Category Archives: Investment

Solving The Investing Problem


This post is about solving the investing problem. Or at least, an attempt to solve it optimally.

From economics’ point of view, we want to maximise the utility of scarce resources (e.g.: our money) by minimising the waste (e.g.: loss). With that, we could become more productive (e.g.: wealthier) then we currently are without requiring additional work or resources. We want to get more out of what is currently available to us by being more efficient.

Following the same reasoning, we can approximate investing as a minimax problem. In other words, it is an optimisation problem. The optimal solution would lead us to minimising risk while maximising return. We want to gain as much as possible from our capital while avoiding all possible losses.

min(risk) then max(return)

Note: min(risk) means minimising risk and max(return) means maximising return.

min(risk) comes first before max(return). Without min(risk), the max(return) is meaningless: We might lose it all no matter how high our return is. We need to look at the downsides before looking at the upsides.

Be able to successfully transport the treasure out of a cave full of explosives while using a burning torch doesn’t negate the fact that you are an idiot.

min(risk) involves minimising the potential of losses. The first rule of investment success is to never lose money. Or to minimise the losses.

Example: If we lose 50 % of our capital, it takes us 100 % gain to break even. It is common sense then that the more we lose, the harder it is to get ahead. It is easier to get a satisfactory result if we never lose money. Therefore, min(risk) is important.

With min(risk), we can make tons of mistakes and still turn out fine. Without, making one mistake will get us into trouble.

The Relationship Between Risk and Reward

Investing involves risk. Therefore, we must examine the relationship between risk and reward.

Common sense has it that the higher the risk, the greater the return. But this is only true up to a certain extend. Higher risk also means greater probability of ruin.

When taking high risk, there are two possible extreme outcomes: extremely good or extremely bad results. The latter is more probable than the former. If we take extreme risk, the end result would most probably be bad. Therefore, higher risk does not always lead to higher return.

However, if no risk is taken, no change will happen. We need to somehow take some risk to achieve our objective to maximising our return.

Risk Paradox

It is bad when we take no risk at all. It is also bad when we take extreme risk. There is a dilemma.

One of the fundamental principle in economics (refer to Naked Economics: Undressing the Dismal Science) could help us deal with this dilemma. It is called the law of diminishing returns which states roughly that increasing investments (e.g.: in production) will lead to increasing returns but only up to a point. From that point onwards, more investments will lead to decreasing returns.

That law can be summarised with an inverted-U curve below.

The Law of Diminishing Returns

The Law of Diminishing Returns

Kelly criterion (refer to Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street), which is a formula used of optimal money management in investing or betting, is also having a shape of an inverted-U curve.

Kelly Formula

Kelly Formula

Another example would be the use of salt in our everyday life. If we don’t use salt at all in cooking, the food will be tasteless. Adding a little bit of salt will make the food tastier. However, adding too much salt will spoil the meal. This phenomenon can also be represented by the inverted-U curve.

Inverted-U Curve

Inverted-U Curve

The inverted-U curve describes the non-linear characteristic of reality. It tells us that more is not always good just like risk. There is an optimal point between the two extremes where the return is maximised.

Being inspired by the above observations, we know that the optimal risk level is somewhere in the middle. Most people don’t like risk. In fact, people are risk-adverse by default as proven in prospect theory (refer to Thinking, Fast and Slow). But the greatest return is achieved by taking a moderate risk. To compromise, we need to make the risk as low as possible but not lower. The concept is similar to what Albert Einstein had famously said “Everything should be made as simple as possible, but not simpler”. The same for risk, it should be kept as low as possible, but not lower.

How to min(risk)?

We learn that we could increase our odd of success by keeping risk as low as possible but not lower.

Here are some pointers to reduce the risk of ruin.

  • invest for the long term: countless of studies have shown that the longer we invest (e.g.: ten years and beyond), the least likely we are to lose money.
  • invest in low volatility stocks: high volatility stocks are always considered as high risk stocks. Low volatility stocks have the opposite effect. With lower volatility stocks, we can keep the risk as low as possible. Low volatility stocks are the result of less people looking at them. They tend therefore to be under-priced or overlooked by others.
  • invest in companies with cash: cash is king. Companies with plenty of cash can weather financial storms much better than companies with no cash.
  • acquire cheap asset by buying at low price: margin of safety. The wider the margin of safety, the lower the risk. In investing, the more we overpay for something, the higher the risk of losing money.
  • diversify: diversification is the only free lunch in the market. It avoids the non-systemic risk of investing in a single company. Diversify in 25 to 30 stocks has lower risk than concentrating on single stock.
  • avoid leverage: leverage is good when time is good. It is a disaster when time is bad. We need to make sure our investment can weather all seasons by avoiding leverage.
  • invest in knowledge: read and learn as much financial knowledge as possible. Knowledge reduces risk. Being able to think independently is critical when investing.

