How To Cut Your Dependency on Mr. Market

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Investors spend enormous amount of time analysing companies, industries, trends and simply try to understand how the business works. That is of course very much needed and at least basic understanding is absolutely essential for correct asset valuation. However, in the very end of the valuation process one deeply subjective variable may enter into the calculation. And it may change everything.
The variable at hand is a discount rate, which is required when using the dividend discount model, discounted cash-flow model, residual income model etc. (if IRR is not used, which has its own problems). All these models are widely used. But what financial theory teaches us does not have to always be the most appropriate option. This has been shown in the well-written article by Michal Mareš, CFA, which is also available at the CFA Society Czech Republic Blog[1].
The importance of the discount rate is shown below. The table displays the upside/downside of an intrinsic value relatively to price using different inputs as growth and discount rate.
Figure 1: Influence of Basic Inputs on Intrinsic Value
Discount rate
Terminal growth rate
6,0%
7,0%
8,0%
9,0%
10,0%
2%
104%
52%
21%
1%
-14%
1%
66%
32%
9%
-7%
-19%
0%
44%
18%
0%
-13%
-23%
-1%
28%
9%
-6%
-17%
-26%
-2%
18%
1%
-11%
-21%
-29%
Source: Author’s Calculation
The question is, what should we use as a discount rate? I would divide theories into two groups. First one incorporates risk into the discount rate - CAPM, Fama-French three-factor model, Carhart four-factor model, build-up approach. These models are widely used. According to the study of Prof. Wagner at Zurich University, the multi-factor models are able to explain approximately 78% of the stock market returns[2]. That may be taken as a satisfactory high value. Capital asset pricing model, whereas, explains only 63 % of returns and an unconditional dependency on CAPM may be considered dangerous. Especially when valuing illiquid shares.
However, I would like to introduce another approach, where the risk is not incorporated into the discount rate. The concept is based on opportunity cost. Basic economic law, which has been also popularized by famous investor Warren Buffett, is taught at Economics 101. The approach has its own shortcomings, but it may provide an investor with another view on the markets. Useful especially for those, who would like to cut their dependency on Mr. Market’s volatile frame of minds.
Discount rate as a proxy for cost of equity may be also interpreted as a required rate of return. What the required rate of return should be? The opportunity cost. In other words, it should be expected return on the investor’s second best investment. What is it for the majority of non-professional investors? The return on a widely diversified index as MSCI World Index or alternatively S&P 500.
The Expected Rate of Return on S&P 500
The expected rate of return on an index may be paradoxically easier to predict than the rate of return on a single investment. The total return on an index consists of two parts. One reflecting the fundamentals and the other reflecting the behaviour of investors[3].
Let’s start with the easier part to describe, even though not easier to understand or explain - emotional return.
The Emotional Return
The emotional return is the change in P/E during the forecasted period. Price to Earnings ratio actually expresses how much are investors willing to pay for each dollar of earnings. P/E is materially correlated with investors’ emotions. If they become less risk averse or the risk-free rates are very low, as they currently are, P/E is skyrocketing.

The inverted value of P/E is so called earnings yield. It falls as the P/E rises during times of low-interest rates.

Investors simply directly or indirectly consider their opportunity costs. In other words, they compare all the investments at hand and try to pick the one with the highest risk-return profile. If the P/E is low (earnings yield is high), the investment is more appealing.

But what earnings yield is high enough? The answer for the this question lies once again in the principle of opportunity costs. The relationship may be shown i.e. using the S&P 500 Earnings Yield. As the FED rates fall, bond rates fall and consequently earnings yields fall, since the investors shift their cash into more appealing stocks. As the interest rates stay lower for longer, investors become less risk averse. Money is cheap, its “wage” (interest rate) is low and hunt for yield begins.
Figure 2: Fed Funds rate and yields relationship






Source: FRED Economic Research, Shiller’s Data[5]
Change in P/E isn’t only the outcome of interest rates, but is also influenced heavily by investors fear or greed. Emotions are unfortunately extremely hard to quantify and economists and psychologists will have to come together to figure this out. Currently, the most famous proponent of necessity of adding irrationality into investors consideration is Nobel Prize Winner Robert Shiller. Shiller’s wife is a clinical psychologist, which is I believe more than a coincidence.
The Fundamental Return
The fundamental return is determined by adding earnings growth and dividend yield. It is the product of real economic variables - productivity and growth[6].
In general, growth investors focus on the earnings growth, income investors on the dividend yield and value investors on the low P/E ratio. The superior investor should focus on all three components.


