Equity Risk Premiums (ERP) and Stocks: Bullish or Bearish Indicator

If you have been following my blog postings, you are probably aware that I have an obsession with equity risk premiums (ERP), and have done an annual survey paper on the topic  every year since 2008 (with the 2013 update here). I also post a monthly update for the ERP for the S&P 500 at the start of the month on my website. As a consequence, my attention was drawn to a post by Fernando Duarte and Carlo Rosa, economists at the Fed in New York, on the topic. They argue that equity risk premiums are at historic highs, primarily because the US treasury rates are low, and note that these high equity risk premiums are a precursor to good stock returns in the future. I don’t disagree with their authors that equity risk premiums are high, relative to history and that the low risk free rate is in large part responsible these large premiums, but I am less sanguine about using the ERP as a market timing device, especially at this time in history.

Measurement approaches

There are three ways of estimating an equity risk premium. One is to look at the difference between the average historical return you would have earned investing in stocks and the return on a risk free investment. This historical premium for the 1928-2013 time period would have stood at about 4.20%, if computed as the difference in compounded returns on US stocks and on the 10-year US treasury bond. (I know. I know. We can have a debate about whether the US treasury is truly risk free, but that is a discussion for a different forum.) The second is to survey portfolio managers, CFOs or investors about what they think stocks will generate as returns in future periods and back out the equity risk premium from these survey numbers. In early 2013, that survey premium would have yielded between 3.8% (from the CFO survey) to 4.8% (portfolio managers) to 5% (analysts). Finally, you can back out a forward looking premium, based upon current stock prices and expected cash flows, akin to estimating the yield to maturity on a bond. That is the process that I use at the start of every month to compute the ERP for US stocks, and that number stood at 5.45% On May 18, 2013. 

What is the ERP? 

The equity risk premium is the extra return that investors demand over and above a risk free rate to invest in equities as a class. Thus, it is a receptacle for investor hopes and fears, with the number rising when the fear quotient dominates the hope quotient. In buoyant times, when investors are not fazed by risk and hope is the dominant force, equity risk premiums can fall. In the graph below, you can see my estimates of the implied equity risk premium for US stocks from 1961 to 2012 (year ends) with annotations providing my rationale for the shifts over time periods. 

The average implied equity risk premium over the entire period is 4.02% and that number is the basis for the bullishness that some investors/analysts bring to the market. If the equity risk premium, currently at 5.45%, does drop to 4.02% , the S&P 500 would trade at 2270, an increase of 26.5% on current levels. And history, as Duarte and Rosa note, is on your side, albeit with significant noise, in making this assumption that equity risk premiums revert back to norms over time. As I will argue in the next section, the high ERP in 2013 is very different from high ERPs in previous time periods and extrapolating from past history can be dangerous. 

A Fed-engineered ERP?

This equity risk premium, though, is over and above the risk free rate. To provide a sense of the interplay between the risk free rate and the equity risk premium, I plot the expected return on stocks (based upon future cash flows and current stock prices), decomposed into the equity risk premium and  the and the risk free rate each year from 1962 to 2012. 

Over the last decade, the expected return on stocks has stayed surprisingly stable at between 8-9% and almost all of the variation in the ERP over the decade has come from the risk free rate. In particular, the higher ERP over the last five years can be entirely attributed to the risk free rates dropping to historic lows. In fact, the expected return on stocks on May 18, 2013 of 7.40% is close to the historic low for this number of 6.91% at the end of 1998. 

So what? While the relationship between the level of the ERP and the risk free rate has weakened over the last decade, the two numbers have historically moved in the same direction: as risk free rates go up (down), equity risk premiums have risen (fallen). In fact, a regression of the ERP on the ten-year US treasury bond rate from 1960-2012 is presented below: 

ERP = .0348                            + .0842 (US T. Bond Rate) R squared = 4.68% 

(1.57) 

Thus, an increase of 1% in the ten-year bond rate (from 2% to 3%, for instance) increases the ERP by 0.0842%. In fact, running the regression through from 1960-2003 (excluding the last decade) yields an ever stronger result: 

ERP = .0202                           + .2592 (US T. Bond Rate) R squared = 43.52% 

(5.62) 

During this period, a 1% increase in interest rates would have led to an increase of 0.26% in the ERP. The last decade has weakened the relationship between the ERP and the T.Bond rate dramatically.

