Einstein and Finance

I attended the CFA Society Malaysia Career Day 2016 at Aloft KL Sentral on Sunday 28-Aug-2016.  It was a great event.  There were panel discussions by financial industry leaders, exhibition booths by investment banks and research houses.  I enjoyed the event as it gave me the opportunity to talk to many finance experts, and most of them were very friendly and approachable.

During the events, many were curious why a R&D engineer like me would like to switch to finance field.  When I told them I was inspired by Albert Einstein, their reaction was – “Huh?!”.  This prompted me to write this article.  No technical ingredient today, just some history and thoughts.

As a physics graduate, my idol is Albert Einstein.  During the time when I was working on my Master thesis, I fully utilized the database to look for works by Einstein, asides from my thesis research area.  One day, while searching on the internet, I came across an article where it claimed that Einstein once said that the greatest man’s invention was “Compounding Interest”.  Curiosity kills the cat.  Ever since then, I started to look for more information about finance.  After submitting my master thesis, I decided to enroll in the CFA program and managed to pass all three levels of the exams.

But, did Einstein really said that the greatest man’s invention was “Compounding Interest?  Was the source of the citation reliable?  Over the years, I could not find any solid proof that Einstein made that claim personally.  There were many versions of claim floating around in the internet.  Every piece sounded very genuine but none of them were legitimate.  Highly likely, it could be just an urban legend.

Nevertheless, there is really a linkage between Einstein and finance.  Not on compounding interest but on Stochastic Process.  In finance, the characteristic of how an asset evolved randomly is called a stochastic process.  It was first introduced by a French mathematician, Louis Bacheliar, in his PhD thesis “Theory of Speculation” in 1900.  But his work was not widely recognized at that time due to some minor flaws, which were later found to be acceptable.  Later in 1905, Einstein independently (unaware of Bachelier’s work) proposed a similar mathematical model to explain the random movement of atoms (link).  Einstein’s work attracted other scientists to further improve the stochastic process model and eventually it become a well-established foundation for many financial models such as the Black-Scholes model.

Lastly, did Einstein make any good money in stock market?  There are websites claimed that Einstein lost his Nobel Prize money in 1929 crash.  But again, no solid citation on this claim.  However, there was one great Physicist lost a small fortune in a stock bubble.  Guess who?  

Modern Portfolio Theory by Nobel Prize Winner

Harry Markowitz, the winner of 1990 Nobel Prize in Economics, introduced Modern portfolio theory (MPT) in The Journal of Finance on March 1952 (Read more here).  MPT sometimes is called mean-variance portfolio theory because the mathematical models focus on optimizing the risk and return of the portfolio.  This article will focus on using the MPT to construct the portfolios with real world example.  Readers who are interested to understand the underlying concept can google “Modern Portfolio Theory”.

The mathematical model of MPT can be easily constructed by using Excel spreadsheet with Solvers add-ins.  Once the model is ready, users can build the portfolio by keying in the historical returns of the asset classes into the spreadsheet.  It is generally believed that a portfolio shall hold at least 30 stocks in order to enjoy the benefit of diversification (link).  But for the ease of illustration, only ten heaviest weighted stocks that are listed more than 10-years in the FTSE KLCI are chosen for modeling purpose.  Figure 1 is the weightage of 30 stocks in FTSE KLCI as at 17 June 2016 published by FTSE (link).

Figure 1

Table 1 is the 10-years return of the ten selected stocks extracted from MorningStar.com.  The geometry return and standard deviation are calculated using Excel.  Table 2 is the correlation coefficient matrix that is required to calculate the portfolio variance, estimated by Excel as well.  The objective of the model is to find the asset allocations that meet the investors’ risk-return requirement.  Table 3 is the results of the simulation, comparing equally weighted allocation, minimum risk allocation, maximum return allocation and maximum risk-return allocation.

Table 1

Table 2

Table 3

The equally weighted portfolio has the lowest return at 6.02% with highest risk at 23.80%.  The minimum risk portfolio consists of 2.74% CIMB, 54.27% PETGAS, 7.38% KLK and 35.62% MISC.  By holding such portfolio, the risk is greatly reduced to 10.22%, with slightly higher return at 7.14%.  Investors who look for maximum return can always pick the highest return single stock and invest 100% into it.  The MPT model also shows the same result with 100% allocation to PBBANK with 13.52% return at 15.93% risk.  However, the risk of the single stock portfolio is significantly higher than the minimum risk portfolio.  Lastly, by holding 67.06% of PBBANK and 32.94% of PETGAS, investor can reduce the risk to 13.20% yet still enjoying 12.74% return.