How to max(return)?

After keeping the risk under control, it is time to focus on max(return).

  • find growth in earnings: not all growth is created equal. Some growth is organic (e.g.: high returns on capital) which may be slow but steady. Some growth is artificial (e.g.: over-investment) which may be fast but non-sustainable.
  • find the least capital intensive companies: some companies are cash cows. Some companies require large R&D cost, have machines to maintain, etc. The companies will have more money to return to shareholders if they don’t need those money.
  • follow dividend/income: more than 50 % of total stock returns over the past several decade are coming from dividends.
  • buy low when there is maximum pessimism: margin of safety. Margin of safety lets us kill two birds with one stone by creating low-risk and high return investments. This is often called value investing. It works and continues to work simply due to its imperfection: it will under-perform the market over short-term. People avoid under-performing stocks. Also, looking at the price range of any company over 52-week period, we notice that something is not right. How could a company’s value change so much in so short time? The market must be pricing the company terribly wrong at certain point. We could take advantage of that mispricing.
  • favour small cap: size matters. It is easier for a company with $10 million market-cap to grow to $1000 million than a company with $10 billion market-cap to grow to $1000 billion.
  • minimise cost: trading cost matters. Keep cost low. 1 % fee means 1 % lower return.
  • minimise number of trades: the more frequent you buy and sell, the more miserable your results and your life are.
  • be patient: stocks take time to turn into a 100-baggers. 25-years are the average time for a stock to return a 100-bagger.
  • stay away from the stock market: out of sight, out of mind. We make better decisions without the influence of Mr Market.

Styles of Investing

Knowing how to min(risk) and max(return), we can come up with an infinity of styles of investing.

Currently, there are many documents that describe different styles of investing which incorporate the min(risk) and max(return) approach. Here is a list of applications for reference:

There are many roads that lead to Rome.

Whether it is a long-term (passive) or short-term (active) style.

I prefer long-term and passive investing with the minimum maintenance investment like timberland investment. This is because timber just grows year in and year out with no human intervention. It protects us against inflation and deflation. We can never have enough of it.

Harvard University invests a lot of its endowment fund in timberland in Brazil and Australia (refer to The Alternative Answer: The Nontraditional Investments That Drive the World’s Best Performing Portfolios).

Buying companies that grow like timberland make me sleep sound and nice at night. This is the objective of solving the investing problem.

Short-term and active investment style using momentum is another possibility but more work is required. It all depends on personal preference.

Final Thoughts

Emotion moves the stock price. It makes the price fluctuates. It is also contagious.

People are either shunned by volatility or addicted by it: extreme cases where in one case people avoid the market completely while in another case people are taking too much risk.

Know your limit else the reality will teach you a costly lesson.

It is easy to understand why some people are addicted to high volatility stocks: they lead to get-rich-quick fallacy. Stocks that double in day are wonderful. Stocks that halve in a single day is another story.

Be a contrarian by buying low volatility stocks is one example.

Another possibility is to make use of volatility. Volatility is value investors’ best friend. For value investors, volatility is not a risk. It is a tool for us to buy low and cheap. We can take advantage of it.

Investing using min(risk) and max(return) approach is a good bet. We have a lot of wonderful results documented in the list of reference above. The world of investing is full of possibilities.





The Survival of The Luckiest

Today is your lucky day.

Luck fascinates me. It is always an interesting topic for me. Anything that is related to chance, randomness, or luck intrigues me. This leads me to the following observations.

In today’s world, it is no longer the survival of the fittest, or the strongest or the most adaptable. It is the survival of the luckiest.

There is No Reason for Our Existence on Earth

Only those who are lucky can survive. And those who are extremely lucky, thrive. It goes naturally that those who are unlucky get eliminated. We are the lucky ones. Some species of animals are extinct. They are the unlucky ones.

Environment plays a big role in explaining luck. External factors, that are random and unpredictable, are influencing everyone’s life. Different environment promotes different culture, different atmosphere and different style of living, therefore creating different outcome for different people.

The “weak” (e.g. patients who are very sick) survive thanks to easy access to the latest technology (e.g. medicine). They can then thrive. It is the environment that is the most adaptable that leads to the survival of the luckiest (or the weakest). For people that don’t have access to this modern environment, they die.

