There was a slight delay in getting me the proofs for my book, but I was able to send my edits and comments back yesterday. I think that the book should be released soon after my publisher incorporates the changes. My guess is that will be in May or June 2021.
The below is not the final look of the cover, but it should be pretty close.
In my prior blog post, I discussed how investors put money in the wrong Zoom stock and caused an unrelated stock’s price to increase by over 300% over a two-month period. Now, we have an even clearer example of how price can substantially deviate from value. On January 7, Elon Musk tweeted “Use Signal.” This was in reference to a messaging app. However, the price of an unrelated OTC pink sheet stock named Signal Advance (ticker: SIGL) that had a closing price of $0.60 on January 6 shot up and closed at over $7 on Friday, January 8. What’s surprising is that Signal the messaging app tweeted that same day that it was not affiliated with SIGL. More surprising is that, after the weekend, SIGL stock increased to over $70 at one point to close on Monday, January 11, at a price of over $38 on more than 2 million shares traded and a market cap of over $2.5 billion. This is astonishing for a company that does not have any SEC filings related to the last four years of operations, only filed its 2016 Form 10-K in March 2019 (no SEC filings two years prior to that), and reported total assets in 2016 of $2,891 (that’s less than three thousand dollars) with no revenues for each year from 2014 to 2016. By the end of the following week, SIGL closed on January 15 at $13.54, more than 20x its pre-Musk tweet price of $0.60. After another week, the closed at $6.25 on January 22, which is still at more than 10x the price before Musk’s tweet. Thus, even when investors made a “mistake” and a clear “correction” has been issued and widely disseminated, we can see that the market price of the stock still deviated substantially from the firm’s value and it can do so for a very long time.
At 4:56 AM on January 7, 2021, Elon Musk sent out the tweet “Use Signal” to his followers.
What he meant was the messaging app Signal. However, people somehow ended up buying the stock of “Signal Advance” and bidding up its price significantly This has been widely covered. For example, see articles here, here, and here,
Signal Advance is trading in the OTC/Pink Sheets and, prior to Musk’s tweet, closed at $0.60 on January 6. As we can see from the intraday price chart from CNBC above, Signal Advance’s stock moved up pretty quickly following Musk’s tweet and reached an intraday high of $9.49 early on January 8. That’s a 1,482% return from the January 6 close.
Signal, the messaging app, published a tweet at 11:12 AM on January 8 clarifying that it was not Signal Advance (see below). By that time, investors still had half a trading day to “correct” their mistake. Despite this, the last trade on January 8 was at $7.19, which is still a 1,098% return from the January 6 close. According to CNBC, on January 8, there were 874,950 shares of Signal Advance stock that traded. Not sure how many of those hundreds or thousands of investors traded after the Signal messaging app tweet, but the end result is that Signal Advance’s stock price still closed on January 8 up 1,098% higher than its “pre-mistake” price of $0.60.
After half a trading day on Friday, an entire weekend, and a full trading day on Monday to digest the “correction,” investors pushed Signal Advance stock to $70.85 per share (i.e., 9.9x the prior day’s close) on Monday, January 11. By the close of trading, Signal Advance had a price of $38.70 per on 2.2 milllion shares traded That puts Signal Advance’s market capitalization at $2.5 billion. To put that figure in context, as reported by CNBC, the company reported no revenues in 2015 and 2016 and only has a single full-time employee.
On January 12, Signal Advance’s stock closed at $10 — down 74% from the close the day before but still over 16x its pre-“mistake” price of $0.60. At the end of the week, on January 15, SIGL stock closed higher at $13.54 on over 800k of volume. The stock was up 18% from the prior day’s close.
After another week has passed, SIGL stock is trading closed at $6.25 on January 22. This is still more than 10x the pre-Musk tween price of $0.60.
What Does All This Mean?
There are several critical lessons from this real world example. First, hundreds or thousands of investors can bid up a company’s stock price even with a mistake (i.e., information that has nothing to do with the company at all), let alone the company’s value. SIGL basically has not reported any financial information and has one full-time employee. Therefore, there is no reason the prices we observe reflect the firm’s value .
Second, price and value could deviate substantially with such deviations occurring really quickly and lasting for a very long time. Even after a week when corrective and widely disseminated information was disclosed, the stock price still closed at over 20x the pre-Musk tweet price of $0.60 per share. There is no argument here for a complex disclosure of the correction. The correction in this case is as simple as you can get. Investors were informed by the correct company – the messaging app Signal – that they were not investing in the correct company and this correction was widely disseminated and covered by many sources.
