Monday, August 14, 2006

Back-of-the-Envelope Equity Premium

Historically, corporate equity has returned about 6% more annually on average compared to government bonds. If I expected the equity premium to be that high going forward, I would be fully invested. In fact, I would be maxing out my HELOC to buy stock. But a 6% equity premium seems like quite an unreasonable expectation at this point in time. What might be a more reasonable expectation?

I’ve tried two methods to come to an answer. The first method assumes that dividends will grow at the same rate as GDP, then estimates expected real GDP growth, adds the dividend yield, and compares the result to the 10-year TIPS yield. The second method assumes that corporate profits will return to their historical fraction of national income, adjusts current earnings accordingly, adds the expected inflation rate, and compares the result to the nominal 10-year Treasury yield.

Method 1. To estimate real GDP growth (for the US), I take the trend labor productivity growth rate of 2.7% (based on my exponential smoother optimized for an 8-quarter-ahead forecast) and add an assumed labor force growth rate of 1%, so the estimated real GDP growth rate is 3.7%. The dividend yield on the S&P 500 is 1.95% according to this week’s Barron’s, and the 10-year TIPS yield is 2.32%. The calculation 3.70% + 1.95% - 2.32% gives an estimated equity premium of 3.33%. It’s not nearly as “puzzling” as the historical 6%, but as a long-term investor, I still find 3.3% pretty impressive. If that’s the right figure, then I’m in.

Method 2. Barron’s reports the earnings yield on the S&P 500 as 5.74%. In 2005, after-tax corporate profits were 8.94% of US national income, compared to an average of 6.64% since 1948. Adjusting the latest earnings gives an earnings yield of 5.74% x (6.64/8.94) = 4.26%. The expected inflation rate is 2.5% (always). The 10-year Treasury yields 4.98%. The calculation 4.26% + 2.50% - 4.98% gives an estimated equity premium of 1.78%. If that’s the right figure then I’m out – way out.

Not that a 1.78% premium is really all that bad for a long-term investor, but I have some short-term concerns that would make me willing to risk missing out on a few years of 1.78% excess returns:
  1. With the premium so far below its historical average, I would expect some reversion. By reversion, I mean stock prices going down.

  2. Under this method, I’m assuming that corporate profits will revert to their historical fraction of national income. I’m guessing that when that happens, it won’t be a good time to own stock.

  3. I think Wall Street may be underestimating the chance of a recession.

  4. Nouriel Roubini provides a convincing set of parallels between today and 1987.

So, by method 1, stocks are a good deal for someone with my preferences. By method 2, they’re not. Taking an average, (3.33% + 1.78%) / 2 = 2.55%. At that price, I’m on the fence.

Labels: , , , , , ,

12 Comments:

Anonymous pireader said...

Believe your Method 2 leaves out growth in earnings per share.

Let's suppose that S&P earnings per share grow "forever" in tandem with GDP -- perhaps 5.5% p.a. (3% real plus 2.5% for inflation).

A share is a claim on that future earnings stream, so its price today is just the value of those future earnings discounted back. For these numbers, that only works if the discount rate is 11.24% (=5.74%+5.5%)

If a share's discount rate is 11% p.a., then we expect its value to grow at about 11% each year. Which is an equity premium of ~6% above the long-term T-bond (~5%).

This is pretty standard stuff. Am I missing somethinG?

Wed Aug 16, 12:34:00 AM EDT  
Anonymous pireader said...

The previous post has a calculational error. It should read:

Believe your Method 2 leaves out growth in earnings per share.

Let's suppose that S&P earnings per share grow "forever" in tandem with GDP -- perhaps 5.5% p.a. (3% real plus 2.5% for inflation).

A share is a claim on that future earnings stream, so its price today is just the value of those future earnings discounted back. For these numbers, that only works if the discount rate is 9.76% (=4.26%+5.5%)

If a share's discount rate is 9.76% p.a., then we expect its value to grow at about 9.76% each year. Which is an equity premium of ~5% above the long-term T-bond (~5%).

This is pretty standard stuff. Am I missing something?

Wed Aug 16, 12:40:00 AM EDT  
Blogger knzn said...

Growth in earnings should only be included if the source is something other than reinvested earnings, or to the extent that the return on those reinvested earnings is greater than the return on the original investment (which might be the case either because the return on capital is higher in the future or because the original equity was selling at a discount to its replacement cost).

If growth in earnings is merely due to reinvestment of retained earnings at the same rate of return, then it would be double counting to take into account earnings growth in addition to the full original earnings. For example suppose a stock has a 5% earnings yield and pays no dividends, and suppose the return on reinvested earnings is also 5%. Then earnings will grow at a 5% rate, but you are getting no dividends, and the value of the company is growing at the same rate, so the total rate of return is 5%, not 10%.

According to BLS data, US capital is actually getting less productive (as one might expect, given that the capital stock is increasing relative to available labor). It’s hard to say what the replacement cost might be, but stocks are selling at large multiples of book value, so I’m assuming they aren’t selling at a significant discount to replacement cost. Therefore I’m attributing all expected (real) earnings growth to reinvestment at the same rate of return.

Wed Aug 16, 06:27:00 AM EDT  
Blogger knzn said...

Continuing my last comment…You could make a case that there are other sources of earnings growth, such as the value of land owned by corporations, which could continue to rise as the population rises even if there is no reinvestment, or the value of knowledge which can be costlessly spread over a rising population. So my method 2 could be understating the equity premium, but method 1 is probably overstating it (given what might be an optimistic assumption about productivity growth and failure to account for the inflation risk premium), so I’m still pretty comfortable with the range they give.