To prove that the theory fits into to the real world, I have calculated fundamental and emotional returns of S&P 500. The sum of the two parts fairly well explains stock market total returns over both long and short term periods. 
Figure 3: Expected return model’s application on S&P 500
(values as CAGR)
1990 - 2015
2005 - 2015
Earnings Growth
6,2%
5,6%
Dividends
2,1%
2,1%
Fundamental Return
8,3%
7,7%
Starting P/E
15,1
20,0
Ending P/E
20,0
20,0
Emotional Return
1,1%
0,0%
Total Return
9,4%
7,7%
Source: Author’s Calculation
In addition, the longer the holding period is, the more important the fundamental return is. Over the very long-term horizon, the effect of emotional return is marginal. For example if the P/E contracted from 20 to 15 over the 30 years, it would make only -1 % a year CAGR[4]. Over such a long-term periods, dividend yield and earnings growth rate are much more important than “market noise” displayed in P/E ratio. As the period becomes shorter, the change in P/E starts to be more important. The variable is, nevertheless, unpredictable over the few months or years horizons. Investment for such a short-term period is a pure speculation, which only disguises as investment.
Figure 4: Contribution of Fundamental and Emotional Return to the Overall Market Return

Source: Financial Physics
In order to calculate reasonable expected return, investors should determine values of the three basic components in the model. These components still have their own drivers. It depends on an investor what granularity he chooses. The chart below shows the basic principle, nevertheless, does not seek to depict all the meaningful variables.
Figure 4: Fundamental Return’s Drivers
Source: Financial Physics
Expected rate of return on S&P 500 may be as shown in the table below. The calculation is based on a trend of variables returning to their average (based on 2003 - 2015 period).
Figure 5: The Expected Return on S&P 500
next 10 years
Terminal
Real Sales Growth
3,97%
3,97%
Change in Net Margin
-0,97%
0,00%
Inflation
1,00%
2,00%
Earnings Growth
4,00%
5,97%
Dividend Yield
2,00%
2,00%
Fundamental Return
6,00%
7,97%
Starting P/E
23,56
20,06
Ending P/E
20,06
20,06
Change in P/E
-1,58%
0,00%
Emotional Return
-1,58%
0,00%
Total Return
4,42%
7,97%
Source: Author’s Calculation
As a matter of course, different investors have different beliefs and the ex-ante rate of return will vary. The concept, however, stays the same. The expected rate of return should be also calculated for every year separately, since the expectations i.e. for inflation will vary.
Opportunity Cost as a Basis for Discount Rates
The previously described theory explains what drives the total return on S&P 500. How is it connected to the discount rate? As was stated at the beginning, the required rate of return should be the rate of return on the investor’s second best investment. If an investor’s second best investment is a simple ETF on S&P 500, it’s expected return may be taken as an approximation for his cost of equity.
That is still not the end of the story. A sound investor has to create a margin of safety to take risk into account. The concept greatly explained by Benjamin Graham is still important to the present. Here, unfortunately, the art part of the investing comes. Investors may calculate the intrinsic value of a company using the expected rate of return on an S&P 500 as a discount rate and then apply M-o-S of appropriate value. That should give them very specific idea of the investment being undervalued, fairly valued or overvalued. The margin of safety vary, but usually will be in 20 to 50 percent range.
It is of high importance to say that the root of valuation must be an investor’s understanding of the business. Without such a knowledge not only he won’t estimate the expected cash-flows correctly, but his approximation of the appropriate margin of safety will also be of a poor quality.
Interesting fact is that CAPM is not that much different from the previously explained theory. Its form is widely known.
The beta of the whole index is by definition equal to 1. Then, the cost of equity according to CAPM is also equal to expected market return. The difference is obviously when calculating cost of equity of individual companies, which do not have beta coefficient equal to one.
Conclusion
Milton Friedman once said: “It takes a model to beat a model.” That holds true till these days. The assumptions of CAPM or multi-factor models are not 100 % reasonable, but the models are able to predict market returns fairly well.
The goal of this article was to introduce different way of approaching the discount rate without using beta and being dependent on market volatility. Currently, analysts value the companies and come up with target prices of various values. Although one of the assumptions of the CAPM model is market efficiency. Target price should be then always equal to the current price. Analyst’s position, who use the CAPM, is therefore at the very least ambiguous.
Model using the opportunity cost is by no means perfect. It shifts the problem of risk-counting from the discount rate to the margin of safety, but fails to quantify what its value should be. However, it may give investors and analysts useful view on the markets and with enough experience also help with coming up with an appropriate cost of equity (which is not dependent on Mr. Market’s mood). Naturally, analysts may use both a standard model and the introduced model to check how consistent the cost of equity is.
Author: Michal Šperka


Zdroje:
1) Do cen a do melounů se nevidí. CFA Society Czech Republic Blog [online]. [cit. 2016-11-21]. Dostupné z: http://cfasocietycz.blogspot.cz/2016/09/do-cen-do-melounu-se-nevidi.html
2) CAPM vs. Multifactor Models: Evidence from Switzerland. University of Zurich [online]. [cit. 2016-11-21]. Dostupné z: https://www.merlin.uzh.ch/publication/show/11247
3) The Importance of Dividend Yields and Earnings Growth to Stock Returns. Morningstar [online]. 2016 [cit. 2016-11-21]. Dostupné z: https://sg.morningstar.com/ap/news/Market-Watch/115502/The-Importance-of-Dividend-Yields-and-Earnings-Growth-to-Stock-Returns.aspx
4) CAGR = Compounded Annual Growth Rate
5) Robert Shiller's Data [online]. 2016 [cit. 2016-11-21]. Dostupné z: http://www.multpl.com/

 6) Financial Physics Model. Financial Physics Model [online]. 2016 [cit. 2016-11-21]. Dostupné z: http://www.financialphysics.net/model.html

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