Although one may argue this is an extreme case, it shows that the above lessons can generate a continuum of possibilities for other firms. This also calls into question how information is being processed by the investors as well as how much of a stock’s price has to do with underlying value versus investors’ mood and momentum. In the case of SIGL, it seems the effect is purely one related to mood and momentum and not changes in the value of the stock .
Value is how much an asset is worth and is based on fundamentals, like risk, profitability, and growth. Price is how much you pay for an asset and, while affected by changes in fundamentals, is also affected by investors’ mood and momentum. Sometimes people interchange the terms price and value. Some argue that price is the best estimate of value as it reflects the collective wisdom of hundreds or thousands of investors putting their money on the line. However, earlier this year, we were shown a clear real-world example that price and value can be very different. This is the tale of two Zooms – Zoom Video Communications and Zoom Technologies.
Most people have been on a Zoom video call by now. But, do you know what that company’s ticker is? Is it “ZOOM?” Well, as it turns out, ZOOM was the ticker for a company named Zoom Technologies. Isn’t this the same company that developed the video conferencing software many of us have been using? No, it is not. So, why is this relevant? ZOOM saw its stock price increase from $2.47 per share on February 3 to $10.40 per share on March 26 (i.e., a 320% return in less than two months). On March 26, the SEC suspended trading of ZOOM because people were confusing ZOOM for Zoom Video Communications, which has the ticker ZM – i.e., ZM is the company that makes the video conferencing software. ZM’s stock price increased 60% over the same two-month period, which is not paltry by any measure but is one-fifth of ZOOM’s price increase.
In the SEC’s press release, it said ZOOM had an absence of any public disclosure, including disclosures related to its financial condition and its operations, since 2015. In other words, we don’t even know that ZOOM actually did anything since 2015. In fact, to fix the name confusion issue, ZOOM now trades under the ticker ZTNO and its stock price has fallen below $1.00 beginning April 20. ZOOM’s price on December 11 was $0.165 per share. Therefore, the 300% increase in ZOOM’s stock price could not have anything to do with the change in ZOOM’s value.
The tale of two Zooms is a clear real-world example of how mood and momentum alone could drive a substantial change in the price of a company’s stock. In other words, the collective wisdom of hundreds or thousands of investors could be reflective of investors’ mood and momentum and not reflective of a change in the company’s value.
The moral of this story is simple: price can deviate substantially from value. Moreover, and likely a more important implication of this story, if 300% is a feasible deviation between price and value, then it would not be unreasonable to expect that relatively smaller but still substantial deviations between price and value could occur.
Using data from Ibbotson SBBI from Jan 1981 to Sep 2020, a $100 investment in large stocks would have ended up with $7,293 while the same $100 investment in small stocks would have only resulted in $5,387. In other words, an investment in large stocks outperformed an investment in small stocks by 35% during the post-Banz period. This evidence is inconsistent with the existence of a size effect which was premised on small stocks outperforming large stocks on a risk adjusted basis.
Also, a closer read of Asness’ (the other Cliff that discusses the size effect) post actually reveals an even more interesting finding — the size effect may not have even existed at all even using the Banz period data. Asness found that there were errors with how the old data was constructed. After fixing these errors, it appears that the size effect may never have existed at all. We should all spend a few moments to let that sink in.
This post updates my size effect analysis using the latest Ibbotson data. From January 1982 to August 2020, a $100 investment in large cap stocks would result in $7,577 by the rnd of Aigust 2020 while the same investment in small cap stocks would result in $5,990. In other words, an investment in large cap stocks would have yielded a 26% higher return than an investment in small cap stocks. Thus, if small cap stocks do not outperform large cap stocks on a raw basis, small cap stocks would not outperform large cap stocks on a risk-adjusted basis.
During the last month, another nail was put on the size effect coffin. This time it was by Cliff Asness. Many proponents of the size effect claimed Asness’ paper as support for the size effect. Asness came out and clarified this misinterpretation. In no uncertain terms, Asness stated that there is no size effect. Read about it here.
Add the above to Fama and French’s more recent papers that essentially showed, when using more recent data (relative to their 1993 paper), that there is no economically significant size effect. So, at this point, it is not clear what remaining support there is for the existence of a size effect.
