Baby steps in constructing a stock portfolio

Fundamentals 06-1: There are two aspects in managing any stock portfolio - construction and maintenance.  This post focuses on the construction of a stock portfolio while maintenance issues are covered in "Baby steps in maintaining a stock portfolio".

How to construct a stock portfolio

Generally, when portfolio construction is mentioned, it is with reference to asset allocation.  For example:

“Asset allocation is a broad strategy that determines the mix of assets to hold in a portfolio...Security selection is the process of identifying individual securities within a certain asset class...” Investopedia

The Oxford dictionary has defined a portfolio as a range of investments held by a person or organization.  

What is a stock portfolio then?  A stock portfolio is a collection of stocks that an investor has selected.

This then raises the following questions when it comes to constructing the stock portfolio:
  • How do you select the stocks?
  • How many stocks should you have?
  • How much to invest in each stock?
  • How do you establish the position?

This article focuses on how a stock portfolio is formed.  As such issues relating to managing the portfolio eg portfolio performance and rebalancing will not be covered here.

While many of the concepts presented are general in nature, the focus is on establishing a stock portfolio based on a bottom-up, stock-picking, fundamental analysis.

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Contents

  • Why have a stock portfolio?
  • How do you select the stocks in the portfolio?
  • How many stocks should you have in the portfolio?
  • How much to invest in each stock?
  • How to establish the position
  • Pulling it all together

Why have a stock portfolio?

If you know that a particular stock is going to give the best return in the future, you would be an idiot not to put all your money into this one stock.

The reality is that we cannot foresee the future and we don’t know which stock will perform. So, we spread our money to several stocks. We diversify thereby establishing a stock portfolio. 

The idea behind diversification is that if one stock does badly, we hope that the others will do well enough to offset the one that did badly.

Having a diversified stock portfolio then is about risk management. When it comes to risk, there are 2 schools of thought:
  • Those that view risk as volatility.
  • Those that view it as a permanent loss of capital.

However, risk management via a diversified stock portfolio is independent of how you view risk. 

More importantly, the extent of the diversification is dependent on having uncorrelated stocks. 


How do you select the stocks in the stock portfolio?

There are 2 ways to form a stock portfolio.
  • Top-down - this involves looking at big picture economic factors.
  • Bottom-up - this involves looking at company-specific factors.

Top-down

A top-down approach is a macro approach.  In many ways, it is a continuation of the asset allocation process. 

It examines various economic factors to see how they affect individual stocks.  You take into account the following to define the stock portfolio.
  • Investment goals.
  • Risk tolerance.
  • Investment time-frame.

You define the stock portfolio in broad categories or sectors such as the following.
  • Growth vs Income.
  • Conservative vs Aggressive.
  • International vs Domestic.

You then zoom in to identify those companies within the selected category.  From here, you can then either select individual stocks or ETFs that represent the category or sector. 

The following are often seen as the advantages and disadvantages of the top-down approach.
  • More efficient use of an investor’s time and attention to relevant data.
  • Allows you to diversify your investments across different sectors.
  • May produce a more long-term or strategic portfolio and favour passive indexed strategies.
  • But it may also miss out on a large number of potentially profitable opportunities.

Bottom-up approach to construct a stock portfolio

Bottom-up

In the bottom-up approach, you try to identify specific companies based on your investment criteria. You build up the stock portfolio one by one based on the appropriate selection criteria. 
  • If you are a value investor, then you select the stocks whose prices < intrinsic values.
  • If you are a growth investor, the stock selection would be based on growth prospects.
  • If you follow the Graham school, then you would be looking for Net Nets

The stock portfolio’s main focus will be individual securities performance. The pros and cons of a bottom-up approach are: 
  • It may be limited to the investor’s knowledge of individual securities.
  • Better choice as there are more stocks to pick from.
  • The portfolio may have better returns as individual companies could perform well. This is despite the performance of their industry or the current economic climate.
  • More suitable for investors with a long-term investment horizon.
  • Time-consuming.
  • Possibility of overexposure to one sector.

As a retail investor, my goal is to identify the stocks for the portfolio.  In practice, I use a combination of top-down and bottom-up approaches.

Since the majority of my effort is on individual company analysis, I call myself a bottom-up stock-picker.


How many stocks should you have in the portfolio?

By adding stocks to a portfolio that are not correlated with stocks already held, you can reduce the portfolio risk.

Studies have shown that the benefits of adding stocks to a portfolio decrease with the size of the stock portfolio.

The chart below extracted from “A Random Walk Down Wall Street” by Burton G Malkiel illustrates the diminishing return feature.