As the sample size is small in this model, many stocks in the model with low return and high risk are disqualified during the simulation.  One can increase the sample size to 300 in order to achieve at least 30 stocks allocation.  Another way of doing this is manually pick 30 – 60 stocks that have similar expected return with different risk, and then run the MPT simulation to obtain the optimum allocation.

MPT is often applied on constructing a portfolio that consists of mutual fund, exchange traded fund, bond fund and other funds that are already diversified within its asset class.  As such, the mathematical model can be greatly simplified to holding 3 – 5 well-diversified funds.

Disclaimer:  The above asset allocation calculations do not imply any buy or sell recommendation.   The author disclaims all liabilities arising from any use of the information contained in this article.

Using GARCH to estimate implied volatility (IV) for structured warrant

In previous article, we discussed about the trading strategy for structured warrants (Read more here).  One of the important criteria is the implied volatility (IV) estimation.  If the structured warrants issuers provide the IV number, we can use it directly in the excel spreadsheet.  That is for short term trading purpose.

If an investor decided to buy the structured warrant and exercise the option at the maturity, then the evaluation approach is different.  For such scenario, one cannot use the IV provided by the issuer because investor has to pay for higher premium if the IV is higher than market rate or statistical rate.

Consider an out of money call warrant that has more than three month’s maturity, where its underlying asset is Hang Seng Index.  The IV provided by one issuer in Malaysia is 27.0% (see Figure 1).  Whereas, the average IV of call warrant with more than 3 months maturity quoted by an issuer in Hong Kong Stock Exchange is 20.96% (see Figure 2) (link). 

Clearly, the call warrant issued by Malaysia issuer carries a premium.  It may look pricier but one has to factor in the exchange rate volatility for a call warrant with foreign underlying asset.

Figure 1

Figure 2

Question: What if there is no similar readily available call or put warrant traded in the market, how can the investor estimate the IV?

Answer: The investor can use the statistical rate to estimate the IV.  One of the popular methods to estimate volatility is the GARCH model.

The generalized autoregressive conditional heteroscedasticity (GARCH) model was developed in 1986 by Tim Bollerslev, a Danish economist (Read more here).  Unlike the conventional volatility estimation, which provided only one value for entire period of analysis; the GARCH model will factor in the most recent market movement impact into the volatility estimation.   There is a very comprehensive lecture note by MIT OpenCourseWare, those who are interested in the background of the mathematics can refer to this link.

I have developed a simple excel spreadsheet model to calculate the IV of Hang Seng Future Index.  User only needs to download the daily closing price for the Index into the spreadsheet and run the solver to get the IV.  Figure 3 is the snapshot of the GARCH excel spreadsheet.  The estimated number is 21.01%, which is very close to the IV quoted by Hong Kong stock exchange issuer, 20.97%.  Table 1 is the comparison between different IV quoted or estimated from different sources.

Figure 3

  Table 1

Method	HSI Implied Volatility	Comment
Market rate (Malaysia issuer)	27.0%	foreign exchange rate influence
Market rate (Hong Kong issuer)	20.96%	-
Statistical rate (Historical)	19.96%	-
Statistical rate (GARCH)	21.01%	-

In order to provide an apple to apple comparison, let’s consider another example that excludes the impact of foreign exchange rate.  Figure 4 is the IV published by a Malaysia issuer.  The IV is 17.5%.  Figure 5 is the KLCI annualized volatility chart estimated by GARCH model, published by the New York University Stern School of Business (link).  Figure 6 is the KLCI GARCH model using my excel spreadsheet.

 

For meticulous readers, I would like to highlight that the 8.56% in Figure 5 is the predicted volatility for the next day (12 August 2016).  Which means, the volatility estimated using GARCH model on 11 August 2016 is 8.56% - 0.40% = 8.16%.  As this is the annualized number, which means that the assumption of total trading days per year is important.  In US market, it is generally assumed that the average trading days per year is 250.  Thus, putting 250 in the excel spreadsheet will obtain the same results as the number published by NYU Stern.  In fact, the total trading days per year for Bursa Malaysia is around 246 days according to the Bursa Malaysia Annual Report (link).  The volatility for KLCI will be slightly lower at 8.09%.  Table 2 is the comparison of various volatility estimations by different methods.

Figure 4

Figure 5

Figure 6

Table 2

	Method	Trading days assumption	KLCI Volatility
Malaysia Issuer	?	?	17.5%
NYU Stern	GARCH	250	8.16%
My Spreadsheet	GARCH	250	8.16%
My Spreadsheet	GARCH	246	8.09%

Again, it is very obvious that the IV published by the Malaysia warrant issuer is very high compare to the volatility estimated by GARCH model, this time is without the influence of foreign exchange.  There is no right or wrong as the name of the IV suggested – “Implied” is the key word.  It is simply the expectation of the issuer to quote any number that the issuer think is appropriate.  However, for retail investors, using GARCH model is a very convenient way to evaluate the price of the structured warrant.

