How P/E ratios and other multiples are grossly misused

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foodhype
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How P/E ratios and other multiples are grossly misused

Post by foodhype »

Let's look at the most popular multiple, the price-to-earnings ratio. On the surface, it seems like a swiss army knife. It directly relates price to earnings.

This can be useful for extreme cases. If a business is trading at a P/E of 2, can easily maintain its current earnings for 10 years, and there is some obvious reason why the market will eventually recognize and correct its mistake, it may be worth investigating. The issue, however, is when people blindly assume that P/E is a useful metric -- outside of extreme cases -- for comparing companies, markets, valuations; for projecting returns; for labeling things as "cheap" or "expensive"; etc. This becomes obvious to an astute observer after looking at where the numbers come from.

We all basically understand what earnings are, but what about price? How do investors estimate the intrinsic value of a business? The most basic approach is a discounted cash flow.

Image

DCF = discounted cash flow
CF_i = cash flow period i
r = interest rate
n = time in years before the future cash flow occurs

In laymen's terms, the investor estimates the future cash flows of the business and discounts them to account for interest rates.

Now why am I showing you this formula? It's to emphasize a key observation. Look at where the exponents are. The valuation is heavily influenced by interest rates. Prices (and hence P/Es) should be much higher if low interest rates are expected. There is another exponent hiding in the cash flow terms, and that is the earnings growth expected each year. Companies that can predictably maintain a high earnings growth rate over a long period of time deserve a much higher price (and hence a much higher P/E).

The effects of interest rates and earnings growth rates on intrinsic value are non-linear, whereas P/E is a linear relationship. If interest rates are expected to be relatively low and a company has durable competitive advantages and high barriers to entry that will allow it to maintain a solid earnings growth for a long period of time, it deserves a much higher P/E. This principal can apply to individual companies, large markets, different time periods, etc.

Please stop using linear multiples to evaluate non-linear effects. Try calculating a DCF a few times just to get a feel for how much the exponential terms matter.
Last edited by foodhype on Sat Apr 10, 2021 6:15 pm, edited 1 time in total.
MathWizard
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by MathWizard »

I'm not disagreeing that P/E is a simplistic measure, but
it would be more enlightening if you would provide an example or two which shows how you value a business using DCF, and how you feel that someone would use a P/E ratio to arrive at an incorrect number.
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foodhype
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

MathWizard wrote: Fri Apr 09, 2021 9:45 pm I'm not disagreeing that P/E is a simplistic measure, but
it would be more enlightening if you would provide an example or two which shows how you value a business using DCF, and how you feel that someone would use a P/E ratio to arrive at an incorrect number.
The issue isn't so much that people come up with an incorrect number; it's that they never come up with any number at all because they short circuit to a conclusion based only on the P/E looking "high" or "low" compared to some multiple they are anchoring to.

I will do a few pretend valuations for you guys to illustrate how much the exponential terms matter.

Let's suppose we are valuing Alphabet. (Don't take the specific figures used too seriously. I'm trying to keep the valuation simple.) Assume the initial market cap is $1.4 trillion, earnings last year was $40 billion, and the earnings growth over the last year was 17%. The P/E is roughly 35, which most people would consider to be "high".

Scenario 1: Assume Alphabet's earnings growth rate will drop 1% each year (i.e. 16% the first year, 15% the second year, etc) until it stabilizes at 2% (i.e. GDP growth rate). Conservatively estimate that the average interest rate over the lifetime of the company is 7% (triple the current rate of 2.34%).

A traditional DCF valuation would yield a valuation of $1.9 trillion or 26% above the market price.

Scenario 2: Same as Scenario 1 but assume interest rates only go up to 4% and stay there.

This would yield a valuation of $5.1 trillion or 73% above market price.

Scenario 3: Same as scenario 1 but assume Alphabet's earnings growth rate drops by 2% each year until it stabilizes at 2%.

This would yield a valuation of $1.2 trillion or 12% below the market price.

The moral of the story is that the P/Es are a very poor man's valuation.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by Beensabu »

How does one determine CF_n year to future year?
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by LFKB »

P/E is also bad for valuation for highly levered companies. Interest expense can weigh down the E greatly leading to a misleadingly high P/E ratio. In these cases, you can use EV/EBITDA, EV/EBIT, a DCF, etc for a better valuation lens.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

Beensabu wrote: Fri Apr 09, 2021 11:16 pm How does one determine CF_n year to future year?
The cash flow terms are always estimates of the business's future cash flows. For example, an investor like Warren Buffett would read the business's annual reports, study the business over long periods of time, and then use his knowledge to estimate what he believes the cash flows will be in 5, 10, and 20 years. (As you might have noticed, nothing about valuation is precise.)

For example, here are some recent quarterly and annual reports for Alphabet: https://abc.xyz/investor/

In the case of Alphabet, you might say that last year's cash flow value was its 2020 operating income ($41 billion). And then you might project forward based on everything that you know about the business to get CF_i for some future year i.

Someone like Warren Buffett, and most value investors for that matter, would consider a company like Alphabet too difficult to value, because forecasting the future cash flows of a company that is constantly changing can be extremely difficult. On the other hand, Buffett felt more comfortable investing in Apple because he saw that it was a consumer business with extremely loyal users who would always buy a new iPhone and never switch to Android because of how much they valued the brand and were locked into its ecosystem. Therefore, he could be confident when he started purchasing shares in 2016 that cash flows would be the same or higher 10 and 20 years in the future than they were in 2016. (Someone like Warren Buffett has done valuations for so long that he wouldn't even explicitly calculate a DCF in this scenario; it would be totally obvious to someone like him who can calculate compound interest in his head immediately.)

When most investors do a DCF, they assume the company's growth will eventually slow down until it hits some terminal growth rate that will continue forever. This would typically be some number close to the long-term expected GDP growth rate (e.g. 2%). As long as the terminal growth rate is lower than the interest rate, the DCF will eventually converge to some value (i.e. whether the company is expected to last 100 years or 99999 years shouldn't change its valuation much). You can also cut the valuation short if you think the company will only last X years.
Last edited by foodhype on Sat Apr 10, 2021 12:23 am, edited 1 time in total.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by watchnerd »

foodhype wrote: Fri Apr 09, 2021 9:27 pm Let's look at the most popular multiple, the price-to-earnings ratio. On the surface, it seems like a swiss army knife. It directly relates price to earnings.

