Simple Mathematics To Know For Investing

Mathematics, or math/maths, depending on which part of the world you came from, is a subject which almost all of us had encountered in school, and somehow developed into a sort of love-hate relationship with it. However, like it or not, maths (I shall use this short form for this post) is inescapable from our daily lives, such as calculating how much change to get back for a $3.50 meal with a $10 note, and whether two six-inch pizzas are equal to a 12-inch one, etc.

For investing, I shall present two maths concepts to better your knowledge.

 

(Picture credit: athree23 from pixabay.com)

 

#1: Compounding

The famous physicist Albert Einstein once quoted that compounding is the eighth wonder of the world. Yet, several people did not know that there is a second part to the quote, which is “he who understands it, earns it…he who doesn’t…pays it”.

Let us understand the basics of compounding. Supposedly, you deposit $1000 in a financial instrument that pays you a 5% returns every year. After one year, you would have a total of $1050 ($1000 + (5% of $1000 = $50)). After the second year, you will get $1102.50 ($1050 + (5% of $1050 = $52.50)), and so on. For any given number of years (n), the compounding formula is:

P + (1 + r) ⁿ, where P is the principal (the initial $1000), r is the returns (5%) and n is the number of years.

The above illustration fits into the “he who understands it, earns it” narrative, but compounding also has a dark side to it, which is the “he who doesn’t…pays it” part. How so?

Instead of returns on the r, replace it with the bank interest charges that you need to pay for a loan, or the annual inflation rate. Imagine taking out a loan that has double digit interest rate, or the value of your $1000 today becoming $995 next year.

Hence, there are two lessons to be derived here; one is to avoid high interest-bearing loans, and the other is to invest your monies with decent returns instead of keeping it and getting eaten by inflation.

 

#2: Percentage Gain And Loss

I came across a maths scenario that goes like this:

I had lost 50% this year, so I need to gain 50% back to make it even.

If you remove the “%” behind, yes that is correct, but in a percentage, it is based on something and not an absolute value in itself. Using the scenario mentioned, I had lost 50% of $1000 which is a $500 loss and that means I have $500 left. Making it back 50% of what I had left (50% of $500 = $250) is only $500 + $250 = $750, and I still have a shortfall of $250 to the original $1000.

For percentages, the formula requires two values: the initial and the final. Thus, percentage change is:

(Final value – Initial value) / Initial value x 100%

So, to go back to $1000 from $500, the actual required percentage gain would be:

($1000 - $500) / $500 x 100% = 100%

Putting in perspective, here are the percentage losses and the actual required percentage gains to break even:

Percentage Loss	Actual Percentage Gain to Breakeven
10%	11%
20%	25%
30%	43%
40%	67%
50%	100%
60%	150%
70%	233%
80%	400%
90%	900%

 

After looking at the table, some of you may feel daunted by the prospect of losses and the subsequent larger jump to return. For a share price drop of say, 30%, 43% is needed to go back to breakeven, and some viewed a 43% jump is a tall order.

But there are numerous examples of prices that recovered, and then eventually surpassed the original price. This is true for counters that have strong fundamentals, whose prices were, to say the least, temporarily crashed due to bad news that could possibly be affecting only for a short term, and this presented a good opportunity to average down and load up.

Where Did You Get The Capital From?

During an investment discussion, one of my acquaintances had asked an interesting question, which is:

“You have been updating about which counter you had bought into, and you seldom sell any. Where did you get the capital from?”

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Here are the capital sources:

Capital Source #1: Cash Injections

If you had read the makeup of The Bedokian Portfolio, there is a small portion (earmarked 5% for our case) dedicated to cash. This amount is purely used for investing, and it is not mingled with our normal savings and emergency funds. This is the major capital source especially for our portfolio build with disposal income.

So, what are the tributaries contributing to this cash portion?  On a regular basis there are two: from the portfolio itself (dividends from equities, distributions from real estate investment trusts, coupons from bonds and interest from cash in banks) and monthly contributions from our salaries. This is typical for most people who have an investment plan and portfolio in place. 

