

Diversification effect (extension to several assets)

With many assets, suppose the weights of all securities are positive. As long as the correlations between pairs of securities are less than 1, the standard deviation of a portfolio of many assets is less than the weighted average of the standard deviations of the individual securities.

Why should I be interested in this post?

Understanding correlation is an essential skill for any investor seeking to build a well-diversified portfolio that can withstand market volatility and achieve long-term growth. By carefully analyzing correlation dynamics and incorporating correlation analysis into their investment strategies, investors can effectively manage risk exposure and build resilient portfolios that can weather market storms and emerge stronger on the other side.

Related posts on the SimTrade blog

   ▶ Youssef LOURAOUI Portfolio

   ▶ Jayati WALIA Standard deviation

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   ▶ Lou PERRONE Navigating the Balance Between Risk and Reward in Finance

Useful resources

Prof. Longin’s ESSEC Master in Management “Fundamentals of finance” course.

William Pouder’s ESSEC BBA “Finance” course.

About the author

The article was written in December 2023 by Raphael TRAEN (ESSEC Business School, Global BBA, 2023-2024).

Analysis of “The Madoff Affair” documentary

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Analysis of “The Madoff Affair” documentary

Raphael TRAEN

In this article, Raphael TRAEN (ESSEC Business School, Global BBA, 2023-2024) analyzes “The Madoff Affair” documentary and explains the key financial concepts related to this documentary.

Key characters in the documentary

  • Bernard Madoff: key person, the admitted mastermind of the Ponzi scheme
  • Avellino: partner in Avellino and Bienes, advising its clients to invest with Madoff
  • Bienes: accountant for Madoff’s father-in-law, later partner in Avellino and Bienes, advising its clients to invest with Madoff

Summary of the documentary

Bernard Lawrence Madoff (“Bernie”) was an American stockbroker, market maker and an unofficial investment advisor (because he did not have the necessary license to do so) who operated what has been considered the largest Ponzi scheme in history. He defrauded investors out of billions over a long period.

The Madoff Affair

How did the scheme work?

Madoff’s Ponzi scheme was a classic example of a “pyramid scheme,” in which money from new investors is used to pay returns to earlier investors, creating the illusion of strong returns. Madoff claimed to be investing in a “secret” arbitrage strategy that generated consistent returns, even during periods of market downturn.

In reality, Madoff was simply lying to investors and using the money to pay returns to existing investors and to enrich himself. He kept his scheme going by attracting new investors, who were lured by the promise of high returns and the reputation of Madoff, who was a well-respected figure on Wall Street.


Bernard Madoff was able to maintain his Ponzi scheme for so long in part because he had help from two of his closest associates: Avellino and Bienes. Avellino and Bienes were investment advisors who were responsible for soliciting investments from Madoff’s funds. They were also responsible for creating false account statements that showed investors were making consistently high returns.

Avellino and Bienes first met Madoff and were impressed by his reputation and his consistent track record of high returns. They even approached Madoff about managing their own investments. Madoff agreed, and Avellino and Bienes began to introduce Madoff to their own clients.

Avellino and Bienes were instrumental in helping Madoff build his Ponzi scheme. They were able to attract new investors to Madoff’s funds by touting his track record and his reputation for integrity.

Technical details about the Madoff investment strategy

Bernie Madoff told his investors he was using a legitimate investing strategy called split-strike conversion. This strategy involves buying a stock index and simultaneously purchasing put options to limit the downside potential and selling call options to generate additional income.

Evolution of the Fairfield Sentry fund of Madoff Evolution of the Fairfield Sentry fund of Madoff Source: Madoff

Statistical measures of the Fairfield Sentry fund of Madoff Statistical measures of the Fairfield Sentry fund of Madoff Source: Bernard and Boyle (2009)

Should you be more interested in this strategy I definitely recommend watching the following video explaining the strategy with an example:

Bernie Madoff’s infamous split-strike conversion strategy

Theoretically, this strategy aims to provide a steady stream of income while protecting against significant losses. However, Madoff’s claims about his split-strike conversion strategy were entirely fabricated. He was not actually making these trades or generating the reported returns. Instead, he was using money from new investors to pay off existing investors, replicating a classic Ponzi scheme. This is also further confirmed by the picture I added above comparing the different strategies. The Fairfield Sentry fund was one controlled by Madoff. You can immediately see that the return is higher than what it would be according to the strategy and also that the standard deviation is much lower.