Diminishing benefit of diversification

The question then is how many stocks should you have to achieve an optimum risk profile?

Unfortunately, the question of “optimum” is not so straight forward as the following extracts show:

1)  On page 214 of their book “Investment Analysis and Portfolio Management”, Frank Reilly and Keith Brown reported that:

“The results indicated that the major benefits of diversification were achieved rather quickly, with about 90 percent of the maximum benefit of diversification derived from portfolios of 12 to 18 stocks.”

2) “We show that a well-diversified portfolio of randomly chosen stocks must include at least 30 stocks for a borrowing investor and 40 stocks for a lending investor.  This contradicts the widely accepted notion that the benefits of diversification are virtually exhausted when a portfolio contains approximately 10 stocks.”   How many stocks make a diversified portfolio, Meir Statman Jstor

3) “Increasing the number of imperfectly correlated securities in a portfolio reduces the range of its returns around the market return. Although the marginal reduction in range diminishes as the number of securities increases, holding 30 or more is clearly worthwhile.”  Portfolio Diversification Strategies, Roger B. Upson, Paul F. Jessup, and Keishiro Matsumoto, Jstor


The main challenges when interpreting such studies are:
  • In real life, the correlations between stocks are not static.
  • Many studies are based on a random selection of stocks. In practice, stock selection is not random.
  • Many of the studies are based on the view of risk as volatility. 

But more importantly, the goal of the stock portfolio is not only to reduce risk. You invest to generate returns and here lies the dilemma. 
  • A more concentrated portfolio will achieve a larger dollar return compared to a more diversified portfolio.
  • A more diversified portfolio will lead to lower risk than a more concentrated portfolio.

You then have to find a balance between these two. This is where your view of risk comes into play.  Is it volatility or permanent loss of capital?

If you believe that risk is volatility, you have a risk-reward trade-off.  You see risks as broken into systematic and non-systematic risks. 

Non-systematic risks can be diversified away while you have to bear the systematic risks.
  • The theory states that for a given level of risk, there is the best return portfolio. For a given return, there is a portfolio that has the least risk.
  • There is no such thing as the best of both factors and you have to choose which you want to focus on.  
  • The ultimate is the market portfolio and you are left with indexing. 

On the other hand, the permanent loss of capital followers believe that systematic and unsystematic risks do not capture all the investment risks. 
  • There are also behaviorial risks and investment process risks.
  • There are other risk mitigation measures than diversification. Examples are having a margin of safety, having a conservative investment process, and adopting measures to minimize behavioral biases.

Investors like Warren Buffett and Monish Prabai who follow the permanent loss of capital school believe in having a concentrated portfolio.  They believe that their knowledge of the businesses minimizes the investment risks. And they have a host of other mitigation strategies to minimize the risks. 

What are your options as a layman given that there are proponents for both ends of the concentrated vs diversified spectrum?
  • The nature of market sentiments is such that sectors tend to be correlated and it would be a challenge to find 10 to 20 uncorrelated stocks.  
  • Given this, then you may need to identify 30 to 40 stocks and then adopt a different set of measures to minimize the correlation.

Ensuring diversification

Ensuring diversification and low correlation

To ensure diversification, you should also assess the degree of concentration under various criteria. Some of the criteria that I have used to form groups include:
  • Sectors or industry
  • Market cap or size
  • Business performance or Investment type - turnaround, compounders, cyclical, dividends

The idea is to select stocks based on different economic, political, technological, and even market sentiment factors. My rules of thumb for diversification are:
  • Single stock concentration - the market value of a stock should not be more than 10% of the market value of the total portfolio.
  • Group concentration - the market value of the stocks within a group should not be more than 30% of the market value of the total portfolio.

I currently have a portfolio of 27 stocks and the profiles of the stocks are as shown below.


My portfolio sector profile

My portfolio market cap profile

My portfolio investment type profile


As can be seen, I am currently slightly over-concentrated in one size in the market cap group. This is because of the current Covid-19 situation.   This would be reviewed during the re-balancing stage.


How much to invest in each stock?

In the previous section, I have a rule that the maximum amount invested for a particular stock should not be more than 10% of the total market value of the stock portfolio.

If you follow this to the logical conclusion and allocate 10% to each stock in the portfolio, you would end up with 10 stocks. 

You can see that there is a relationship between the 3 key parameters of a portfolio.
  • The total amount to be invested for the portfolio.
  • The number of stocks in the portfolio.
  • The amount to be allocated to each stock ie the position size.