This can be useful for extreme cases. If a business is trading at a P/E of 2, can easily maintain its current earnings for 10 years, and there is some obvious reason why the market will eventually recognize and correct its mistake, it may be worth investigating. The issue, however, is when people blindly assume that P/E is a useful metric -- outside of extreme cases -- for comparing companies, markets, valuations; for projecting returns; for labeling things as "cheap" or "expensive"; etc. This becomes obvious to an astute observer after looking at where the numbers come from.

We all basically understand what earnings are, but what about price? How do investors estimate the intrinsic value of a business? The most basic approach is a discounted cash flow.

Image

DCF = discounted cash flow
CF_i = cash flow period i
r = interest rate
n = time in years before the future cash flow occurs

In laymen's terms, the investor estimates the future cash flows of the business and discounts them to account for interest rates.

Now why am I showing you this formula? It's to emphasize a key observation. Look at where the exponents are. The valuation is heavily influenced by interest rates. Prices (and hence P/Es) should be much higher if low interest rates are expected. There is another exponent hiding in the cash flow terms, and that is the earnings growth expected each year. Companies that can predictably maintain a high earnings growth rate over a long period of time deserve a much higher price (and hence a much higher P/E).

The effects of interest rates and earnings growth rates on intrinsic value are non-linear, whereas P/E is a linear relationship. If interest rates are expected to be relatively low and a company has durable competitive advantages and high barriers to entry that will allow it to maintain a solid earnings growth for a long period of time, it deserves a much higher P/E. This principal can apply to individual companies, large markets, different time periods, etc.

Please stop using linear multiples to evaluate non-linear effects. Try calculating a DCF a few times just to get a feel for how much the exponential terms matter.
Fair Value Cape, which incorporates rates into valuation, solves this problem for you.

https://mebfaber.com/wp-content/uploads ... ecasts.pdf
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by Nathan Drake »

Still doesn’t explain why certain international developed and emerging markets are basically trading at historically normal P/E ratios despite having historically abnormal (extremely low) interest rates.

US equities certainly are trading at much higher valuations, justified or not. If interest rates suddenly increase going forward and low interest rates are priced in, that’s going to result in bad investment outcomes in the short term due to the change in market expectation.

Also, many growth companies just have growth. They have no underlying earnings. So the reasonable P/E ratios for such companies based on DCF go completely out the window
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by Beensabu »

foodhype wrote: Fri Apr 09, 2021 11:45 pm
Beensabu wrote: Fri Apr 09, 2021 11:16 pm How does one determine CF_n year to future year?
The cash flow terms are always estimates of the business's future cash flows. For example, an investor like Warren Buffett would read the business's annual reports, study the business over long periods of time, and then use his knowledge to estimate what he believes the cash flows will be in 5, 10, and 20 years. (As you might have noticed, nothing about valuation is precise.)

For example, here are some recent quarterly and annual reports for Alphabet: https://abc.xyz/investor/

In the case of Alphabet, you might say that last year's cash flow value was its 2020 operating income ($41 billion). And then you might project forward based on everything that you know about the business to get CF_i for some future year i.

Someone like Warren Buffett, and most value investors for that matter, would consider a company like Alphabet too difficult to value, because forecasting the future cash flows of a company that is constantly changing can be extremely difficult. On the other hand, Buffett felt more comfortable investing in Apple because he saw that it was a consumer business with extremely loyal users who would always buy a new iPhone and never switch to Android because of how much they valued the brand and were locked into its ecosystem. Therefore, he could be confident when he started purchasing shares in 2016 that cash flows would be the same or higher 10 and 20 years in the future than they were in 2016. (Someone like Warren Buffett has done valuations for so long that he wouldn't even explicitly calculate a DCF in this scenario; it would be totally obvious to someone like him who can calculate compound interest in his head immediately.)

When most investors do a DCF, they assume the company's growth will eventually slow down until it hits some terminal growth rate that will continue forever. This would typically be some number close to the long-term expected GDP growth rate (e.g. 2%). As long as the terminal growth rate is lower than the interest rate, the DCF will eventually converge to some value (i.e. whether the company is expected to last 100 years or 99999 years shouldn't change its valuation much). You can also cut the valuation short if you think the company will only last X years.
Thank you! Is it possible to apply some semblance of this method of valuation to a fund, or a sector, or a national stock market for projection of earnings growth rate, or is it best suited to review of individual companies? Would you suggest a method of valuation in those instances besides the fair value CAPE that watchnerd has mentioned, or do you see any issues with that metric?
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

watchnerd wrote: Sat Apr 10, 2021 12:21 am
foodhype wrote: Fri Apr 09, 2021 9:27 pm Let's look at the most popular multiple, the price-to-earnings ratio. On the surface, it seems like a swiss army knife. It directly relates price to earnings.

This can be useful for extreme cases. If a business is trading at a P/E of 2, can easily maintain its current earnings for 10 years, and there is some obvious reason why the market will eventually recognize and correct its mistake, it may be worth investigating. The issue, however, is when people blindly assume that P/E is a useful metric -- outside of extreme cases -- for comparing companies, markets, valuations; for projecting returns; for labeling things as "cheap" or "expensive"; etc. This becomes obvious to an astute observer after looking at where the numbers come from.

We all basically understand what earnings are, but what about price? How do investors estimate the intrinsic value of a business? The most basic approach is a discounted cash flow.

Image

DCF = discounted cash flow
CF_i = cash flow period i
r = interest rate
n = time in years before the future cash flow occurs

In laymen's terms, the investor estimates the future cash flows of the business and discounts them to account for interest rates.

Now why am I showing you this formula? It's to emphasize a key observation. Look at where the exponents are. The valuation is heavily influenced by interest rates. Prices (and hence P/Es) should be much higher if low interest rates are expected. There is another exponent hiding in the cash flow terms, and that is the earnings growth expected each year. Companies that can predictably maintain a high earnings growth rate over a long period of time deserve a much higher price (and hence a much higher P/E).

The effects of interest rates and earnings growth rates on intrinsic value are non-linear, whereas P/E is a linear relationship. If interest rates are expected to be relatively low and a company has durable competitive advantages and high barriers to entry that will allow it to maintain a solid earnings growth for a long period of time, it deserves a much higher P/E. This principal can apply to individual companies, large markets, different time periods, etc.

Please stop using linear multiples to evaluate non-linear effects. Try calculating a DCF a few times just to get a feel for how much the exponential terms matter.
Fair Value Cape, which incorporates rates into valuation, solves this problem for you.

https://mebfaber.com/wp-content/uploads ... ecasts.pdf
Nathan Drake wrote: Sat Apr 10, 2021 12:35 am Still doesn’t explain why certain international developed and emerging markets are basically trading at historically normal P/E ratios despite having historically abnormal (extremely low) interest rates.

