Originally published by PokfuLam Investments
No, not the Church of England: Cost of Equity. In effect, it is the manifestation of the “risk” component of the basic principle of financial assets, i.e. Risk v Reward. If you can’t validly measure the relevant cost of equity, then you can’t validly weigh risk versus return.
A net present value of expected returns calculation uses a cost of equity figure as the discount rate. It effectively enables risk to be offset against returns. All you need is the right expected return stream to discount, and bingo, you have a value that you can compare to the price and decide whether to buy or sell.
All very easy, but……
Without a Model of Market Pricing, Estimating C of E is Problematic
There is a problem - the results of the process don’t mean anything individually or overall unless the results over time explain how market pricing works: what Fama (1965) describes as explaining both a large percentage of the variation in, and absolute levels of, market prices. Given the discount rate, and the process used to estimate it, has such a major impact on the price suggested, as well as the potential changes in the implied values, it becomes critical to decide on the nature of the figures used to calculate it.
What is surprising is that there remains argument over the very nature of many fragments of equity market pricing, even if the NPV of Expected Returns basis of valuation has been long-established.
There is still no basis for return streams being discounted by markets in setting prices, or over what period.
A basis for long-term growth estimates has not been established.
Is the basis for the ERP constant (and therefore risk is unchanging) as is suggested by using an average excess returns calculation, or does it change?
If the ERP does change, we don’t know what factors are most important in determining those changes.
What is the appropriate risk-free interest rate proxy for the calculation?
Does the market risk premium matter, or is the only risk that matters that of the individual investor?
The argument over whether the market equity risk premium is stable is only part of the issue. Many still argue over whether “value” at the market level is an equilibrium line that prices tend back towards (which is implied by stable ERPs), and it becomes obvious that we still have a long way to go to understand the basics of equity market pricing.
The reason that measuring risk has been a problem for so long has been the way it has been estimated for individual stocks: interest rates + average excess returns (for the market) x beta (for individual stocks). Easy. But:
Average excess returns suggest that the key input to risk estimates doesn’t change, and the calculations are generally based on periods as long as 50 years. Does anyone really believe that market investment risk hasn’t changed in 50 years? Through the GFC? In the aftermath of the Tech Bust? Post the 1987 Crash? That investment risk didn’t change in the aftermath of any of these events or all the other intermittent periods where prices have suddenly varied?
Betas are being increasingly questioned as academic analysis has accumulated against the basic assumptions of the calculations. The most important issue is that of the inability to prove efficiency (Fama (1991)) meaning that any calculation contains an unquantified error.
Even the basis for the risk-free rate of return is in question, with many using long bond rates as appropriate rather than shorter term rates (although there are still those who insist on the use of long-term bond yields despite abundant evidence to support the use of shorter term rates depending on the market). This is largely due to a basic belief that corporate value = stock value assumption: an assumption that our analysis shows to be false.
If Fama (1991) is correct in that the strong-form of market efficiency is false as a theory, and that the Joint Hypothesis Theorem means that no assumptions on market efficiency can be made without first establishing an effective working model of market pricing (and there is no reason or published basis for suggesting that he is not), then the currently accepted methodology for estimating individual stock cost of equity cannot be accurate within any acceptable margin of error.
Fama’s findings create the greatest problems for the estimation of individual stock risk relative to the market (beta). There are four key reasons for this:
The concept that actual achieved prices at the market level reflect all knowable risk factors is not provable, nor realistically conceivable;
A similar concept that prices equally fully reflect all expected future returns is also not provable or conceivable. This means that the proposition of an equilibrium pricing level that gives any kind of relevant measure of average excess returns that the market will trend towards must also be false (Fama and French (1992));
Again, the lack of validity of average excess returns as the basis for estimating risk at the stock level MUST make beta invalid as a provable and successful indicator of market relative risk.
What is not widely understood is that one of the key assumptions necessary for the effective use of beta to measure market relative risk is that stocks MUST be mature for beta to work: i.e. that the company’s fundamentals are unchanging, and therefore relative returns will be stable over time. Unfortunately, this assumption is completely unrealistic in a real-world environment. This is the layman’s version of the findings of Fama and French (1992), (1996), (2000) and (2006) amongst others.