As the portfolio grows over time thanks to capital gains and compounding, so does the yield amount, which is fed into the cash part. A 5% cash yield on a $10,000 portfolio is $500, but a 5% cash yield on a $100,000 one is $5,000, and $5,000 could purchase more securities than $500. Add this to your regular contribution, which may have increased thanks to rise in salaries, you would have a larger cash pool to invest with.

There are further exceptions unique to us, such as liquidating our past investment-linked plans, endowment funds and a matured child education endowment policy, and they greatly increased our cash injections.

Capital Source #2: CPF-OA And SRS

The next capital source for us is our CPF, specifically the CPF Ordinary Account (CPF-OA). Since we had finished our mortgage payments and had hit our prevailing Full Retirement Sum, the door for investing the CPF-OA had opened. The main aim of investing in CPF-OA is to have better returns than the current 2.5% rate, though with some added risk. The use of CPF-OA as a capital source comes with limitations, such as the choice of securities and the amount used.

35% of the investible CPF-OA savings can be used for individual local securities and selected exchange traded funds (known as the “35% stock limit”), and a larger amount is allowed for professionally managed products. We invested using funds from these two sub-pools in the CPF-OA, though not to the limit, giving us some spare capital for future allocation.

For our SRS, though miniscule as compared to our CPF, it is still a source of capital that can be deployed, if necessary, though for now it is used on a robo-advisory portfolio.

Conclusion

My acquaintance was a bit surprised and felt “awakened” by the answer, because it is obvious yet hidden in plain sight. I am glad that he had learnt something new, and I hope you had some takeaways, too.

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Alphabet And Apple: Latest Quarterly Results

The past week had seen some notable technology companies reporting their quarterly earnings. For this post, I will look at the two holdings which I had declared must-haves for an investor who is venturing into the United States (U.S.) market for the first time, and we will see if this trend continues to be so.

Apple MacBook showing Google website (Picture credit: Firmbee from pixabay.com)

Alphabet

On 29 Oct 2024, Alphabet had announced stellar third-quarter earnings, with earnings per share (EPS) and revenue beating estimates by 14.6% (US$2.12 vs US$1.85) and 2.3% (US$88.27 bn vs US$86.30 bn) respectively. Overall, revenue increased by around 15% year-on-year (YOY), with the Cloud segment revenue jumped nearly 35% YOY. Other major segments such as Search Advertising, YouTube and Google Play increased 12%, 12% and 28% YOY, respectively.

The share price jumped to above US$180 before settling at US$172.65 by the week ending 1 Nov 2024. This represented a year-to-date (YTD) performance of +22.51%.

Apple

Apple announced their fourth-quarter earnings on 31 Oct 2024, with EPS and revenue beating estimates by 2.5% (US$1.64 adjusted vs US$1.60 estimated) and 0.4% (US$94.93 bn vs US$94.58 bn estimated) respectively. Services and iPhone revenue streams improved 16% and 3% YOY respectively, but the overall revenue reduced by 1% YOY, which was dragged down by MacBook (-34% YOY), iPad (-10% YOY) and Wearables (-3% YOY).

Apple’s share price dropped from the US$233-ish to US$222-ish, but YTD is still profitable at +15.78% by the end of 1 Nov 2024.

The Bedokian’s Take

Both companies share common characteristics with each other (besides sharing the same first letter): Both are part of the Magnificent 7 that saw huge growth over the past couple of years; both are leveraging on the rising trend of AI (artificial intelligence or Apple Intelligence) in their products and/or services; and both are magnets of suits from regulatory authorities worldwide and targets of policies in the current geopolitical landscape. These in my opinion are the make or slight break for Alphabet and Apple.

Valuation wise, Alphabet seems to be “cheaper” than Apple in terms of the Price-to-Earnings (PE) ratio. As of 1 Nov 2024, Alphabet’s PE ratio was at 22.9, lower than Apple’s 36.6, and the current S&P500 PE, which is to be seen as the “average”, was standing at 29.2. 