Dollar cost averaging (DCA) is a investment strategy in which you systematically invest money over the long term without regard for timing the market. In this post, I discuss DCA in the context of long-term savings. If you applied DCA and you invested $100 each month since January 2010 in the S&P 500 Index ETF, you would end up with over $24,000 by June 2020. That’s an average return of 12% per year. As I show below, starting on different dates through June 2020, DCA returns are generally around the 9% to 12% per year range. As such, it would seem like DCA is a good investment strategy. So, what are the critical questions you should ask if you are considering DCA? In my opinion, there are only two.
Question 1: How do you feel about systematic investing?
One of the most challenging things is to get people to save money. For example, the personal savings rate in the U.S. prior to 2020 was in the 6% to 9% range. Sometimes systematic investing can help. With systematic investing, you invest a fixed amount each month. It could be $100, $500, or whatever amount. Think of it as taking the same money out of your paycheck each month and putting it into some investment. You would make that investment regardless of what the market has done, is doing, or is expected to do. This takes market timing and emotions out of the investing equation. But, systematic investing may not be for everybody, so you have to think about your individual situation and whether systematic investing makes sense for you.
Question 2: Do you believe in the power of compounding?
That sounds like a trick question. However, it really is not. DCA is applying the power of compounding to multiple investments. Think about investing $100 each month into an asset that, hypothetically, earns 10% per year for the next 10 years. The $100 investment in Month 1 will become $257.32 at the end of 10 years . The $100 investment in Year 2 will turn into $255.29 at the end of nine years and 11 months. You do this systematically and the 120 investments of $100 each month for 10 years would yield $19,987.18 off a nominal sum of $12,000 in investments. The above is an example of combining systematically investing $100 and the power of compounding. Of course, returns are not going to be a fixed 10% per year and it could fluctuate from positive to negative. So with a long-term investment horizon, you may be tempted to pull money out or not continue investing. For example, in the height of the COVID-19 pandemic during mid-March 2020, would you have stopped systematically investing or would you have pulled your money out of equities? Thus, this question really has more to do with whether you believe in the power of compounding enough to stay the course.
Illustration of DCA’s performance
The below table shows what would have happened had you invested $100 each month in the S&P 500 Index ETF at different start dates but all ending in June 2020. For example, if you invested $100 each month beginning January 2000, you would have $68,104 by June 2020. Because we have multiple cash flows, we use the internal rate of return (IRR) as the measure of return. The IRR of that investment is 9.03% per year, which is decent over such a long period that included the 2008/2009 financial crisis and the COVID-19 pandemic in the first half of 2020. Other start dates yield IRRs generally ranging from 9% to 12%, which are also not paltry levels.
Investment Period Start Date Through June 2020
June 2020 Value
IRR
January 2000
$68,104
9.03%
January 2001
$64,323
9.45%
January 2002
$59,843
9.81%
January 2003
$54,556
10.03%
January 2004
$49,060
10.17%
January 2005
$44,530
10.46%
January 2006
$40,364
10.84%
January 2007
$36,582
11.32%
January 2008
$33,295
12.03%
January 2009
$29,459
12.51%
January 2010
$24,423
12.07%
January 2011
$20,367
11.79%
January 2012
$16,890
11.54%
January 2013
$13,715
11.01%
January 2014
$11,069
10.62%
January 2015
$8,898
10.78%
January 2016
$6,901
10.87%
January 2017
$4,977
9.68%
January 2018
$3,354
8.87%
January 2019
$1,949
10.47%
Bottom-line
DCA could be a good way for people to save over the long term. However, just like any investment strategy, DCA may be for you or it may not be for you. In this post, I posed the two questions I think that you should think about if you are considering DCA.
I recently received the updated Ibbotson data for August 2020. Last month, I showed that following the publication of Banz’s article on the size effect in 1981 (i.e., January 1982 to June 2020), large cap stocks have outperformed small cap stocks by 20%. I update the results of the above analysis with the addition of July 2020 SBBI data.
Had we invested $100 in large cap stocks (as classified by Ibbotson) at the start of 1982, we would have $7,069 by the end of July 2020. By contrast, the same $100 would have only yielded $5,718 by the end of July 2020 had we invested that in small cap stocks. Thus, the investment in large cap stocks outperformed small cap stocks by 24%.
Given the above, the data demonstrates that there continues to be no evidence that a size effect exists.