If you assume that the portfolio will have about 30 to 40 stocks, then the average amount to be invested in each stock will range from 2.5 % to 3.3 % of the total portfolio value. Of course, if the amount for each stock is not the same, then the range would be wider.  

I have mentioned earlier that there was an upper limit of 10% based on the risk mitigation criteria. How was the 10% determined?

On one hand, the 10% represents the total amount I was prepared to lose in one stock. The amount would vary with the risk tolerance of an individual.
  • A more risk-averse person may set a lower limit.
  • I doubt there is anyone who is prepared to risk 100% as it could be ruinous if the one investment tanks.

On the other hand, the 10% limits the gain from that stock.
  • If the total amount allocated to a portfolio is $ 100,000, a 10% investment in one stock is equivalent to $ 10,000.  If this stock gains 25 %, this is equivalent to $ 2,500.
  • If the amount invested in the stock was 20% i.e. $ 20,000, the same 25 % stock gain would result in $ 5,000.

You have to balance between risk and return.  What are the parameters to be considered then when determining this balance?

I found that the Expectancy Formula and Kelly Formula are helpful in determining the position size. 

Expectancy

Expectancy 

Although I am a long-term investor, I find that the trading concepts regarding expectancy can give some insights into the stock construction issues.

Trading expectancy is a calculation that shows what the typical profit is for each trade placed. If it’s negative, the strategy is a loser. If it’s positive, the strategy is a winner. 

Expectancy can be represented by the following formula.

Expectancy = (Win % x Win Size) – (Loss % x Loss Size)

A winning strategy is one where the trading expectancy is positive. You can improve the trade expectancy by either improving:
  • The win % or probability of winning.  Note that because the win and loss probability must add up to 1, a higher win probability will automatically reduce the loss probability.
  • The win-size to loss-size ratio. 

While a trader may not be able to control the win size, he is able to control the loss size by having a stop loss and a lower exposure to a single stock or trade.

Unlike a trader, as a long-term investor, the number of transactions each year is small. So, every stock should have a high expectancy.  This can be achieved by:
  • Having a large margin of safety - This affects both the win probability and the win-size to loss-size ratio.
  • Investing in dividend-paying stocks helps the win-size to loss-size ratio.
  • Developing your investment skills helps to improve your probability of winning. 

In general, the higher the expectancy the greater the amount to be invested. The optimal amount is one that would maximize the overall expected return on a portfolio. 

The Kelly Formula provides one way to determine the optimal amount.

Kelly Formula

Kelly Formula

The Kelly Formula was created by John Kelly, a researcher at Bell Labs, who originally developed the formula to analyze long-distance telephone signal noise.

It is a bet sizing formula that leads almost surely to higher wealth compared to any other strategy in the long run.
  • It assumes that your objective is long term capital growth. 
  • It reinvests profits, and thus puts them at risk. 

There are two basic components to the Kelly Formula. 
  • The first is the win probability.
  • The second is the win-size to loss-size ratio.

The Kelly's Formula is:

K% = W − [ (1−W) / R ]
 
K%  =  The % capital to put in a single investment

W   =   Win probability 

R    =   Win-size / loss-size ratio

The percentage that the equation produces represents the investment size. For example, 
  • If historically your win 60% of the time, then you can assume that W = 0.6.
  • If historically your average gain is 25 % compared to an average loss of 20 % of the investment, then R = 1.25.
  • K % = 0.6 - [ (1 - 0.6) / 1.25 ]  = 0.28  ie you should invest 28 % of your capital.

This system is based on pure mathematics and works for binary bets that do not apply to the stock market. Besides in the stock market, none of the components can be precisely quantified. 

Even if you can guesstimate the components, I find that the Kelly formula results in an investment size that is much greater than the risk cap that I have set. So, while not practical in terms of using the numbers, I find the principles applicable:
  • You invest the most in the stock with the greatest probability of winning and the best win-size to loss-size ratio. 
  • This can be translated into investing more into those where you have the best conviction and/or highest margin of safety.

Establishing the criteria

The guidelines to determining how much to invest in each stock then boil down to investing as much as possible to the ones with the highest conviction subject to the risk cap.

But in order to have a diversified portfolio, you should have 20 to 30 stocks and this determines the average amount to be invested in each stock.