In light of this evidence, consider again two periods with high ERPs. In 1981, the ERP was 5.73%, but it was on top of a ten-year US treasury bond rate of 13.98%, yielding an expected return for stocks of 19.71%. On May 1, 2013, the ERP is at 5.70% but it rests on a US treasury bond rate of 1.65%, resulting in an expected return on 7.35%. An investor betting on ERP declining in 1979 had two forces working in his favor: that the ERP would revert back to historic averages and that the US treasury bond rate would also decline towards past norms An investor in 2013 is faced with the reality that the US treasury bond rate does not have much room to get lower and, if mean reversion holds, has plenty of room to move up, and if history holds, it will take the ERP up with it.

In the table below, I list potential consequences for the S&P 500, in terms of percentage changes in the level of the index, of different combinations of the risk free rate and the ERP: 

Thus, if risk free rates move to 3% and the equity risk premium drops to 5%, the index is undervalued by about 5%, but if rates rise to 4% and the equity risk premium stays at 5.5%, the index is overvalued by 8.28%. There is another interesting aspect to the table that bears emphasizing. While the sum of the risk free rate and equity risk premium is the expected return on stocks, stocks are worth much more for any given expected return, if more of that expected return comes from the risk free rate. In the figure below, note the S&P index levels for an expected return of 9%, using different combinations of the risk free rate and ERP: 

Thus, the same mean reversion that market bulls point to with the ERP can be used to make a bearish case for stocks. The historical average expected return for stocks between 1960 and 2012 of 10.43%, this would translate into the S&P 500 being over valued between 12-40%, depending upon the composition of the expected return. In fact, that is the reason that you have the large divergence in the market between those who use normalized PE ratios and argue that stocks are massively overpriced and those who use the equity risk premium or the Fed model today to make the opposite case.  I am sure that you have your own views on both where the risk free rate and the equity risk premium are headed. If you want to explore the effect on stock prices of changing the variables, please use the linked spreadsheet. 

Bottom line

In a previous post, I noted that stocks do not look over priced. While you may feel that this post is in direct contradiction, let me hasten to provide the bridge between the two.  In the prior post, I noted that stock prices are being sustained by four legs: (1) robust cash flows, taking the form of dividends and buybacks at historic highs for US companies, (2) a recovering economy (and earnings growth that comes with it), (3) ERP at above-normal levels and (4) low risk free rates. Thus, my argument is a relative one: given how other financial assets are being priced and the level of interest rates right now, stocks look reasonably priced. 

The danger, though, is that the US T.Bond rate is not only at a historic low but that it may be too low, relative to its intrinsic level, based upon expected inflation and expected real growth (a topic for another blog post coming soon). If you believe that the T.Bond rate is too low, then you have the possibility that you are in the midst of a Fed-induced market bubble(s) and that script never has a good ending. The scary part is that there are no obvious safe havens: gold and silver have had a good run but don’t seem like a bargain and central banks around the world seem to be following the Fed’s script of low interest rates. You could use derivatives to buy short term insurance against a market collapse but, given that you are not alone in your fears about the market, you will pay a hefty price. 

There is a middle ground. In my last ERP update, I argued that stock market investors were dancing to the Fed’s tune and wondering whether the music would stop. Let me rephrase that. If the market is dancing to the Fed’s tune, it is not a question of whether the music will stop, but when. When long term interest rates move back up, as they inevitably will, the question of how much the equity markets will be affected will depend in large part on whether the ERP declines enough to offset the interest rate effect. Thus, while I would not be arguing that stocks are cheap, simply because the ERP today is higher than historic norms, I am not ready to scale down the equity portion of my portfolio (especially since I have no place to put that money). Looking at the table of market sensitivity to risk free rate/ERP combinations, there are enough soft landing scenarios for the market that I will continue to buy individual stocks, while keeping an eye on the ERP & T.Bond rate.

Apple: News, Noise and Value

As has been the case for much of the last two years, the Apple earnings report on April 24, 2013 was a media event, previewed endlessly on investment sites, covered heavily by the media and tweeted about by both Apple fans and foes. While I try to stay away from the hype around earnings reports, this is a good occasion to revisit my earlier posts on Apple, and especially the one I made at the start of this year on its valuation.