Though financially, the two are fundamentally strong in their balance sheets and free cash flow, the main concern for Apple is that it is facing a decelerating revenue growth. This would impact its valuation and subsequently may cause a downward pressure on its share price. Still, based on the latest number of active Apple devices worldwide, it climbed from 1.5 billion in 2020 to 2.2 billion in 2023¹, demonstrating its wide moat effect. As for Alphabet, it still holds market leading services like YouTube and search advertising, so the moat is relatively safe.

With the companies’ resiliency shown in their moat status, I still opine that they are good to go, though circumstantially for my case I would view it as an average up. A thorough fundamental analysis is still required on your end should you want to enter them for the first time.

Disclosure

Bedokian’s average price for Alphabet (US$131.43) and Apple (US$93.07) based on US$/S$ exchange rate of 1.32.

Disclaimer

1 – Laricchia, Federica. Number of Apple’s active devices in selected years from 2016 to 2023. Statista. 19 May 2023. https://www.statista.com/statistics/1383887/number-of-apple-active-devices/ (accessed 2 Nov 2024)

Investing Your Supplementary Retirement Scheme Account?

Supplementary Retirement Scheme, or SRS for short, was introduced in 2001 and it is part of the Singapore Government’s multi-pronged strategy to address the financial needs of a greying population. It is a voluntary scheme that complements the Central Provident Fund (CPF). Thus, the SRS forms part of the basic make-up of our portfolio multiverse structure, along with the CPF and investment portfolio using disposable income. 

Besides saving for retirement, the monies that go into the SRS account are eligible for tax relief, so there may be some tax savings depending on the total relief amount and income bracket of the individual. The contribution limit for Singapore Citizens and Permanent Residents is SGD 15,300 and SGD 35,700 for foreigners per calendar year, and that means the deadline for the contribution is on or before 31 December.

 

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Should I Open An SRS Account?

Before jumping into the how of investing in one’s SRS, we need to address the why first, and honestly there is no correct answer. In my view, if you have some spare cash lying around and want to reduce your tax bill, why not start it? 

Granted that the spare cash can be deployed into your disposable income portfolio, but that does not bring down your tax payable. Similarly, you may have maxed out your CPF contribution limit and still have some more headroom to the SGD 80,000 personal income tax relief cap. If you had hit both aforementioned conditions, then the case for opening an SRS account is stronger.

Even then, if you had not hit those conditions, you could still open an SRS account, like my case; I want to reduce my tax payable, so I just contribute to it. When I started my SRS, my CPF SA had already hit the prevailing full retirement sum for some time, so any further topping up via voluntary contribution does not invite tax relief. Also, I view SRS as a form of forced savings from which I have a stash of funds by age 62 (for me. Now is 63).

 

Investing Your SRS

If left uninvested, the funds in the SRS earn 0.05% per annum based on the latest information available, which is akin to a typical savings account. From an investment viewpoint, that yield hardly compensates for the inflation rate, hence investing it is a no-brainer option.

Unlike CPF where there are limited investable amounts and choices, you can plonk in the entire SRS into various financial instruments (shares, bonds, exchange traded funds, unit trusts, etc.), endowment annuity plans, bank fixed deposits and bank structured deposits. As with any investment decision, the choice of what to invest in depends on your product preferences and familiarity, risk appetite and tolerance. You can have more than one type of product within your SRS, for it is in itself, a portfolio universe.

 

Open Your SRS

If you have yet to open an SRS account, it is advisable to do so as soon as possible. The official retirement age in Singapore is set to go higher at 64 after 1 July 2026¹. Opening the SRS account would “lock” the withdrawable age at the prevailing retirement age, i.e. if you open now, you are able to start drawing down your SRS account from age 63, regardless of what is the prevailing retirement age when you reach 63. You can have only one SRS account, and you can open your SRS account with either DBS, OCBC or UOB.

 

Bonus Paragraph: What Is Inside The Bedokian’s SRS?

Now I am doing a regular contribution to a robo-advisory portfolio consisting of 60/40 fixed income/equities make-up, with an annualized internal rate of return of 9.48% so far. As I do not invest the whole works and have spare funds inside, I may deploy the balance in individual securities. 