The downfall of the scheme

The Madoff Ponzi scheme began to unravel in the fall of 2008, as the global financial crisis took hold. As investors grew increasingly nervous about their investments, they began to withdraw their money from Madoff’s funds. Madoff was unable to meet these withdrawals, and the scheme collapsed.

In December 2008, Madoff’s sons, Mark and Andrew, confronted him about the scheme. Madoff confessed to his sons, and they immediately contacted the FBI.

One important person we should certainly not forget to mention is Markopolos, an American investor who accused Bernard Madoff of running a Ponzi scheme. He warned the SEC multiple times about Madoff’s suspicious investment returns and opaque investment strategy, but the SEC did not take action until after the collapse of Madoff’s Ponzi scheme in 2008. Markopolos was subsequently hailed as a hero for his efforts to expose the fraud.

Markopolos also believed that Madoff was using his position as a market maker to front-run his clients’ trades. This means that Madoff was using his knowledge of his clients’ impending trades to make profitable trades for himself before his clients’ trades were executed. This would allow Madoff to profit from the difference in price between the time his clients’ trades were executed and the time he made his trades.

Financial concepts related to the documentary

Investment returns

Madoff’s scheme relied on the promise of consistent, high returns even during periods of market downturn. This was a red flag for many investors, as it is unrealistic for any investment strategy to guarantee such consistent performance.

Greed

Madoff’s scheme was fueled by the greed of both investors and Madoff himself. Investors were willing to overlook red flags because they were attracted to the promise of high returns. Madoff was motivated by his own insatiable desire for wealth and power.

Regulatory oversight

The Securities and Exchange Commission (SEC) failed to detect Madoff’s scheme for many years. This failure allowed Madoff to operate his scheme for many years and highlights the need for stronger enforcement of financial regulations.

What lessons can be learned?

Beware of “too good to be true” opportunities

If an investment opportunity sounds too good to be true, it probably is. Investors should be wary of any investment that promises consistently high returns no matter which market conditions, especially if there is no clear explanation of how those returns are being generated.

Do your own research

Before investing in any fund or product, investors should thoroughly research the company or individual running the investment and understand the risks involved. The Madoff Ponzi scheme is a reminder that even seemingly respectable individuals can commit fraud on a massive scale. It is important for investors to be vigilant and to do their homework before investing their hard-earned money.

Madoff’s cynicism

« In an era of faceless organization owned by other equally faceless organizations, Bernard L. Madoff Investment Securities LLC harks back to an earlier era in the financial world: the owner’s name is on the door. Clients know that Bernard Madoff has a personal interest in maintaining the unblemished record of value, fair-dealing and high ethical standards that has always been the firm’s hallmark. »

Why should I be interested in this post?

As a student pursuing a business or  finance degree at ESSEC, I think you will be very fascinated by the Madoff Ponzi scheme for its multifaceted lessons in ethics, financial practices, and regulatory oversight. The scale of the fraud, its longevity, and the involvement of high-profile individuals make it a very interesting case study in the financial world. It is one of the largest financial frauds ever. There are many lessons to be learned.

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Useful resources

Academic articles

Bernard C. and P.P. Boyle (2009) “Mr. Madoff’s Amazing Returns: An Analysis of the Split-Strike Conversion Strategy” The Journal of Derivatives, 17(1): 62-76.

Monroe H., A. Carvajal and C. Pattillo (2010) “Perils of Ponzis” Finance & development, 47(1).

Videos

FRONTLINE PBS The Madoff Affair (full documentary on YouTube)

TPM TV Roundtable Discussion With Bernard Madoff (YouTube video about regulation by Madoff)

Associated Press Executive: SEC Ignored Warnings About Madoff (YouTube video about the testimony of Harry Markopolos)

TPM TV Roundtable Discussion With Bernard Madoff (YouTube video about the testimony of Harry Markopolos)

About the author

The article was written in December 2023 by Raphael TRAEN (ESSEC Business School, Global BBA, 2023-2024).