US equities certainly are trading at much higher valuations, justified or not. If interest rates suddenly increase going forward and low interest rates are priced in, that’s going to result in bad investment outcomes in the short term due to the change in market expectation.

Also, many growth companies just have growth. They have no underlying earnings. So the reasonable P/E ratios for such companies based on DCF go completely out the window
A method that attempts to solve the problem needs to take into account both exponential terms: interest rates and earnings growth expectations.

For example, the earnings growth rate of the U.S. stock market has been ~18.6% over the past 5 years, whereas the the rate for the international market was only ~8.4%. This difference has been primarily driven by the dominance of technology companies over the past 5 years. (For example, software companies in lucrative industries are extremely well suited for high return on capital employed compared to high capex, low margin, low growth businesses, such as airlines.) Thus, Fair Value CAPE would be a poor way to compare the US and international market valuations unless you accounted for earnings growth expectations -- a crude first approximation might be to compare sector-by-sector (e.g. don't compare Chinese airline companies to US software companies).

Another crucial component in valuing a business is whether or not the business has a wide moat or durable competitive advantage to defend its growth over long periods of time. The reason this is so important is that even relatively modest growth allows a business to become extremely valuable if it maintains that growth over long periods of time. The moat can also free up the business to expand into new areas and can force competitors to spend lots of money to compete. In the case of the U.S., most of the largest businesses by market capitalization have absurdly wide moats protecting healthy growth. Yes, there are a few high flyers that will need to come back down to earth, but as a whole, the U.S. has fabulous businesses.
Last edited by foodhype on Sat Apr 10, 2021 2:27 am, edited 3 times in total.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

Beensabu wrote: Sat Apr 10, 2021 12:42 am
foodhype wrote: Fri Apr 09, 2021 11:45 pm
Beensabu wrote: Fri Apr 09, 2021 11:16 pm How does one determine CF_n year to future year?
The cash flow terms are always estimates of the business's future cash flows. For example, an investor like Warren Buffett would read the business's annual reports, study the business over long periods of time, and then use his knowledge to estimate what he believes the cash flows will be in 5, 10, and 20 years. (As you might have noticed, nothing about valuation is precise.)

For example, here are some recent quarterly and annual reports for Alphabet: https://abc.xyz/investor/

In the case of Alphabet, you might say that last year's cash flow value was its 2020 operating income ($41 billion). And then you might project forward based on everything that you know about the business to get CF_i for some future year i.

Someone like Warren Buffett, and most value investors for that matter, would consider a company like Alphabet too difficult to value, because forecasting the future cash flows of a company that is constantly changing can be extremely difficult. On the other hand, Buffett felt more comfortable investing in Apple because he saw that it was a consumer business with extremely loyal users who would always buy a new iPhone and never switch to Android because of how much they valued the brand and were locked into its ecosystem. Therefore, he could be confident when he started purchasing shares in 2016 that cash flows would be the same or higher 10 and 20 years in the future than they were in 2016. (Someone like Warren Buffett has done valuations for so long that he wouldn't even explicitly calculate a DCF in this scenario; it would be totally obvious to someone like him who can calculate compound interest in his head immediately.)

When most investors do a DCF, they assume the company's growth will eventually slow down until it hits some terminal growth rate that will continue forever. This would typically be some number close to the long-term expected GDP growth rate (e.g. 2%). As long as the terminal growth rate is lower than the interest rate, the DCF will eventually converge to some value (i.e. whether the company is expected to last 100 years or 99999 years shouldn't change its valuation much). You can also cut the valuation short if you think the company will only last X years.
Thank you! Is it possible to apply some semblance of this method of valuation to a fund, or a sector, or a national stock market for projection of earnings growth rate, or is it best suited to review of individual companies? Would you suggest a method of valuation in those instances besides the fair value CAPE that watchnerd has mentioned, or do you see any issues with that metric?
It may not be ideal, but if you want to use something like Fair Value CAPE, ensure that you're at least comparing apples to apples. It would be more fair, for example, to compare European banks to American banks than to compare Chinese airline companies to US software companies. It would be misleading, for example, to use Fair Value CAPE to compare the entire US stock market to the entire international stock market. If you wanted to achieve something like that, I don't know exactly how it would turn out, but it might be worth comparing Fair Value CAPE sector by sector to get a ballpark idea if valuations are higher or lower. Don't assume anything about this is precise.

The main point I want to make with all of this is to avoid using linear ratios to compare things with exponential terms. In particular interest rates and earnings growth rate expectations have non-linear effects on P/Es. If I were to apply knowledge of DCFs to valuing large markets, I would focus less on doing some sort of explicit DCF and focus more on the fact that the exponential terms -- interest rate expectations and long-term earnings growth rate expectations -- dominate the valuation. Durable long-term competitive advantages -- which allow the company to maintain solid growth -- have a massive impact on the long-term growth rate expectations. There's nothing in the world quite like monopolies that can keep growing for a long time.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by patrick013 »

foodhype wrote: Fri Apr 09, 2021 9:27 pm Please stop using linear multiples to evaluate non-linear effects. Try calculating a DCF a few times just to get a feel for how much the exponential terms matter.
If I evaluate a company based on 5 or maybe 10 years of past and
expected earnings using the Prime rate or the yield of a longterm
corporate BBB bond to gauge PE I'm faced with some time lag to get
the calc into equilibrium but it does move towards that. Using
the PE to gauge an IRR based on accounting EPS without going too
far into infinity in practice. Without dividends we're still buying
an equity value of production lacking direct cash flow to the investor.

Even the S&P 500 spreadsheet uses a PEG ratio to help investors
avoid overpriced stocks or indexes in a normal market. Growth
stocks can have PEG's of 2 or more. PEG Ratio

Your approach is a fine academic theory.
age in bonds, buy-and-hold, 10 year business cycle
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by vineviz »

foodhype wrote: Fri Apr 09, 2021 9:27 pm The issue, however, is when people blindly assume that P/E is a useful metric -- outside of extreme cases -- for comparing companies, markets, valuations; for projecting returns; for labeling things as "cheap" or "expensive"; etc. This becomes obvious to an astute observer after looking at where the numbers come from.
If this is, in fact, the core issue then perhaps the argument would be bolstered with some evidence that people do - in fact - "blindly assume that P/E is a useful metric".

