Index tracking aims to replicate the returns of a given index as closely as possible, by trading in various investment products.

This passive investment style is getting popular because, given that company research is not required and the target index composition is known, the total expense ratio (TER) is always lower compared to the active managed fund. Also, the Efficient Market Hypothesis (EMH) stated that equilibrium market prices fully reflect all available info, nothing can be done to systematically beat the market through active management. If EMH works, the index that represents the market is already the best strategy that investors should choose. In addition, Burton G Malkiel (2003) concluded in his paper that investors are likely to achieve for higher returns by employing a passive indexing strategy than they are likely to achieve from active portfolio management.

To perform index tracking, there are several replication strategies which can be adopted. They are full replication, optimization, stratified sampling, synthetic approach and Blended/Pragmatic approach. Among which, the full replication and optimization are very common. The performance of these replication strategies is determined by tracking error (TE) in finance. It is a measure of how closely a portfolio follows the index to which it is benchmarked. The method of calculating the TE varies, but the most common one is called the standard deviation of the active returns. It is caclulated based on root mean square (RMS) as shown below:

Source: http://en.wikipedia.org/w/index.php?title=Tracking_error&oldid=544329895

For full replication strategy, australian scholars explained that TE is related to index revisions, share issuances, spin-offs, share repurchases, index replication strategy itself and fund size. For optimization approach, scholars have conducted widely research on reducing TE to solve index tracking problems. One of the popular research is done by Nigel Meade & Gerald R. Salkin (1990). They suggested that the TE can be minimized by using a multivariate model that is formulated as a quadratic programme. One must choose an objective function that is an appropriate function for tracking error ie. The difference between portfolio return and the index return. On the other hand, this function should come along with the set of constraints imposed on the solution. E.g.: restriction on the positions on each asset or the number of assets selected in the portfolio, etc. In their paper, they discussed the portfolio performance by using not just TE, but also readustment policies, no. of shares, transaction costs and portfolio & index return difference. Other TE optimization methods include Genetic Algorithms for investment portfolio selection form J Shapcott (1992), Franesco Corielli (2002)'s Factor Based Index Tracking. Methods that extend the idea of quadratic programming include An evolutionary heuristic for the index tracking by Beasley et al (2002), differential evolution to solve constrained index tracking problems by Maringer (2008) and Threshold Accepting to obtain the portfolio compositions that track market index return from Gilli and Kelezi (2002).

Though many methods about TE optimization are suggested, Marshall E. Blume and Roger M. Edelen from the university of Pennsylvania indicated that it is virtually impossible to maintain tracking errors without holding all the stocks in proportion to the index in their 2002 paper "On replicating the S&P 500 index". They stressed that omitting even a few stocks can introduce unacceptable tracking errors. To conclude, the indexing objective is easy to understand but it is actually not a simple strategy and has little room for error.

Reference:

Passive management. (2013). In Wikipedia, The Free Encyclopedia. Retrieved from http://en.wikipedia.org/w/index.php?title=Passive_management&oldid=544027300

Malkiel. B. G. (2003). Passive Investment Strategies and Efficient Markets. Retrieved from http://www.ifa.com/Media/images/PDF%20files/Malkiel_PassiveInvestmentStrategiesandEf ficientMarkets%20(2).pdf

Jin. Z., Maringer. D. (2009). Index Mutual Fund Replication. Retrieved from http://comisef.eu/files/Jin1.pdf

王偉丞. (2008). 增值指數基金績效分析-創新「多剖面調整」建構模型. 國立中山大學財務管理學系研究所.

Tracking error. (2013). In Wikipedia, The Free Encyclopedia. Retrieved from http://en.wikipedia.org/w/index.php?title=Tracking_error&oldid=544329895

Frino. A., Gallagher. D.R., Neubert. A. S. & Oetomo. T. N. (2001). Index Design and Implications for Index Tracking. Retrieved from http://wwwdocs.fce.unsw.edu.au/banking/workpap/wp9_03.pdf

Meade. N. & Salkin. G. R. (1990) Developing and Maintaining an Equity Index Fund. Journal of Operational Research Society. Vol. 41, No. 7, pp. 599-607.