Disclaimer

Reference

Supplementary Retirement Scheme. Ministry of Finance. 7 Dec 2017. https://www.mof.gov.sg/docs/default-source/default-document-library/schemes/individuals/supplementary-retirement-scheme/srs_booklet---7-dec-2017e42cafd2dab847f78b5cfb6919b476b2.pdf  (accessed 20 Oct 2024)

 

1 – Boo, Krist. S’pore retirement age to go up to 64 in 2026, re-employment age to rise to 69. The Straits Times. 6 Mar 2024. https://www.straitstimes.com/singapore/politics/s-pore-retirement-age-to-go-up-to-64-in-2026-re-employment-age-to-rise-to-69 (accessed 20 Oct 2024)

Know This, And You Are Halfway Knowing How The Market Works

I admit that the title of this post sounds like a click bait, but it is mostly true, at least based on my observations and conclusions.  In a way I had somehow stumbled upon a hypothesis that works most of the time.

Picture generated by Meta AI

So, what is this wondrous hypothesis that could half answer how the markets work?

It goes like this:

Capital, assumed it is limited at the point of time, would either flow to assets that provide the most deemed yield, or to perceived safe assets, or both.

In layman speak, it would be:

Capital would go to securities that provide “more bang for the buck” and/or to a perceived safe haven.

If you had been reading my blog for at least the past three years, you may find the second italicized quote familiar; I had mentioned something along that line in this post, where I also emphasized on the importance of diversification. However, we can apply more from this hypothesis besides just diversification, and the accompanying trait of rebalancing. One way is to go contrarian.

 

Going Contrarian

The good thing about this hypothesis is that you can counter its logic and still profit from it. This is known as “going contrarian”.

When capital starts to move fast and huge, like a flash flood, you will notice big movements in the prices of assets and securities. As a retail investor, when these things are happening, it may be a bit late as other people would have jumped on the bandwagon before you, although maybe you are lucky enough to be at the tail end of it. The contrarian part is, since most are going with the metaphorical wave, why not go against it?

The thing about going contrarian is not to do it wholesale and blindly; it is important to pick the right ones and capitalise on it. For instance, if you are an active investor who goes for individual equities and real estate investment trust (REIT) counters, picking those that were financially healthy but got unfortunately dragged down by the overall bear situation was a good case of going contrarian intelligently. 

Though the contrarian way sounds like an act of portfolio rebalancing, which is long term in nature, it could also be used in medium term or short trading terms, too. 

Going The Way Of The Dodo

As an investor, whether going for growth or dividends, we like to own companies that are near-monopolistic, or at least having a wide moat, as they are seen to be financially stable and strong given their steady or growing user base of their products and services. However, due to some poor management decisions and foresight, a great company may devolve into good, then bad, and then gone, either being bought over by someone (partially or fully) or doing business in some other fields. There are a few classic examples of these companies; the oft-reported stories would be Kodak and Nokia, where they had lost their dominance in their main products.

Picture generated by Meta AI

While it is easy to point out the causes of past declines due to hindsight, at present we do not know if a company and/or its product and/or service is facing obsolescence. While there are many potentials out there now, sometimes a change in management team, product or service range, or “white knight” investors, may save the situation.

The Bedokian’s View

As mentioned, it is not easy to identify such companies especially when things are still in a flux. The good thing is, except for companies that engage in financial fraud and/or suffering from a huge unmitigated public relations disaster, this decay generally would take several months to years to develop, so observant investors could see the writings on the wall and get the hint that it is time to say farewell.

The first thing an investor must know is not to fall in love with any counter, and not to harbour any hope given the known not-so-good circumstances surrounding the company. Love and hope, though good attributes in a personal sense, are not to be brought into investing, where staying objective and rationale is key.