Over the course of my career I've talked to hundreds of financial analysts and company executives about the ways they value companies (others and their own), for instance, and I don't think I've ever met one who was "blind" to the strengths and weaknesses of P/E ratios.

DCF is the gold standard for a reason, but in practice the assumptions required to conduct a DCF-based valuation leave a lot of room for optimism or outright mistakes to creep into the model. It only takes a small error on a variable that is growing exponentially to result in a gross over-estimation of a company's value.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by JackoC »

foodhype wrote: Fri Apr 09, 2021 9:27 pm Let's look at the most popular multiple, the price-to-earnings ratio. On the surface, it seems like a swiss army knife. It directly relates price to earnings.

Image

DCF = discounted cash flow
CF_i = cash flow period i
r = interest rate
n = time in years before the future cash flow occurs

The effects of interest rates and earnings growth rates on intrinsic value are non-linear, whereas P/E is a linear relationship. If interest rates are expected to be relatively low and a company has durable competitive advantages and high barriers to entry that will allow it to maintain a solid earnings growth for a long period of time, it deserves a much higher P/E. This principal can apply to individual companies, large markets, different time periods, etc.

Please stop using linear multiples to evaluate non-linear effects. Try calculating a DCF a few times just to get a feel for how much the exponential terms matter.
But as n approaches infinity that equation converges to DCF=CF/r, assuming CF and r are constant: the value of a perpetual is in fact a(n inverse) linear function of the discount rate. This equation has even had direct real world application. For example the 2-3/4% British government 'consol' perpetual issued in 1888 had a price around 17 pence per GBP face value when consol yields topped out around 16% (2.75/16) in the early 1980's, but around GBP 1.7 per GBP face when it was among the last consol issues redeemed in the mid 2010's with yield around 1.6% (2.75/1.6): 10 times higher yield, 10 times lower price.

In case of a stock the equation isn't directly applicable because the CF is assumed to grow over time. But the value of a stock held forever will be the total PV of all dividends forever. Direct extension of the first equation comes out to Price=Dividend/(r-g) where r is the discount rate and g the dividend growth rate, the Gordon Growth Model. By first principals of 'modern finance' the appropriate discount rate for the 'market portfolio' of stocks is the (risky) market return, call it k, r=k.

Now substitute for Dividend, Earnings Per Share*(1-Retention Ratio), E*(1-R): the dividend is the portion of earnings not retained. Also assume the retained earnings are reinvested in projects earning k: assume companies earn their cost of capital on reinvestments. If so g=k*R and P=D/(r-g) becomes P=E*1(1-R)/(k-k*R), which simplifies to k=E/P
k=1/PE ratio.
see, with clearer graphics here, also in numerous other basic references.
https://www.investopedia.com/articles/04/012104.asp

Therefore we must carefully distinguish two different things which get confused over and over on this forum.
"they short circuit to a conclusion based only on the P/E looking "high" or "low" compared to some multiple they are anchoring to."
This refers to people deriving a relationship between current PE and expected future PE, usually via regression analysis of past starting PE (often a smoothed PE like CAPE[10]) and subsequent return *including changes in PE*.

What I am pointing out is not the same as that. It's the fundamental relationship between PE and expected return at constant PE. We can absolutely also look for holes in the assumptions which make the above derivation so neat, it's a book length topic. But the derivation has nothing to do with 'anchoring' to any particular value of PE. Also note we're not looking at the PE of particular companies here but of 'the market' in CAPM terms: the basic framework of modern finance tells us that risk vs. return is mainly meaningful in context of the whole 'market portfolio' of risky assets. And it points to the basic difference between looking at the relationship of subsequent stock return to starting CAPE in the past vs somebody looking at whether the East or West won the NBA All Star Game and subsequent stock return that year. The second is purely empirical (with any relationship which turns up being manifestly a statistical quirk) whereas the first is exploring the empirical history of something we know has at least some fundamental validity, per the above. Although again, the regression of starting CAPE v subsequent stock return importantly includes subsequent change in CAPE, which is where a lot of the noise in the regression comes from. The simplified theoretical derivation is notionally based on buy and hold forever, so makes no reference to future changes in PE.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

patrick013 wrote: Sat Apr 10, 2021 10:20 am If I evaluate a company based on 5 or maybe 10 years of past and
expected earnings using the Prime rate or the yield of a longterm
corporate BBB bond to gauge PE I'm faced with some time lag to get
the calc into equilibrium but it does move towards that. Using
the PE to gauge an IRR based on accounting EPS without going too
far into infinity in practice. Without dividends we're still buying
an equity value of production lacking direct cash flow to the investor.

Even the S&P 500 spreadsheet uses a PEG ratio to help investors
avoid overpriced stocks or indexes in a normal market. Growth
stocks can have PEG's of 2 or more. PEG Ratio

Your approach is a fine academic theory.
PEG ratio is just adding one more linear relationship to P/E. I appreciate the thought behind PEG of trying to incorporate earnings growth, but it's still another poor man's valuation.
vineviz wrote: Sat Apr 10, 2021 10:39 am If this is, in fact, the core issue then perhaps the argument would be bolstered with some evidence that people do - in fact - "blindly assume that P/E is a useful metric".

Over the course of my career I've talked to hundreds of financial analysts and company executives about the ways they value companies (others and their own), for instance, and I don't think I've ever met one who was "blind" to the strengths and weaknesses of P/E ratios.

DCF is the gold standard for a reason, but in practice the assumptions required to conduct a DCF-based valuation leave a lot of room for optimism or outright mistakes to creep into the model. It only takes a small error on a variable that is growing exponentially to result in a gross over-estimation of a company's value.
In this case, I'm referring less to investment professionals, although I've even seen superinvestors anchor to P/Es, especially in value investing funds. Old habits die hard.

The reason DCF is the gold standard is that, if you could predict the future and plug in the right terms, you could use DCF to directly calculate the business's intrinsic value. The fact that it only takes small input errors to produce large output errors is a reflection of the reality of valuation. When people just compare industry P/Es, for example, they are effectively passing part of the buck to someone else to do the valuation. That doesn't mean they won't make any money; it just means somebody else has to be mostly right. Some people try to get around this by just focusing on forecasting earnings for the next 5 - 10 years and assuming the multiple will go up, remain stable, or go down, and this avoids the issues with terminal values, but they're still depending on the base valuations to be correct.
JackoC wrote: Sat Apr 10, 2021 10:45 am But as n approaches infinity that equation converges to DCF=CF/r, assuming CF and r are constant: the value of a perpetual is in fact a(n inverse) linear function of the discount rate. This equation has even had direct real world application. For example the 2-3/4% British government 'consol' perpetual issued in 1888 had a price around 17 pence per GBP face value when consol yields topped out around 16% (2.75/16) in the early 1980's, but around GBP 1.7 per GBP face when it was among the last consol issues redeemed in the mid 2010's with yield around 1.6% (2.75/1.6): 10 times higher yield, 10 times lower price.