Blume. M. E. & Edelen. R. M. (2002). On Replicating the S&P 500 Index. University of Pennsylvania. Retrieved from http://finance.wharton.upenn.edu/~rlwctr/papers/0208.pdf

Investors/lenders usually assess the risk/opportunity profile of the company at least based on the company's worth. There are several standard methods for valuing companies. Examples are the cost approach, market approach and income approach. For non capital intensive and insignificant tangible assets owned stocks, income approach is widely used.

The income approach employs the discounted cash flow (DCF) method of valuation. DFC derives the present value of expected cash flow based on a discount rate that is itself based on the unique risk profile for the company.

DCF consists of two steps:

1, Define the future benefits stream.

In company valuations where this is an actual track record of performance, the future income stream must be adjusted or normalized for factors like non-recurring or unusual items. We usually rely entirely on the future benefit stream as forecasted in the Cash Flow statement.

2, Apply a discount factor to the stream to determine its new present value.

The key to this formula is the discount rate. The discount rate should include all the risk factors. It represents the rate of return expected based on specific market factors and risks associated with the deal. One way of establishing rate is by using an approach called the build-up method.

The build up method creates a discount rate by adding incremental risk factors to a riskless rate of return. In other words, we start with a rate of return that I would expect froma virtually risk-free investment (historically, this has been 20-year Treasury bonds), and then add incremental risk factors to it in order to arrive at a discount rate that considers all factors associated with the investment.

The build up method has two basic categories of risk that are added to the riskless rate: systemic and unsystemic risk. Systemic risk is risk associated with macro economic factors that affect economic conditions. Examples are political climate and international, socio-cultural, and demographic issues. Unsystemic risk is risk directly associated with the investment opportunity. Examples are the size of the company and specific risk factors such as direct competition, product development, and technical risk.

The build up method can be structured as follows:

Discount Rate = Riskless rate + Systemic risk + Unsystemic risk

Detail build up method should give accurate discount rate that can help better determine the company's worth.

Reference:

Sawyer. T. Y. (2009). Pro Excel Financial Modeling: Building Models for Technology Startups. Apress.

Capital is necessary to buy the assets required to obtain future Cash Flows. The objective is to raise capital at the lowest possible cost of capital. The cost of capital under any circumstances always means the economic cost attract investors or lenders in a competitive environment where they are carefully analyzing and comparing investment opportunities. The cost of capital can be thought of as an opportunity cost, that is, the cost of foregoing the next best alternative investments of similar risk. The cost of capital is market driven, comparable to other investment of similar risk.

The managers needs to raise capital at the lowest possible cost, because the cost of capital is actually the amount of company ownership that needed to be sold for raising capital.

For example, the amount of cash needed is $650,000. If the company is valued at $1,000,000, the investor would expect 65% ownership of the company to make the investment. That is calculated by using the formula below:

%Ownership = Cash needed / Company Value

At a valuation of $1,500,000, the investor would expect 43.33 percent ownership of the company. At a valuation of $2,000,000, the investor would expect 32.5 percent ownership of the company.

So, the higher the company valuation, the lower the cost of the investment to the business owner, and less of the company will be given away.

Reference:

Sawyer. T. Y. (2009). Pro Excel Financial Modeling: Building Models for Technology Startups. Apress.

The process of entry and the ability of entrants to compete on equal terms with the established firms are critical. If new comers can develop and distribute new products on an equal footing with incumbents (e.g. equal ability to differentiate), then all products effectively are commodities.

Company is usually regarded as high value company or company with strong franchise if, compared to other companies, its both actual and potential earnings are above the average in the industry for a sustained period. (Note: Brand has value actually, but if brand value = brand build cost then brand will not be the source of value in the company)

The nature of a franchise or value is only created when the incumbent has abilities that new entrants cannot match. It comes from competitive advantage (CA) and revenue advantage (RA).