Wed Aug 16, 06:37:00 AM EDT  
Blogger spencerengland said...

One of the big difference between now and 1987 is valuation. In 1987 the s&P 500 pe peaked at 22 just before the crash while my model said that given current inflation and interest rates the pe should have been 14. So the market was 50% overvalued and essentially all the crash did was eliminate that overvaluation -- it also caused the fed to abort the tightening that was in progress.

Now the s&p 500 pe is around 16
and my pe model say it should be around 16 so we do not have the big overvaluation currently that needs to be eliminated as we did in 1987.

In both cases I'm using trailing operating earnings rather then forecast eps. In 1987 I kept being told the market was OK because we were going to get a 33% gain in eps in 1988 and on that basis the market was not overvalued. They were right too, we did get a 33% increase in EPS in 1988 but that did not prevent
the 1987 crash.


Otherwise you analysis of the market is very good. Over the long run the market PE seems to have 5 to 15 years secular swings from below 10 to over 20 and back to below 10. We now appear to be on one of those long term down swings.

Wed Aug 16, 11:33:00 AM EDT  
Anonymous Anonymous said...

福~
「朵
語‧,最一件事,就。好,你西.............................................................................................................
..................

Wed Apr 01, 10:35:00 AM EDT  
Blogger . said...

酒店喝酒,禮服店,酒店小姐,酒店領檯,便服店,鋼琴酒吧,酒店兼職,酒店兼差,酒店打工,伴唱小姐,暑假打工,酒店上班,酒店兼職,ktv酒店,酒店,酒店公關,酒店兼差,酒店上班,酒店打工,禮服酒店,禮服店,酒店小姐,酒店兼差,暑假打工,酒店經紀,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,寒假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,暑假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,寒假打工,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,暑假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店兼差,暑假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,寒假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,暑假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,寒假打工,酒店小姐,台北酒店,禮服店 ,酒店小姐,酒店經紀,酒店兼差,暑假打工,酒店小姐,禮服店 ,酒店小姐,酒店經紀,酒店兼差,寒假打工,酒店小姐,禮服店 ,酒店小姐,酒店經紀,酒店兼差,暑假打工,酒店小姐,禮服店 ,酒店小姐,酒店經紀,酒店兼差,寒假打工,酒店小姐,禮服店 ,酒店小姐,酒店經紀,酒店兼差,暑假打工,酒店小姐,酒店傳播,酒店經紀人,酒店,酒店,酒店,酒店 ,禮服店 , 酒店小姐,酒店經紀,酒店兼差,暑假打工,招待所,酒店小姐,酒店兼差,寒假打工,酒店上班,暑假打工,酒店公關,酒店兼職,禮服店 , 酒店小姐 ,酒店經紀 ,酒店兼差,暑假打工,酒店,酒店,酒店經紀,酒店領檯 ,禮服店 ,酒店小姐 ,酒店經紀 ,酒店兼差,暑假打工, 酒店上班,禮服店 ,酒店小姐 ,酒店經紀 ,酒店兼差,暑假打工, 酒店上班,禮服店 ,酒店小姐 ,酒店經紀 ,酒店兼差,暑假打工, 酒店上班,酒店經紀,酒店經紀,酒店經紀

Tue Apr 21, 07:08:00 PM EDT  
Blogger how to buy air shoes said...

Some new style Puma Speed is in fashion this year. chaussure puma is Puma Shoes in french. Many france like seach “chaussure sport” by the internet when they need buy the Puma shoes or buy the nike max shoes.The information age is really convenient. By the way ,the puma CAT is really good chaussures puma ,don’t forget buy the puma mens shoes and nike air max ltd by the internet when you need them . Do you know Nike Air Shoes is a best Air Shoes .

Spring is coming, and how to choose the polo shirts is the main concern of many people. ralph lauren polo shirts is a classic type and reliable. ed hardy clothing is more in line with the aesthetic ideas of young people, so many young people filled with a variety of ed hardy clothes in their wardrobes. New style ed hardy womens shirt match the new style ed hardy sunglasses , it is a good idea.
Do you think this season is not for ugg boots ? maybe yes .but this season is best time that can buy the cheap ugg boots. Many sellers are selling discounted. Do not miss . Please view my blog and fc2 blog .thank you .

Tue May 19, 05:17:00 AM EDT  
Anonymous Anonymous said...

コンタクトレンズ
国内格安航空券
おまとめローン
留学
インプラント
CloneDVD

Mon Jul 13, 12:43:00 AM EDT  
Anonymous Anonymous said...

クレジットカード 現金化
会社設立
キャッシング
ダンボール
アダルトDVD
水 通販
アルカリイオン水

Mon Jul 13, 12:43:00 AM EDT  
Anonymous Anonymous said...

Manolo Blahnik Boots
|Jimmy Choo Printed pony shoes with frills and stud detail
|Jimmy Choo Printed snake and rooster sandals
Christian Louboutin DV Diamonds 100 sandals
Christian Louboutin Ernesta patent sandals

Wed Sep 22, 12:06:00 PM EDT  
Blogger dfadf said...

Microsoft Office
Office 2010
Microsoft Office 2010
Office 2010 key
Office 2010 download
Office 2010 Professional
Microsoft outlook
Outlook 2010
Windows 7
Microsoft outlook 2010

Tue Nov 02, 01:52:00 AM EDT  

Post a Comment

Links to this post:

Create a Link

<< Home