In case of a stock the equation isn't directly applicable because the CF is assumed to grow over time. But the value of a stock held forever will be the total PV of all dividends forever. Direct extension of the first equation comes out to Price=Dividend/(r-g) where r is the discount rate and g the dividend growth rate, the Gordon Growth Model. By first principals of 'modern finance' the appropriate discount rate for the 'market portfolio' of stocks is the (risky) market return, call it k, r=k.
The principals of modern finance and modern portfolio theory are misleading in how they treat risk. There's two basic ways to derive the discount rate.

The modern finance method might use something like the WACC or "beta" or the current stock market return k in an attempt to bake the risk premium into the discount rate. This method requires estimating the expected value of future cash flows. It's not necessarily total nonsense to try to bake risk into the discount rate, but the aforementioned metrics modern finance uses for the risk part are mostly nonsense.

Another way is to use the risk free rate (e.g. 30-year treasury yield) and maybe add some buffer to account for the possibility that interest rates go up to some value X. We'll call this the Warren Buffett approach. This method requires estimating "certainty equivalent cash flows". Someone like Buffett would just estimate the cash flows that he's near certain about over the next 10+ years; he might then demand a margin of safety before actually buying the stock. This method also has the advantage that the constant discount rate allows him to compare across investment alternatives.

Nowadays someone like Buffett would tend to pay less attention to big margins of safety and more attention to finding "wonderful businesses at a fair price" i.e. businesses with good management and durable competitive advantages that will allow their earnings to grow for extremely long periods of time with low capital expenditures required to maintain the growth.
Last edited by foodhype on Sat Apr 10, 2021 2:22 pm, edited 3 times in total.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by vineviz »

foodhype wrote: Sat Apr 10, 2021 12:14 pm The fact that it only takes small input errors to produce large output errors is a reflection of the reality of valuation. When people just compare industry P/Es, for example, they are effectively passing part of the buck to someone else to do the valuation.
And the reason that people, even (especially) experts, “pass the buck” is that doing so quite often leads to better forecasts.

Behavioral psychologists have long known there is “wisdom in crowds”: the consensus forecasts of all experts is often more accurate than the forecasts of the best individual experts.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

vineviz wrote: Sat Apr 10, 2021 1:03 pm
foodhype wrote: Sat Apr 10, 2021 12:14 pm The fact that it only takes small input errors to produce large output errors is a reflection of the reality of valuation. When people just compare industry P/Es, for example, they are effectively passing part of the buck to someone else to do the valuation.
And the reason that people, even (especially) experts, “pass the buck” is that doing so quite often leads to better forecasts.

Behavioral psychologists have long known there is “wisdom in crowds”: the consensus forecasts of all experts is often more accurate than the forecasts of the best individual experts.
There is some truth in that. However, someone investing in individual businesses has to do better in some way than the rest of the market to justify that it's worth investing in individual businesses as opposed to the market as a whole, whether that means increasing reward or decreasing risk. They must be contrarian to play that game. To rely on the consensus forecast, while simultaneously diverging from it and assuming it's wrong in some way, can be problematic. It might work if the investor is sure they know something that the market doesn't, but even then they're depending on the consensus being right on everything else. Yes, many professionals do this. Yes, it avoids the terminal value issue. But it still makes a massive, often error-prone assumption.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by patrick013 »

foodhype wrote: Sat Apr 10, 2021 12:14 pm
patrick013 wrote: Sat Apr 10, 2021 10:20 am Even the S&P 500 spreadsheet uses a PEG ratio to help investors
avoid overpriced stocks or indexes in a normal market. Growth
stocks can have PEG's of 2 or more. PEG Ratio

Your approach is a fine academic theory.
PEG ratio is just adding one more linear relationship to P/E. I appreciate the thought behind PEG of trying to incorporate earnings growth, but it's still another poor man's valuation.
Most analysts I appreciate use a 5 year plan with a bottom up approach.
A static 5 year forward period to place a value on an investment. Why
it would be linear I can't fathom as the current trend has the most
weight in the valuation whereas linear sounds like a long term forecast
line of some type. Performance needs to be evaluated before long term
price adjustments are made in future 5 year periods.

Discounting too long can lead to overpricing on future performance that
may be unealistic. Discounting would depend on units of production,
inflation, growth and estimates thereof but logically those factors aren't
infinite. It looks to me that accurate pricing and optimism comes from
good short and intermediate term trends. Without rigid discounting an
IRR is in use anyway in a 5 year forward equity evaluation thru comparing
future stock price earnings yield with relevant interest yields.

Of the methods available it's one of the better IMO.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by vineviz »

foodhype wrote: Sat Apr 10, 2021 1:46 pm There is some truth in that. However, someone investing in individual businesses has to do better in some way than the rest of the market to justify that it's worth investing in individual businesses as opposed to the market as a whole, whether that means increasing reward or decreasing risk.
Which brings us back to the straw man: who is buying controlling stakes in companies using only a P/E ratio? No one.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by JackoC »

foodhype wrote: Sat Apr 10, 2021 12:14 pm
JackoC wrote: Sat Apr 10, 2021 10:45 am But as n approaches infinity that equation converges to DCF=CF/r, assuming CF and r are constant: the value of a perpetual is in fact a(n inverse) linear function of the discount rate. This equation has even had direct real world application. For example the 2-3/4% British government 'consol' perpetual issued in 1888 had a price around 17 pence per GBP face value when consol yields topped out around 16% (2.75/16) in the early 1980's, but around GBP 1.7 per GBP face when it was among the last consol issues redeemed in the mid 2010's with yield around 1.6% (2.75/1.6): 10 times higher yield, 10 times lower price.

In case of a stock the equation isn't directly applicable because the CF is assumed to grow over time. But the value of a stock held forever will be the total PV of all dividends forever. Direct extension of the first equation comes out to Price=Dividend/(r-g) where r is the discount rate and g the dividend growth rate, the Gordon Growth Model. By first principals of 'modern finance' the appropriate discount rate for the 'market portfolio' of stocks is the (risky) market return, call it k, r=k.
The principals of modern finance and modern portfolio theory are misleading in how they treat risk. There's two basic ways to derive the discount rate.