CA can be created by the government when it grants a license to one or several firms to engage in some kind of business, leaving everyone else excluded. For example, cable franchises, Broadcast TV stations, Telephone, electric utilities. Other CA can come from basic profit equation of any business:

Revenue - Costs = Profits, so CA =

1. Cost advantage: Production techniques or products that the entrants can not match
2. Patents, whether on the products themselves or on the process of producing them can create one kind of cost based CA
3. Know-how (downward sloping learning curve)
4. Access to cheap resources such as Labor and capital, but this type of CA is hard to find because most resources are mobile and plentifully available on a global basis. Entrants and incumbents can use the same time and efforts to obtain those resources.
5. Unionized Labor -> high resources costs
6. New comer, they can usually enjoy the benefits from the advancement of technology. But, this is no good to everyone, because technology is constantly advancing. So another round of new comers will enjoy the same type of CA too.

And RA usually means Customer demand, easier access to customers, habit (e.g. coca-cola case) and high cost of searching for an alternative (e.g. residential insurance market, Microsoft and IBM ,etc)

Some argue that Economies of Scale (EOS) is one type of CA. But, greenward et al. has another understanding:

If the scale of operations among all the company is the same, the EOS will be eliminated. It must be combined with customer demand advantages because cost structure advantages are very short-lived. Competition is the rule, not the exception. The conjunction of EOS and demand preferences can provide an important degree of franchise longevity, even in the face of changing technology as it allows the company to be able to spend resources on advertising and marketing. It charges less than its smaller competitors and still remains profitable. But, please don't "size" with CA based on EOS. EOS CAs arise only when a firm enjoys a disproportionate share of the relevant MKT. Relevant here means that the market that determines the level of fixed spending. For retailers like Wal-Mart or any of its competitors, distribution systems and ad programme costs are fixed by geographic region.

In the world where MKT prices already exceed asset values, and the margin of safety by that measure is negative, a contemporary value investor had better be able to identify and understand the sources of a company franchise and the nature of its CAs.

Reference:

Greenwald. B. C. N. & Kiviat. B. (2001). Value Investing: From Graham to Buffett and Beyond. Wiley.

Greenward et al. has used the case study of top toaster which is just a hypothetical company to illustrate the meaning of earning power value. Below are the details:

Annual Earning for the last 5 years = 10M

Annual ROI = 10%

As mentioned previously, the EPV formula is given that:

'EPV = adjusted earnings x 1/R', where R is the current cost of capital.

EPV = 10/(1+ 10%) = 100M

Assume: Company Asset Value (AV) = 40M (It includes: Tangible assets - Cash, A/R. Investment p.p.e, and all adjustment to reflect difference between book value and market value, Intangibles - customer recognition & support, Product design and R&D)

EPV - AV = 60M MV = 150M

As only 40M fund is required to run the business with EPV 100M or in other words the new entrants can earn 10M annually by only investing 40M (Total return: 25%), this market will attract potential competitors such as, bright entrepreneur, small appliance business owner or another toaster company executive with access to investment capital and experience with retail outlets.

They will open new plant or expand the capability of an existing one. They will also find a contract to produce the toasters, find or buy an acceptable design and develop attractive packaging and hire experienced sales agent to hawk the stuff. Worse still, it is given that toasters are a commodity product which is interchangeable and selected entirely based on the price basis.

Without a doubt, it will lead to more competition, more toasters, lower toaster prices of all toaster company, lower profit of all toaster company, lower earnings of top tasters and lower top toasters EPV...

This process will eventually end when there are so many indistinguishable toasters on the market that profits and prices have fallen to the level at which none of the suppliers earn more than the cost of capital that investors demand on their money.

To avoid this fate, greenward et al, recommends us to differentiate the product or service. (e.g. advertisement, new feature or new product design) But, if competition is still there, then cost will continue to rise, sales drop. Finally the equilibrium is reached. EPV = AV

The action of differentiation here is actually recognized as franchise which is one of the key elements of finding good company in value investing.

Reference:

Greenwald. B. C. N. & Kiviat. B. (2001). Value Investing: From Graham to Buffett and Beyond. Wiley.