There is the possibility that if the variation in beta is within an acceptable level of error, then it doesn’t matter. But what is an “acceptable” error? This is the problem with not having an accepted market pricing model: it becomes impossible to measure the size of the error at any point-in-time, as well as indicating what happens to it over time.
There has been considerable published work on beta in the past 20 years which shows that:
it changes (or can change) over time depending on the period that calculations are made;
even if the period remains constant, beta is not generally stationary: i.e. that there are very few (if any) stocks that remain fundamentally stable enough for beta to be strictly usable; and
very few liquid stocks comply with the key assumption that if the market stays stable over time, stock returns should stay stable. In other words, if the market index is at 1,000 points, and it goes up 100 points, then down 100 points, a stock priced at $1 should, in theory, still be $1 after the market has returned to 1,000 points regardless of the beta, and that rarely happens.
These findings are problematic individually for the use of available processes to measure risk at the stock level in valuations and to forecast market pricing performance; together, they make it almost operationally useless. This has been a major problem for the industry for decades, and there has been little progress towards overcoming the issues at hand.
If that is the case, then how is it possible to come up with an acceptable stock valuation that has any relevance to market pricing?
Simply, it is impossible, but the first issue is the return stream that is being discounted (see “Capital Gain Expectations and Prices” 18th December 2016).
However, it is at the market (index) level that the biggest practical problem arises, and if that can be successfully overcome, the answer emerges. And as with everything associated with equity markets beyond the very short-term, a working market pricing model is the key.
The Market Risk Premium
We have developed such a model, details of which we published on LinkedIn (NYSE:LNKD) on 12th December, 2016 (“A New View on How Equity Markets Work”). To reiterate, there are several key issues associated with the development of such a model. The first of these is developing a basis for forecasting future dividend and capital gain expectations being used by the market to set prices. Next, was establishing the time horizon being used by markets for those expectations. Thirdly was the establishing of the market’s risk-free interest rate used in setting prices, and the final piece of the puzzle has been the equity risk premium.
Below are the estimates of the ERP for the S&P/ASX 200 based on the development of this model.
If the model works (and there will have been no point in doing it if it didn’t), then one of the first results that can be drawn from the analysis, is to work out what ERP is implied by this IF actual market prices are matched to the model. What that means is that the calculated figure shown in the chart is the figure that equates actual market P/Es with the model’s figures.
We don’t believe that the volatility shown in the calculated number is a valid assessment of real investment risk, so thus, we have estimated what we consider a more realistic figure for the Index ERP, which is much less volatile and is shown as the “estimated” figure on the chart. The difference, in effect, must be due to pricing errors by the market.
That, of course, is still open to question. However, we have substantially reduced the difference the difference between what SHOULD be, and what IS.
There are some interesting results of these calculations. The average of the calculated figure is 7.0%, while the average of our estimate is 7.3%. These figures are not too far from the long-term average excess returns calculation generally used of 6.5%, and that is over 26 years, as against 50 years for the average excess returns calculations. We expect that there would be differences, but they are in the same “ball park”.
With the estimates, there is a degree of subjectivity, largely because of a lack of understanding of the risk premium. Firstly, you must measure it before you can analyse it, and this has always been problematic. Secondly, it becomes necessary to understand the basic nature of risk, which is still very much open to question at this stage.
This is where the issue of market efficiency is so difficult to assess, even with an effective market pricing model. However, we have looked to reduce this subjectivity by developing a separate model for estimating the “real” level of investment risk at a point in time, which is then used to quantify the estimated Index level risk.
A Model of Market Risk Measurement
This model covers 90 separate factors in four separate categories: Socio-Political Risk (Political risks, external risks, social disorder risks, and systematic risks), Domestic Economic Risk (Domestic economic factors, fiscal risks, monetary risks, and infrastructure risks), External Economic Risk (trading risk, foreign credit risk, exchange rate and capital flow risks, and foreign investment risks), and Market Factor Risks (Index asset backing, financial risk, quality of earnings, trading risks, market risk, size risk, management risk and forecast confidence risk).