We often use the capital asset pricing model (CAPM) to estimate the cost of equity. Then, it is only natural to assume that betas used as inputs to the CAPM are also estimated based on the CAPM. However, when estimating betas in practice, most people use what’s called the “market model.” That is the way, for example, the Beta output from the Bloomberg terminal and in many other databases are calculated. Many textbooks would tell you that the reason is that the difference is trivial, so one should not lose sleep over which model to choose. Below I explain when the choice of how beta is calculated matters?
Difference Between CAPM and Market Model
Both these models were developed by Bill Sharpe, who won the Nobel Prize in Economics, so it is not surprising that these two models are very similar. The CAPM is a very influential model in the field of financial economics. From a practical perspective, the difference between the two is that the CAPM estimates beta when the inputs are in excess return form (i.e., we subtract the risk-free return from the stock’s return and market return ). That is,
.
The and are generated by a regression. By contrast, under the market model, we drop the risk-free return form both sides of the equation. That is,
,
where all the variables are defined in the same way as the CAPM. Thus, we can see from the two equations above that if there is a difference, the difference would be generated by the risk-free return.
Example Using Amazon’s Beta
In the chart below, I estimated the rolling 60-month betas for Amazon calculated during each month from December 2014 to June 2010. The black line is the market model beta. Since the beta estimate is estimated with some error rate, the true market model beta in some sense could lie between some band around the market model beta estimate. The pink shaded area represents the 95% confidence interval for market model betas over time.
We then calculated the CAPM betas using four different risk-free returns from the Ibbotson SBBI data: 30-day, 1-year, “intermediate term,” and “long term.” Because the return on the 30-day and 1-year Treasury Bills are very small during this time period, there is a de minimis impact of subtracting those returns when calculating beta. Thus, the rolling betas based on those two risk-free returns almost overlap with the market model betas. If you look closely at the chart, there are lines that overlap with the market model beta.
By contrast, the intermediate-term and long-term risk-free returns have nontrivial monthly returns. Specifically, over our analysis period, Ibbotson’s U.S. Government Intermediate Term Total Return series had monthly returns ranging from -2% to 3% over the period, while Ibbotson’s U.S. Government Long Term Total Return series had monthly returns ranging from -6% to 9%. These nontrivial returns results in a visible difference in the estimated CAPM betas when compared to the market model betas. In the above chart, the blue line represents the intermediate-term CAPM betas and the red line represents the long-term CAPM betas.
Despite the visual difference, the CAPM betas based on intermediate-term and long-term risk-free returns are within the 95% confidence interval of the market model beta. In other words, we may not be able to statistically distinguish the CAPM betas from the market model beta.
But … There Is Still a Valuation Difference
Although we may not be able to statistically distinguish the market model beta from the CAPM betas, which beta we choose can lead to a drastically different valuation conclusion. We can go through a simplified example to show this. In December 2019, using 5 years of monthly returns, the market model beta is 1.50, while the CAPM beta based on a long-term risk-free return is 1.18. Assuming a 1% risk-free rate and 6% equity risk premium, the cost of equity is 10.0% based on the market model beta and 8.1% based on the CAPM beta.
Now, assume we are trying to value a $100 annuity. This is a stream of $100 each year into perpetuity. Using the cost of equity based on the market model beta yields a value of $1,000. By comparison, using the cost of equity based on the CAPM long-term beta yields a value of $1,238. That is, we can get a 23.8% higher valuation simply by choosing to use the CAPM beta instead of the market model beta.
Where Does This Leave Us?
Unfortunately, there is no hard and fast rule here. From a statistical perspective, there is no real difference between the different beta estimates. However, from a valuation perspective, we can get drastically different valuations simply by using the market model beta or CAPM betas. The question that we must ask is which of these betas better reflect the true beta for the firm going forward. In other words, when a situation arises in which the betas could be influenced by choosing either a market model beta or a CAPM beta, we have to do further analysis – which would then depend on the facts and circumstance as of the valuation date – to determine which beta is more appropriate to use.
When estimating beta, we typically have to decide about what frequency the returns (e.g., weekly versus monthly returns) and length of the estimation period (e.g., two years or five years). Some experts have raised an issue with the “reference day” used in beta calculations. For a weekly beta calculation, reference day means whether we calculate the weekly returns using Friday-to-Friday returns or returns based on some other day of the week. For a monthly beta calculation, it is end of month to end of month or some other day during the month. Often the default (i.e., Friday or end-of-month) is used when calculating beta without giving any thought to other reference days.