The modern finance method might use something like the WACC or add "beta" or use the current stock market return in an attempt to bake risk into the discount rate. This method requires estimating the expected value of future cash flows. It's not necessarily total nonsense to try to bake risk into the discount rate, but the aforementioned metrics modern finance uses for the risk part are mostly nonsense.

Another way is to use the risk free rate (e.g. 30-year treasury yield) and maybe add some buffer to account for the possibility that interest rates go up to some value X. We'll call this the Warren Buffett approach. This method requires estimating "certainty equivalent cash flows". Someone like Buffett would just estimate the cash flows that he's near certain about over the next 10+ years; he might then demand a margin of safety before actually buying the stock. This method also has the advantage that the constant discount rate allows him to compare across investment alternatives.

Nowadays someone like Buffett would tend to pay less attention to big margins of safety and more attention to finding "wonderful businesses at a fair price" i.e. businesses with good management and durable competitive advantages that will allow their earnings to grow for extremely long periods of time with low capital expenditures required to maintain the growth.
Your original main theme and repeated was an 'exponential' relationship between discount rate and PV of a stock. But as I pointed out PV=CF/(1+r)+CF/(1+r)^2+...+CF/(1+r)^n converges to PV=CF/r as n gets large as it is for a stock, there is in fact a(n inverse) linear relationship of discount rate to price. That's a pretty basic error by you to have overlooked, and now not mentioned in your response either. I don't think it puts you in the strongest position to then claim on your own authority that "the aforementioned metrics modern finance uses for the risk part are mostly nonsense".

Also note again the Gordon equation, P=D/(r-g) does include estimating the future cashflows, via future growth of the dividend at rate g, the dividend being the main intrinsic element of value in a stock (a stock can have huge value without having paid a dividend yet or being expected to pay one soon, but the value is based on dividends at some point). A steady growth rate g is obviously just a simplified assumption for expository purposes, but it does allow it be illustrated how PE and expected return are related, as per the derivation in previous post.

Again this isn't the end of the whole story. And it's just stating the obvious that all companies don't have the same PE, which nobody 'blindly assumes' unless you can show examples. The derivation in the link is still worthwhile to read and understand.
https://www.investopedia.com/articles/04/012104.asp
It suggests why PE's can vary, due to individual variation around the general assumption that g the dividend growth rate equals the market return k times the retention ratio R. The cost of capital for companies can vary due to their riskiness, and also companies may for prolonged periods be forced by external factors (regulatory, customary, political, agency problems of management v shareholder interest, etc) to retain and reinvest earnings on which they can't make the market return, whereas investors could if given the extra dividend. That implies a lower PE. Companies more able to optimize that would have a higher one. Perhaps some can consistently find opportunities to reinvest above the market rate, due to quasi-monopoly position. The derivation which ends with k=1/PE would not be expected to be accurate for every company but an approximation for the whole market: opportunities to reinvest can't be greatly higher/lower than the market return for the whole market. At the very least studying that derivation doesn't lead one down the blind alley of claiming it has anything do with 'PE is linear'. :happy
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

vineviz wrote: Sat Apr 10, 2021 3:28 pm
foodhype wrote: Sat Apr 10, 2021 1:46 pm There is some truth in that. However, someone investing in individual businesses has to do better in some way than the rest of the market to justify that it's worth investing in individual businesses as opposed to the market as a whole, whether that means increasing reward or decreasing risk.
Which brings us back to the straw man: who is buying controlling stakes in companies using only a P/E ratio? No one.
Who said anything about controlling stakes? That's a straw man.

Most investment professionals never do a DCF as the basis for their valuation. They compare EV/EBITDA and other multiples with industry peers. That doesn't mean that's the only thing they're looking at, and I never claimed it was.

I should also mention that, while I am claiming that even investment professionals are sometimes led astray by too much reliance on comparing multiples, I'm far more concerned with the way macro-economists on news networks and Market Outlook reports compare large markets, such as US vs international, using only CAPE or Fair Value CAPE, without doing a break down to account for growth rate expectations. They might say something like "this is influenced by the booming tech sector" but they rarely bother to actually account for the difference in their numbers. This can lead retail investors to assume the international market is cheaper than the US market if the comparison isn't apples-to-apples.
JackoC wrote: Sat Apr 10, 2021 3:42 pm Your original main theme and repeated was an 'exponential' relationship between discount rate and PV of a stock. But as I pointed out PV=CF/(1+r)+CF/(1+r)^2+...+CF/(1+r)^n converges to PV=CF/r as n gets large as it is for a stock, there is in fact a(n inverse) linear relationship of discount rate to price.
Welp, you're right! And I'm wrong. (I should have remembered that Taylor series from high school...) You are absolutely correct that the relationship between valuations and interest rates is a linear inverse.

I maintain that earnings growth rates have a non-linear impact on valuations, which makes using linear multiples, such as P/E, for making apples-to-oranges comparisons especially misleading.

I also still strongly disagree with the way that modern finance in academia quantifies risk and uses WACC as the discount rate.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by Ben Mathew »

foodhype wrote: Sat Apr 10, 2021 5:35 pm
JackoC wrote: Sat Apr 10, 2021 3:42 pm Your original main theme and repeated was an 'exponential' relationship between discount rate and PV of a stock. But as I pointed out PV=CF/(1+r)+CF/(1+r)^2+...+CF/(1+r)^n converges to PV=CF/r as n gets large as it is for a stock, there is in fact a(n inverse) linear relationship of discount rate to price.
Welp, you're right! And I'm wrong. (I should have remembered that Taylor series from high school...) You are absolutely correct that the relationship between valuations and interest rates is a linear inverse.

I maintain that earnings growth rates have a non-linear impact on valuations, which makes using linear multiples, such as P/E, for making apples-to-oranges comparisons especially misleading.
Earnings (or dividend) growth rate, g, has a similar impact on valuation as the discount rate r. The valuation formula with growth becomes

CF/(r-g)

Both r and g affect valuations non linearly. Small differences in r or g translate to huge differences in valuation. But that has nothing to do with whether you're using P/E ratios or a DCF model. As JackoC said, the P/E metric is derived from the DCF model.

In my experience, people using P/E ratios are usually aware that a higher earnings growth will justify a higher P/E ratio. The debate is more about whether assuming a high earnings growth is justified. Historically, people have been over-enthusiastic in their earnings projections. That's the problem with growth firms in exuberant times. Not whether they will grow. But whether they will grow enough to justify the valuation.
foodhype wrote: Sat Apr 10, 2021 12:14 pm The principals of modern finance and modern portfolio theory are misleading in how they treat risk. There's two basic ways to derive the discount rate.