Changes in each of the qualitative factors included in this analysis are quantified by the use of a survey methodology, with average change in factors and weights being aggregated to then estimate changes to the risk premium.
The fourth category, market factor risks, uses quantitative measures (Index averages) of such measures as price to book, debt to equity, interest cover, cash flow to EPS, EPS growth, average daily trading volumes and return on equity to estimate changes in underlying risk factors that change as fundamental, bottom-up factors change.
While there are many factors involved in the index risk model, we have been able to link shifts in market price (the estimated ERP) to shifts in the combined and quantified measures used. We have been able to do this by focussing on causal relationships between risk and data used to measure it. Only data that is used to measure a specific risk component is included in the analysis. This has been done to avoid the inclusion of data that may appear to validate spurious relationships, and create confusion, or what is often called ”data mining” or “data snooping”.
For those looking for academic support for these findings, these results are consistent with findings by Fama and French between 1992 and 2006. In a series of papers published in this period, Fama and French attempted to test the Capital Asset Pricing Model (of which beta is an important component) and found that one of the key features of the CAPM (that there is a fixed relationship between market movements and stock movements (beta)) doesn’t hold, and that by adding Size, and Price to Book variables (in what is called the Three Factor Model), there is a significant improvement in explaining variations in returns (risk). Additional published papers have confirmed similar findings for the Japanese, Shanghai, and Indian markets.
What we have done is to take these findings considerably further by looking at not only empirical data relationships with the market, but also causal relationships, to potentially get to a final (comprehensive) model more quickly than might otherwise be done.
So, for a data relationship to be valid in our methodology, (e.g. between the market index and dividend growth data for example) we would need to first establish a causal link between dividend growth and expected returns and/or how this would have any relationship with market risk perception.
Interestingly, Fama and French (1993, 1996) were accused of “data snooping” by authors, although others have confirmed their findings.
Measuring Stock Risk Without the CAPM and Beta
What we have also done is look to extend the findings at the Index level, to the valuation of individual stocks.
Given that an index (as a representation of the market) is merely a portfolio of stocks, it should not be a surprise that we have found that there appears to be a relationship between valuations and many of the ratios included in the Market Factor Risk calculations. Given that any data measure can only be relevant to price by impacting either a measure of expected returns, or of a measure of risk (the cost of equity), we have looked to use this data as the basis for a “fundamental beta”.
Our analysis shows the following having relevance in the calculation of this measure in descending order of importance:
Earnings Forecast Variability
Return on Equity
Size
Short-Term Market Sentiment
Liquidity
Cash Flow/EPS
Historical EPS Growth
Price/Book
Debt/Equity
Interest Cover
EPS Stability
Current Ratio
Price Volatility
By comparing each measure (for each individual stock) against Index averages, and the use of cross-sectional pricing to overcome the relative shortage of data points versus prices, we are able to combine all of these measures into the “fundamental beta” measure.
Interestingly, we have been able to show that, for the ASX200 universe of stocks, this measure explains market-relative risk across the portfolio 40% better than if the 5 year “conventional beta” is used instead. In other words, the standard deviation of valuations to prices is 40% lower if fundamental beta is used rather than 5-year beta.
Each of the data measures used is available on an on-going basis via data sellers such as Reuters, meaning that it is generally available to the market to enable the pricing of stocks. This contrasts with the assumption that “all possible information is available to the market” as is required for strong-form market efficiency to be possible, and therefore for beta to be potentially valid.
Conclusion
This work presents what we believe is a major advance in the establishment of the inputs into the valuation of markets and stocks. What is also an advantage is that the processes used are consistent with fundamental analysis processes, as well as being specific in the quantification of a view of stocks, and the factors determining that view.
The overall pricing model that we have developed (“A New View of How Equity Markets Work”: ) is the key. Without it, there would be no way to progress findings and measurement of specific factors in market pricing: specifically:
Components of the return stream expected by the market;
The determinants of those expectations;
The period of those expectations that the market is using in setting prices;
The risk-free interest rate being used by the market to set prices; and (most importantly)
The equity risk premium being used by the market to set prices at both the market and stock levels.
Hopefully, this will allow the industry to move forward in practice, and reduce the mystery associated with the behaviour of equity markets.