Next up, we shall look at the numbers, in particular revenue and free cash flow. A profitable company would minimally have a slight growth in revenue and a not-so-volatile free cash flow. There are other metrics such as return on investment (ROI) and return on equity (ROE), but these are sector/industrial specific and cannot be applied in general. Though typically I tend to look at over two to three years, if the situation deteriorates faster than it should be, then I may set up an exit sooner.

As for how to tell whether the company is getting worse in a short time, I would look at what I call trends and fads (mentioned here). Though this method of mine is to look out for the next big (profitable) thing, it could be adapted for use in guesstimating negative outcomes.

The final word here is that, even after a thorough analysis conducted and yet you still feel queasy on a counter (that unexplainable “gut feel”), then prudently it is better to just let it go. Having a good sleep is good for your physical and mental health.

Macroeconomic Lessons To Learn From The Past Two Years

Due in part to the spike in demand and limited supply of products in the aftermath of COVID-19, and a host of other reasons such as geopolitical ones (e.g. Russian-Ukrainian conflict) and the long period of low interest rates which flushed the economy with cheap-loan capital, caused inflation to rear its ugly head. The subsequent accelerated rise of interest rates that was never seen before since the mid-2000s had brought an unprecedented economic environment in which most younger investors had not experienced before.

The past two years or so had provided useful insights and learning opportunities for us investors, and that is attributed to one macroeconomic policy: interest rates. What I would be sharing in the next few paragraphs are theoretical knowledge found in economics and finance textbooks, and most of the occurrences did happen, thus giving a sort of “classic textbook examples”.

Picture generated by Meta AI

Inflation And Interest Rates

When inflation is perceived to be happening, countries whose central banks can control interest rates (like the United States or U.S.) would raise them to bring inflation down. The rationale behind this is that when interest rates go up, the cost of borrowing would go up, and this slows down capital investments by companies as loans are getting expensive. Simultaneously, for consumers, higher rates meant higher returns from safe instruments such as short-term treasuries and bank deposits, which in turn encourages saving and less spending. All these cool down the economy and lower inflation.

For Singapore, instead of interest rates, our central bank (Monetary Authority of Singapore, MAS) used the exchange rate policy to manage the monetary policy. However, it is noted that our interest rates are very closely correlated with that of the U.S.’ in terms of direction and movement (see here and here for further explanations).

Effects On Asset Classes

Now that you got the gist from the previous paragraph, you could roughly tell what are the asset classes affected by high interest rates. Positively, as mentioned, are cash (in banks and money market funds) and short-term treasuries (less than two years). Negative ones include real estate investment trusts, or REITs (being leveraged investment vehicles, higher rates affect distributions to REIT unitholders), bonds (interest rates and bonds are inversely correlated) and lastly, commodities (which do not provide yield). For equities, though the cost of borrowing may affect the growth of companies, for some sectors such as finance (banks) and technology, as well as cash-rich companies, enjoyed some boom time.

True enough to a certain extent, we saw that REITs were hammered, a lot of people flocking to erstwhile boring treasury bills and fixed deposits, and gold was somehow muted throughout 2022 and 2023, to name a few.

Everything Is A Cycle

Good times do not last, and so are bad ones. All markets and economies go through a cycle, from bust to boom to bust to boom again. Now that the U.S. Federal Reserve had brought down rates, with more planned ahead, we could see treasury bill yields going down, REITs roaring back up, gold surging ahead, etc. The undulating nature of the market and economy, and the behaviours of the asset classes during these cycles, proved the importance of having a diversified portfolio with periodic rebalancing. With diversification and rebalancing, your investment portfolio can be protected from huge downswings and capital losses can be lessened. 

Ceteris Paribus

Last but not least, all economic scenarios and assumptions are accompanied by the term ceteris paribus, which translated from Latin is “all things being equal” (read here for more information). As we know, the economy is like a machine with many moving parts, working and affecting one another at the same time (read here for the economic machine analogy). Thus, even though we can observe “textbook examples” happening, sometimes it may not go according to theory, or even so, it might be other factors at play to give it a “textbook answer”.

Still, in my view, it is better to have some basic economic and financial knowledge to get a grasp of the complicated, yet simple, world of investing.