The modern finance method might use something like the WACC or "beta" or the current stock market return k in an attempt to bake the risk premium into the discount rate. This method requires estimating the expected value of future cash flows. It's not necessarily total nonsense to try to bake risk into the discount rate, but the aforementioned metrics modern finance uses for the risk part are mostly nonsense.
Why do you think this is nonsense? It makes a lot of sense to me. More risky cash flows need to be discounted by higher discount rates reflecting the fact that risky cash flows that are correlated to the market portfolio are not as valuable as safe cash flows or cash flows that are uncorrelated to the market.

If we don't do this, then there wouldn't be an equity premium. Stocks and bonds would yield the same. And that clearly can't be right.
foodhype wrote: Sat Apr 10, 2021 12:14 pm Another way is to use the risk free rate (e.g. 30-year treasury yield) and maybe add some buffer to account for the possibility that interest rates go up to some value X. We'll call this the Warren Buffett approach. This method requires estimating "certainty equivalent cash flows". Someone like Buffett would just estimate the cash flows that he's near certain about over the next 10+ years; he might then demand a margin of safety before actually buying the stock. This method also has the advantage that the constant discount rate allows him to compare across investment alternatives.

Nowadays someone like Buffett would tend to pay less attention to big margins of safety and more attention to finding "wonderful businesses at a fair price" i.e. businesses with good management and durable competitive advantages that will allow their earnings to grow for extremely long periods of time with low capital expenditures required to maintain the growth.
Maybe Buffett can confidently estimate a risk free cash flows of a company. But most of us can't. Most companies have a good chance of going bankrupt. (And honestly, I doubt Buffett can be that confident of the cash flow of his investments given that many of his investments have done badly. His average is great, but he has bet on plenty of losers as well. The original Berkshire Hathaway--the textile manufacturing compnay--itself was not a winner.)
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

Ben Mathew wrote: Sat Apr 10, 2021 6:23 pm Earnings (or dividend) growth rate, g, has a similar impact on valuation as the discount rate r. The valuation formula with growth becomes

CF/(r-g)

Both r and g affect valuations non linearly. Small differences in r or g translate to huge differences in valuation. But that has nothing to do with whether you're using P/E ratios or a DCF model. As JackoC said, the P/E metric is derived from the DCF model.
So are g and CF the terminal growth rate and the cash flow used in the terminal value?

I'm not saying that P/E and DCF don't both display the issue with small differences in interest rates or earnings growth rates translating to huge differences in valuation. I'm saying that P/E is relating price to earnings by linearly dividing price by earnings, which doesn't make the growth and interest rate components obvious. This often misleads people when they try to make macro comparisons (e.g. US vs international) using P/E, CAPE, Fair Value CAPE, etc without accounting for differences in growth rate expectations across industries. With the DCF, the non-linearity is right in front of you.
Ben Mathew wrote: Sat Apr 10, 2021 6:23 pm
foodhype wrote: Sat Apr 10, 2021 12:14 pm The principals of modern finance and modern portfolio theory are misleading in how they treat risk. There's two basic ways to derive the discount rate.

The modern finance method might use something like the WACC or "beta" or the current stock market return k in an attempt to bake the risk premium into the discount rate. This method requires estimating the expected value of future cash flows. It's not necessarily total nonsense to try to bake risk into the discount rate, but the aforementioned metrics modern finance uses for the risk part are mostly nonsense.
Why do you think this is nonsense? It makes a lot of sense to me. More risky cash flows need to be discounted by higher discount rates reflecting the fact that risky cash flows that are correlated to the market portfolio are not as valuable as safe cash flows or cash flows that are uncorrelated to the market.

If we don't do this, then there wouldn't be an equity premium. Stocks and bonds would yield the same. And that clearly can't be right.
foodhype wrote: Sat Apr 10, 2021 12:14 pm Another way is to use the risk free rate (e.g. 30-year treasury yield) and maybe add some buffer to account for the possibility that interest rates go up to some value X. We'll call this the Warren Buffett approach. This method requires estimating "certainty equivalent cash flows". Someone like Buffett would just estimate the cash flows that he's near certain about over the next 10+ years; he might then demand a margin of safety before actually buying the stock. This method also has the advantage that the constant discount rate allows him to compare across investment alternatives.

Nowadays someone like Buffett would tend to pay less attention to big margins of safety and more attention to finding "wonderful businesses at a fair price" i.e. businesses with good management and durable competitive advantages that will allow their earnings to grow for extremely long periods of time with low capital expenditures required to maintain the growth.
Maybe Buffett can confidently estimate a risk free cash flows of a company. But most of us can't. Most companies have a good chance of going bankrupt. (And honestly, I doubt Buffett can be that confident of the cash flow of his investments given that many of his investments have done badly. His average is great, but he has bet on plenty of losers as well. The original Berkshire Hathaway--the textile manufacturing company--itself was not a winner.)
Essentially there's another way to get to the same place that tends to rely a bit less on error-prone measures of risk. That might be margin of safety or it might be more a question of confidence in cash flows. Decades ago, Buffett often demanded a 50% margin of safety for riskier businesses. In recent years, he has focused less on margin of safety and more on finding wonderful businesses (i.e. high ROIC, ROE, ROIIC, etc with wide moats and durable growth prospects) at a fair price.

Buffett doesn't require total certainty of the cash flows. If he did, he would never buy anything. The way that Buffett does it is that he estimates cash flows conservatively, but not excessively conservatively. He does the same thing with interest rates. If the interest rate is 7%, he would use a discount rate around 10%. If rates seem very low, he may add a bit more buffer.

But normally, his practice is to (1) skip it if he doesn't know how to confidently estimate the cash flows; (2) focus on the business risks and how confident he is in the future cash flows; (3) do the valuation; (4) demand some margin of safety; (5) compare it against a universe of investment alternatives; (6) if his expected return is better than any alternatives and not some super low return like 2-3%, then he will buy.