Those who have easy access to resources will have higher chance of surviving. Those who do not, disappear.

The riches or those who have the resources can shape their environment. Therefore, change their destiny.

How to Be Successful?

Those who climb to the top are lucky, given the large pool of skilled and talented people that we have. Most people are intelligent and hard working. But only a few are at the top.

What explain their success? What explain the shape of the distribution curve, especially the farthest right corner? Luck. The luckiest are at the farthest right corner of the curve. They have the right opportunities, the right environment, the right background, the right connections, the right timing, etc.

You don’t have to be the best. You just have to be lucky.

Embrace Luck in Your Life

The force of luck is powerful even though you have little control of it. It can push you to the stratosphere or kill you.

Luck favours the prepared mind. You don’t know when luck will hit you because it is random and elusive and hard to “reproduce”.

Don’t be fooled by randomness. Someone living better than you are not necessarily smarter (or dumber) than you. Randomness alone can creates a variety of experiences in this world. Having an open mind could let you see this world more objectively.

Anything could happen in this world. You can be extremely lucky one day if you (are lucky enough to) live long enough to see it.

Get Lucky by Taking Calculated Risk

999 out of 1000 entrepreneurs fail. Those who succeed are lucky. Those who are extremely successful are extremely lucky. Entrepreneurship is never easy.

Most businesses fail. Given this fact, those businesses that thrive and are extremely profitable and seem like making everything right have stroke the life jackpot. They can milk their fortune for several generations or destroy them at their will.

It is not necessarily the best businesses that survive but the luckiest.

You can tap into their “luck” by buying those “lucky” businesses via the stock markets and prosper with them. This is a win-win situation. These businesses get lucky so that you don’t need to be lucky to get lucky.

You need to expose yourself to luck. Luck sometimes can be (mis-)classified as risk.

You increase your chance of success by buying the proven-to-be-lucky companies that have large earnings. This is the calculated risk.

Stock is The World Greatest Asset Class

In such a world that favours the luckiest, there happens to be one single thing that could bring luck to everyone. It is the stock.

Stock represents a business.

Business pays taxes which are used to develop the country and to pay government bond interest.

Business also pays corporate bond interest.

Business pays rent for properties and other real estate.

Business buys commodities (metal, materials, etc).

Business pays salaries.

Business innovates so that we can live a better life.

Business supports all finances in the world. Therefore, it must have the highest returns of all asset classes.

It is lucky for us to have invented the stock market. Within it, everyone prospers. We are lucky because our economic system, which is supported by a variety of businesses, works extremely well.

Most people are working very hard everyday in the system and some get extremely lucky to be rich and therefore can afford to live a different life.

Final Thought

Finally, luck is not that out of reach after all. We are already living in such a lucky environment.

A simple thought that any time and any where in the world, there are some companies that are getting lucky can make me happy because that brings opportunities for all of us.

You can change your life by moving towards where the resources are. One imperceptible small step at a time. By doing so consistently, you increase your chance to success. Over time, you maximise your lucky factor and you could be the luckiest person on earth.

Double Your Money Within Five Years Through ETFs

Exchange-Traded-Fund (ETF) is a game changer in the investment world. It creates a movement in the right direction where everyone can invest passively in index funds or any market sectors around the world in a very low-cost manner.

Without ETF, people who would like to invest in equities to participate in the economic growth would either invest directly in individual stocks or through mutual-funds.

Individual stock picking is not a trivial skill that anyone could learn easily. It requires tremendous time and effort. It is not everyone’s game. For average Joe, buying mutual funds is the only way to participate in the stock market.

Although mutual funds save people time in managing the portfolio, they charge as high as 5% commission per transaction. That is a big drag to the performance of any mutual funds. Let say a fund returns 10%, the investor only gets 5% after commission. Worse, most mutual funds don’t beat the performance of the passive index funds where the ETFs are tracking.

With ETF, people can keep almost all of the market returns since its expense ratio is usually below 1%. Let say an exchange-traded-fund returns 10%, the investor keeps 9% after expense. That is a huge advantage compare to buying mutual fund.

ETF is diversified in a way that it usually holds a bucket of companies at a time. This reduces the non-systemic risk of buying individual stocks.

ETF provides investors access to any asset classes that are categorised by value, growth, commodity, bond, geography (by country), sector, etc around the world. People can, thus, focus on allocating assets and buying the world market through ETFs.