In practice, I classify the 20 to 30 stocks into 3 groups based on conviction. For example:
  • Group A would be those with the better conviction - allocate 6 % to 8 % of the portfolio value to each stock here.
  • Group B would be those with the average conviction - the amount to be allocated to each stock would be about the portfolio average allocation.  
  • Group C would be those with the lesser conviction - each stock here will be allocated 1 % to 3 % of the portfolio value.
  • The total amount allocated to all the stocks would of course be equal to the portfolio value.
  • I generally have about ¼ of the total number of stocks each in Group A and Group C so that half of the stocks are in Group B.

The profile of my portfolio of 27 stocks is as follows:
  • I have 6 stocks in Group A where the amount invested in each stock averaged about 7 % of the total portfolio value.
  • I have 5 stocks in Group C where the amount invested in each stock averaged about 2 % of the total portfolio value.
  • I have 16 stocks in Group B where the amount invested in each stock averaged about 3 % of the total portfolio value.

I do not use an exact formula to determine the amount to be invested for each stock because:
  • As a bottom-up stock picker, the number of stocks in the portfolio is also dependent on whether I could find the stocks that meet my investment criteria.  There have been occasions where I was hard-pressed to find 20 stocks.
  • The position size is also affected by whether the stock is in the process of being build-up or sold off as I do not enter or exit a position in one go. Rather I do it over some time. Refer to the next section.

However, for those mathematically inclined, there is no reason why you cannot have a formula for the position size based on all the parameters that have been discussed.

How to establish your stock position size

How to establish the position

Once you have identified the stock and have a target amount to invest, do you slowly build-up to the target amount, or do you buy in one lump sum?  You can imagine a similar question when you sell.

In practice, I have never bought or sold in one lump sum. From a buying perspective, this is because:
  • If you split the purchases into several tranches, there is a chance that your average purchased price could be lower.
  • I have found that after owning a stock, I picked up issues that I missed before. This is probably a behavioural issue.  But I find it advantageous to scale into a position rather than buy in one go.

When it comes to selling, I scale out because I have never been able to forecast the peak price.  So, scaling out of a position improves my overall selling price.

However, there have been times when the price dropped dramatically after my first sale.  These are situations when there was some irrational reason for the price spike.  Unfortunately, I can only see this with hindsight.

I still scale-out over 5 or 6 tranches rather than a lump sum sale because there are not many cases of irrational price spikes.

You could improve on your average purchased or selling price if you have a way to identify the market top or bottom. I have come across advice to use technical indicators to do this. 

Unfortunately, my transaction period is usually 3 to 4 weeks.  For such short durations, I have not been very successful in identifying the market top or bottom using technical analysis.  This is after trying with trend, candlesticks, and chart pattern analyses.

In practice, I identify the target price, and then I tried to improve it through scaling in or scaling out as the case applies. 


What is the min amount to start investing?

If you take the view that you need 30 stocks to have a diversified portfolio it must mean that you should have enough funds to establish the 30 stocks portfolio.

In the Bursa Malaysia context, the minimum transaction lot size is 100 shares.  Accordingly, the minimum amount to start investing is the amount required to buy 100 lots of shares in the 30 identified stocks. Based on an average price of RM 2.00 per share, this means that you will require at least RM 6,000 to start investing.


Pulling it all together

  • Having a portfolio of stocks is part of the risk mitigation plan.
  • You can identify the stocks in the portfolio by either a top-down or bottom-up approach.  The important thing is to focus on individual stocks rather than the economy or industry. 
  • Target to have at least 30 stocks uncorrelated stocks in the portfolio.  This is a good balance between maximizing returns from concentration and minimizing risks with diversification.
  • Allocate more to those stocks with the most conviction. From a Kelly Formula perspective, this is better than allocating the same amount to all the stocks.
  • Scale in and scale out of a position rather than buy or sell in one lump sum. 

This post assumes that you have the numerical skills to analyze and value companies. If not, the formulae present here could be overwhelming.

Personally, I don't think you need more than primary school arithmetic to analyze and value companies. But then I am a number-type of guy.  If you are not numerate, rather than try to struggle to analyze and value companies, the alternative is to subscribe to some financial services such as those offered by people like The Motley Fool. Click the link for some free stock advice. They have a long track of business analysis, valuation, and risk assessment and as a member, you can tap into their library. 

END



Investment books that I have read.

Books


Comments





I actually learned valuation from this book. It took me about a year to go through chapter by chapter as I also did the exercises. 

Nowadays Damodaran has YouTube videos of his valuation lectures. The better way to learn is to first watch the relevant video and then read the appropriate chapter in the book.

 

 

 

I read this book years after I learned value investing.  Honestly, I found it dry and boring. But I read it for bragging rights rather than to learn about value investing.

If you are a newbie, I would not recommend this as the first few books to read on value investing.



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