Technically you can get to the same place by trying to bake risk into the discount rate instead of demanding some margin of safety at the end. There's nothing inherently wrong with that. Even Buffett has done it a tiny bit himself. The issue is how do you measure the risk. It's definitely not standard deviation. WACC is often directionally correct but also often way off in magnitude.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

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foodhype wrote: Sat Apr 10, 2021 5:35 pm Most investment professionals never do a DCF as the basis for their valuation.
That's certainly not my experience. I've literally spent thousands of hours of my careers building DCF models and reviewing those done by others. I can promise you there are hundreds of DCF models for AAPl on the hard drives of investment banks, mutual fund companies, and other institutional investors.
foodhype wrote: Sat Apr 10, 2021 5:35 pm I should also mention that, while I am claiming that even investment professionals are sometimes led astray by too much reliance on comparing multiples, I'm far more concerned with the way macro-economists on news networks and Market Outlook reports compare large markets, such as US vs international, using only CAPE or Fair Value CAPE, without doing a break down to account for growth rate expectations. They might say something like "this is influenced by the booming tech sector" but they rarely bother to actually account for the difference in their numbers. This can lead retail investors to assume the international market is cheaper than the US market if the comparison isn't apples-to-apples.
Any conclusion about what most investment professionals do for a living based solely on watching the network news is bound to be distorted, don't you think?
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

vineviz wrote: Sat Apr 10, 2021 8:17 pm
foodhype wrote: Sat Apr 10, 2021 5:35 pm Most investment professionals never do a DCF as the basis for their valuation.
That's certainly not my experience. I've literally spent thousands of hours of my careers building DCF models and reviewing those done by others. I can promise you there are hundreds of DCF models for AAPl on the hard drives of investment banks, mutual fund companies, and other institutional investors.
foodhype wrote: Sat Apr 10, 2021 5:35 pm I should also mention that, while I am claiming that even investment professionals are sometimes led astray by too much reliance on comparing multiples, I'm far more concerned with the way macro-economists on news networks and Market Outlook reports compare large markets, such as US vs international, using only CAPE or Fair Value CAPE, without doing a break down to account for growth rate expectations. They might say something like "this is influenced by the booming tech sector" but they rarely bother to actually account for the difference in their numbers. This can lead retail investors to assume the international market is cheaper than the US market if the comparison isn't apples-to-apples.
Any conclusion about what most investment professionals do for a living based solely on watching the network news is bound to be distorted, don't you think?
I see. Interesting.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by watchnerd »

vineviz wrote: Sat Apr 10, 2021 8:17 pm
foodhype wrote: Sat Apr 10, 2021 5:35 pm Most investment professionals never do a DCF as the basis for their valuation.
That's certainly not my experience. I've literally spent thousands of hours of my careers building DCF models and reviewing those done by others. I can promise you there are hundreds of DCF models for AAPl on the hard drives of investment banks, mutual fund companies, and other institutional investors.
foodhype wrote: Sat Apr 10, 2021 5:35 pm I should also mention that, while I am claiming that even investment professionals are sometimes led astray by too much reliance on comparing multiples, I'm far more concerned with the way macro-economists on news networks and Market Outlook reports compare large markets, such as US vs international, using only CAPE or Fair Value CAPE, without doing a break down to account for growth rate expectations. They might say something like "this is influenced by the booming tech sector" but they rarely bother to actually account for the difference in their numbers. This can lead retail investors to assume the international market is cheaper than the US market if the comparison isn't apples-to-apples.
Any conclusion about what most investment professionals do for a living based solely on watching the network news is bound to be distorted, don't you think?
When I worked in VC and PE, we did them routinely for every deal, even if the numbers were SWAGs.
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Re: How P/E ratios and other multiples are grossly misused

Post by foodhype »

Tentative conclusions:
  • The issues I have described are not widespread among investment professionals in their day-to-day work. The media is misleading.
  • The relationship between valuations and interest rates is actually an inverse linear relationship.
  • Earnings growth rate expectations have a non-linear impact on valuations.
  • P/E, CAPE, and Fair Value CAPE are still a bad way to compare apples to oranges, such as US vs international, where different kinds of businesses deserve different earnings growth rate expectations.
  • The P/E ratio does not typically mislead investment professionals. It may mislead retail investors if they fail to account for interest rates and earning growth expectations and compare apples to oranges.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by Ben Mathew »

foodhype wrote: Sat Apr 10, 2021 8:11 pm
Ben Mathew wrote: Sat Apr 10, 2021 6:23 pm Earnings (or dividend) growth rate, g, has a similar impact on valuation as the discount rate r. The valuation formula with growth becomes

CF/(r-g)

Both r and g affect valuations non linearly. Small differences in r or g translate to huge differences in valuation. But that has nothing to do with whether you're using P/E ratios or a DCF model. As JackoC said, the P/E metric is derived from the DCF model.
So are g and CF the terminal growth rate and the cash flow used in the terminal value?
CF is the cash flow as in your equation, which is dividend or earnings. It grows at the rate g, so the dividend or earnings is CF(1+g) 2 years from now, CF(1+g)^2 3 years from now and so on.

PV=CF/(1+r) + CF(1+g)/(1+r)^2 + CF(1+g)^2/(1+r)^3 + ... = CF/(r-g)

A 1% increase in r and a 1% decrease in g both have the same effect on price.
foodhype wrote: Sat Apr 10, 2021 12:14 pm Technically you can get to the same place by trying to bake risk into the discount rate instead of demanding some margin of safety at the end. There's nothing inherently wrong with that.
Yes, requiring a high margin of safety is equivalent to using a high discount rate. Whichever way a person wants to think about it is fine. The end result is that investors insist on higher discount rates when they think an asset is risky. If you think they have not done so, you can create a low risk / high return portfolio by tilting towards the underpriced assets (low priced assets that have low market correlation). If enough people try to do that, the prices will correct.
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Re: How P/E ratios and other multiples are grossly misused - even by professionals

Post by foodhype »

Ben Mathew wrote: Sat Apr 10, 2021 11:49 pm CF is the cash flow as in your equation, which is dividend or earnings. It grows at the rate g, so the dividend or earnings is CF(1+g) 2 years from now, CF(1+g)^2 3 years from now and so on.

PV=CF/(1+r) + CF(1+g)/(1+r)^2 + CF(1+g)^2/(1+r)^3 + ... = CF/(r-g)

A 1% increase in r and a 1% decrease in g both have the same effect on price.
Interesting. It appears that convergence can only occur if r > g. For companies with double digit expected earnings growth over the next 5 years, for example, it seems this convergence would only occur in the terminal value. I could be messing something up, but it also seems like all of the non-linear effects of earnings growth rate expectations (and maybe interest rates) have to happen before the convergence. In the equation CF / (r - g), doubling r approximately halves the valuation and doubling g approximately doubles the valuation with most real-world values. I would call those inverse linear and linear relationships respectively. But before the convergence, maybe the impact of g and r are non-linear?
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