According to research, 90% of the investment returns are coming from asset allocations instead of market timing.

Most of the ETFs are weighted according to market cap. This means that companies with the highest valuation get the biggest shares in the portfolio. There is also fundamentally weighted ETFs that meet the need of value investors where the most undervalued companies constitute the largest components of the index.

In a way, the fundamentally weighted ETFs have strategy automation built-in where the valuation is inversely proportional to allocation: the most undervalued companies are allocated the most funds. The automated rebalancing actually reduces risk and increases return.

With all the good things, ETFs also come with traps: leveraged ETFs and inverse ETFs. If you don’t understand how they work, stay away from them.

ETFs that could double your money in 5 years

CodeNameCAGR (5 Years)AUMNo. of HoldingsExpense RatioPEPTBVDistribution YieldIndex Weighting MethodologyInception DateBrand
RHSGuggenheim S&P 500 Equal Weight Consumer Staples ETF17.39%$757.02 M340.40%27.135.451.60%Equal11/01/06Guggenheim
PSCCPowerShares S&P SmallCap Consumer Staples Portfolio18.01%$124.15 M140.29%21.832.131.25%Market Cap04/07/10PowerShares
IYCiShares U.S. Consumer Services ETF17.93%$885.26 M1730.45%23.075.011.00%Market Cap06/12/00iShares
FXGFirst Trust Consumer Staples AlphaDEX Fund16.23%$2.47 B380.62%25.883.761.61%Tiered05/08/07First Trust
VCRVanguard Consumer Discretionary Index Fund17.63%$1.93 B3730.10%23.814.721.96%Market Cap01/26/04Vanguard
PSLPowerShares DWA Consumer Staples Momentum Portfolio14.70%$269.79 M300.60%27.235.410.91%Momentum10/12/06PowerShares
VDCVanguard Consumer Staples Index Fund15.10%$3.51 B990.10%25.725.073.35%Market Cap01/26/04Vanguard
SPLVPowershares S&P 500 Low Volatility Portfolio14.54%$7.64 B990.25%23.983.402.01%Volatility05/05/11PowerShares
DVYiShares Select Dividend ETF14.92%$16.27 B940.39%28.062.453.08%Dividend11/03/03iShares
KBWPPowerShares KBW Property & Casualty Insurance Portfolio20.92%$68.91 M230.35%14.631.311.61%Tiered12/02/10PowerShares
ITAiShares U.S. Aerospace & Defense ETF19.16%$879.2 M360.44%33.703.780.85%Market Cap05/01/06iShares
IHIiShares U.S. Medical Devices ETF19.34%$1.43 B470.44%36.873.891.04%Market Cap05/01/06iShares
SPHDPowerShares S&P 500 High Dividend Low Volatility Portfolio--$2.68 B500.30%20.052.453.33%Dividend10/18/12PowerShares
DONWisdomTree MidCap Dividend Fund15.80%$2.04 B9690.38%41.072.642.47%Dividend06/16/06WisdomTree
DHSWisdomTree High Dividend Fund14.64%$1.31 B9620.38%29.632.673.19%Dividend06/16/06WisdomTree
JKDiShares Morningstar Large-Cap ETF15.83%$643.76 M760.20%20.583.332.27%Market Cap06/28/04iShares
PEYPowerShares High Yield Equity Dividend Achievers Portfolio17.60%$1.02 B500.54%43.632.313.19%Dividend12/09/04PowerShares
SDYSPDR S&P Dividend ETF15.41%$14.79 B1070.35%26.413.015.40%Dividend11/08/05SPDR
VIGVanguard Dividend Appreciation Index Fund12.70%$22.56 B1840.09%24.334.242.08%Market Cap04/21/06Vanguard
NOBLProShares S&P 500 Dividend Aristocrats ETF--$2.45 B500.35%24.563.871.79%Equal10/09/13ProShares
WDIVSPDR S&P Global Dividend ETF--$82.31 M990.40%19.751.854.73%Dividend05/29/13SPDR
ETFs that could double your money in 5 years (data collected as of September 2016)

The above are some of the ETFs that have returned around and above 15% compound rate over a 5-year period. That translates to doubling your money over 5 years.

If you had $1 million at the beginning to invest in those ETFs, after 5 years, you would have $2 millions. $1 million richer.

Performance of RHS

Performance of RHS

The image above shows the performance of one of the ETFs.

Final thought

If you had been investing in stocks for more than 5 years but still were unable to double your money, you could consider to switch to buying ETFs instead. ETFs simplify things. My $0.02.