Simple rule – Higher IV means “expensive”!

Disclaimer:  The mathematical calculations in this article do not imply any buy or sell recommendation.   The author disclaims all liabilities arising from any use of the information contained in this article. 

Using Beneish M Score to detect potential financial manipulation

In fundamental analysis, besides looking for the potential earning growth of the company, one has to ensure that the company financial position is healthy.  However, analyzing the company financial statement is not an easy task for many retail investors; one has to go thru many years of annual reports analysis, reading the financial notes and understanding the details of each entry in the financial statement.  Often, the process is very time consuming.

In 1999, Dr. Messod Beneish, an accounting professor at Indiana University’s Kelly School of Business published a research paper called “The Detection of Earning Manipulation”.     He introduced a simple analysis method, the Beneish M Score, to detect potential financial manipulator by using information that is readily available in the financial statement.

The Beneish M Score is calculated using eight financial ratios with different weightage.

M Score= -4.840 + 0.920DSRI + 0.528GMI + 0.404AQI + 0.892SGI + 0.115 DEPI - 0.172SGAI + 4.697TATA - 0.327LVGI

where,

1.       DSRI = Days Sales Receivables Index

2.       GMI = Gross Margin Index

3.       AQI = Asset Quality Index

4.       SGI = Sales Growth Index

5.       DEPI = Depreciation Index

6.       SGAI = Sales, General, Administrative Expenses Index

7.       TATA = Total Accruals to Total Assets

8.       LVGI = Leverage Index

One can easily construct the Beneish M Score model using Excel spreadsheet.  Table 1 shows the Beneish M Score model for INTC.

Table 1

For M Score that is smaller than -1.78 (more negative) is classified as non-manipulator.  Whereas for M Score that is larger than -1.78 (moving towards zero or positive numbers) is classified as potential manipulator.

The below table (Table 2), shows the M-Score for various companies using the excel spreadsheet method.

Table 2

Company	Beneish M-Score
	2015	2014	Benchmark
TEOSENG	0.399121	-2.88335	Normal < -1.78 < Cautious
PENTA	-1.70263	-2.66321	Normal < -1.78 < Cautious
OKA	-2.48998	-2.70577	Normal < -1.78 < Cautious
HOMERIZ	-2.55859	-2.8873	Normal < -1.78 < Cautious
TIMECOM	-2.78086	-2.60162	Normal < -1.78 < Cautious
INTC	-2.8429	-2.90393	Normal < -1.78 < Cautious

There are two companies getting M-Score that are larger than the benchmark -1.78.  The results suggest that these two companies may have higher chances than other in manipulating their financial statement.  As such, investors shall put more effort in studying their financial statement. 

Table 3 shows the M-Score details for TEOSENG.

Table 3

It is very obvious that the large M-Score is mainly contributed by the AQI.  Looking at TEOSENG Balance Sheet on 2015 Annual Report (Figure 1), there is RM931,106 recorded under Investment property.  In notes 7 (Figure 2), it states that this RM931,106 is represented by Leasehold Shophouse. 

According to the definition in the annual report, investment properties are properties held either to earn rental income or for capital appreciation or for both.  As the amount is not significant compare to general property purchase or expenses, my personal guess is probably the management bought a property for production or supply of goods, while a small portion of the property were rented out to earn rental income.  But it is more appropriate to ask this question to the management during AGM.

Figure 1

Figure 2

Table 4 shows the M-Score details for PENTA.

Again, the most significant contributor is the AQI.  Looking at the Balance Sheet of PENTA 2015 annual report (Figure 3), there is an intangible asset of RM10,856,140 recorded.  A quick look on Note 6 (Figure 4) indicates that majority of this amount is coming from the newly acquired subsidiary Origo Ventures (M) Sdn. Bhd.’s project management right.

According to the annual report, Origo Ventures is a property project management company.  The reason for this acquisition is to align with PENTA future development on Smart Home and Building Solutions.  As the acquisition was carried out at a bargain using cash, PENTA booked a profit of RM2,595,407 but recorded a lower cash flow from operating activities.  As a results, the 2015 TATA score is inferior to 2014 TATA score.

Table 4

Figure 3

Figure 4

Personally, I do not see any strong linkage between property project management activities and Smart Home solution development. The management did not provide any detail on the plan in the annual report.  Investors may want to post this question to the management during AGM. 

Disclaimer:  The above analysis does not imply any buy or sell recommendation.   The author disclaims all liabilities arising from any use of the information contained in this article.