Looking at the difference in raw regression betas may indicate quite a bit of difference whether you use Friday betas or a different reference day. But, betas are estimated with statistical error, so looking at raw differences doesn’t really mean much in terms of determining whether the difference is large enough from a statistical point of view. In other words, do the Friday betas really look different enough than Monday, Tuesday, Wednesday, and Thursday betas that we should really care about this.
This Was An Issue For 25% Of Our Sample
To answer this question, I looked at weekly returns and test whether the betas based on other days of the week fall outside the 95% confidence interval of the Friday-to-Friday beta. To do this, I use two years of weekly returns ending December 31, 2019. I chose this end date because I didn’t want to run into empirical issues that was caused by the heightened volatility especially during the onset of the COVID-19 pandemic beginning in early 2020. To make the results more robust, I ran this test using the components of the S&P 500 Index.
The results show that this reference day issue could potentially affect only 25% of the firms in the S&P 500 Index. For those firms, there was a beta based on returns on other days of the week that was outside the 95% confidence interval of the Friday beta. When we dig a little deeper, we find that this difference is concentrated mostly on Wednesday betas. The percentages based on Monday returns is 2%, Tuesday returns is 8%, Wednesday returns is 21%, and Thursday returns is 2%.
Looking at the results above, one number jumps out. Holding the estimation period the same, there is no reason to expect that Friday betas to be different from Wednesday betas. However, for 21% of the firms in the S&P 500 Index, they actually are. Although 21% is not a huge number, 21% is not a trivial number also.
The Valuation Differential Could Be Huge
To illustrate how large the valuation differential could be, I identified the firm with the largest beta differential between Friday and Wednesday in both directions. ConAgra Brands, Inc. (CAG) had a Wednesday beta that was 0.60 lower than its Friday beta, while Eaton Corp (ETN) had a Wednesday beta that was 0.84 higher than its Friday beta.
How do these beta differentials translate into differences in costs of equity and valuation? Assuming that the Equity Risk Premium (ERP) is 6% and the risk-free rate is 2%, CAG’s cost of equity would be 8% based on the Friday beta and 5% based on the Wednesday beta. A $100 annuity would equal $1,216 based on the CAG Friday beta, while the same $100 annuity would equal $2,168 based on the CAG Wednesday beta. That’s a 78% higher valuation just by choosing Wednesday returns instead of Friday returns.
On the other hand, using the same ERP and risk-free rate assumption, ETN’s cost of equity would be 8% based on the Friday beta and 13% based on the Wednesday beta. A $100 annuity would equal $1,325 based on the ETN Friday beta, while the same $100 annuity would equal $793 based on the ETN Wednesday beta. That’s a 40% lower valuation valuation just by choosing Wednesday returns instead of Friday returns.
Which Beta to Choose
The above shows that valuation differentials from choosing a different reference day could be large. Fortunately, these scenarios don’t happen often. However, these scenarios could happen in a decent amount of instances. Unfortunately, there is no way for us know when and by how much it matters without doing the analysis. The challenge when this happens is in determining which beta better reflects the true beta going forward for the firm.
When performing valuations, many analysts add a size premium to the CAPM cost of equity. I’ve previously written about why doing so results in unreliable valuation conclusions. I’ve also written about how there has been no size premium for decades. You can find links to those articles on my website www.cliffordang.com. In this post, I test whether the premise of the size effect – that small stocks outperform large stocks on a risk-adjusted basis – holds using a different dataset.
CFA Institute members recently got access to monthly Ibbotson data. Included in the data are total returns of what Ibbotson classifies as large stocks and small stocks. Using this data, we can test to see if small stocks outperformed large stocks based on Ibbotson’s classification of small stocks and large stocks. Banz’s seminal article was published in 1981, so I cumulated monthly returns from January 1982 to June 2020 for those two series. Using the Ibbotson data, if we had invested $100 in small stocks at the beginning of 1982, we would have gotten $5,555.75 at the end of June 2020. By contrast, the same $100 investment in large stocks would have resulted in $6,691.59. That is, large stocks outperformed small stocks by 20% over this period.
Given the above, using Ibbotson data – just like other data sources – shows that small stocks do not outperform large stocks even on a non risk-adjusted basis.