The Signal amidst the Noise

One of the most difficult parts of being an investor in Apple has become dealing with the cacophony of rumors, stories and news releases that seem to permeate the day-to-day coverage of the stock. Not only do we, as investors, have to determine whether there is truth to a story but we also have to evaluate its impact on value (and indirectly on whether to continue holding the stock). To keep my perspective, as I read these stories, I go back to basics and draw on my “financial balance sheet” view of a company. While it resembles an accounting balance sheet in broad terms, it is different on two dimensions. First, it is a forward looking and value based assessment of a company, rather than being backward looking and historical cost based. Second, it is flexible enough to allow me to record the potential for future growth as an asset, thus giving businesses credit for value that they may create in the future from growth. In very broad terms, here is what Apple’s financial balance sheet  looked like just before the most recent earnings report:

There is nothing surprising about this balance sheet but it brings together much of what has happened to the company between April 2012 and April 2013. During the year, the company has become increasingly dependent upon its smartphone business, accounting for 60% of revenues and even more of operating income, generating immense amounts of cash for the company (with the cash balance climbing $50 billion over the course of the year to hit $145 billion). During the course of the year, we have seen a slowing of revenue growth and pressure on margins, both of which have contributed to declining stock prices. The other big change over the course of the year is that the value of growth potential (from unspecified future products) has faded, at least in the market’s eyes, and this is reflected in the decline of $200 billion in market value over the last nine months.

The Last Earnings Report (April 23, 2013)

The most recent earnings report contained a mix of good news on the financial front (cash and financing mix) and bad or neutral news on the operating asset front. Using the same framework that I used in the last section, here is how I parsed the news in the report:

First, in the no news category, revenue growth is no longer in the double digits and smartphones continue to increase their share of overall revenues & operating income. Well, we knew that already and the revenue growth was well within the expected bounds. Second, the bad news is that margins are shrinking faster than we expected them to, though I get the sense that Apple is understating its margins (by moving some expenses forward) and its guidance for the future with the intent of getting ahead of the expectations game. Third, in near term bad news, the fact there is no mention of any new products or breakthroughs suggests that there will be no revolutionary product announcement (iWatch, iTV, iWhatever) in the next quarter. However, if you are a long term investor, it is mildly disappointing that it looks like that there will be no blockbuster announcements in the next three months but it is clearly not the end of the world.

On the financial side, there was substantial news, much of which I think is positive. 

1. Cash return to stockholders: The decision to decision to return about $100 billion more in  cash to stockholders in buybacks and dividends by 2015  has to be viewed as vindication for those (like David Einhorn) who have arguing that Apple should be explicit about its future plans for cash and that it should distribute a large chunk cash with stockholders. 
2. Buybacks versus Dividends: In a bit of a surprise, the cash return will be more in the form of buybacks than dividends. I, for one, am on board with that decision because hiking the dividends further will essentially make this stock a "dividend" play, with an investor base that will put dividend growth in the future ahead of all other considerations.  If Apple wants to retain the option of entering a new and perhaps more capital intensive business in the future, it is better positioned as a consequence of this decision. 
3. Debt coming? In an even bigger surprise, Apple has opened the door to taking on conventional debt. While the details are still fuzzy and the initial bond issue may be for only about $10 billion, it seems likely that the debt issued will grow beyond that amount. To those who would take issue with this decision, arguing that Apple does not need to borrow with all of its cash reserves, you may be missing the reason why this debt will add to value. If the trade off on debt is that you weigh the tax benefits of debt against the bankruptcy cost, there can be no arguing against the fact that borrowing money will add value for stockholders. To those who feel that it is in some way immoral or unethical, based upon the argument that Apple is sheltering its foreign income from additional US taxes while claiming a tax deduction for interest expenses, I would be more inclined to listen to you if you showed me convincing proof that you make mortgage interest payments every year but did not claim the mortgage tax deduction in your tax returns, because you think that it deprives the treasury of much needed revenue. The US tax code is an abomination, with its treatment of foreign income as exhibit 1, but to ask Apple (and its stockholders) to pay the price for the tax code's failures makes little sense to me. 

In summary, the net effect of the earnings report is negative on operating cash flows (with the declining margins) but positive on the financial side (with any discount on cash dissipating, as a result of the cash return announcement, and the tax benefits from debt augmenting value). 

Intrinsic value impact
In my post from the end of last year, I had reported on an intrinsic valuation of Apple of $609/share, using data as of December 2012, with a distribution of values in a later post. Given that there have been two earnings reports since, I decided to revisit that valuation. In addition to updating the company's numbers (all of the numbers except leases) to reflect the trailing 12 months (through March 31, 2013), I also incorporated the information from the most recent earnings reports to update my forecasts on three variables in particular:

1. Revenue growth: As the competition in the smartphone business continues to increase, I am inclined to lower my expected revenue growth rate for the next 5 years to 5% from my original estimate of 6%. While this is well below the revenue growth of 11.28% over the last year (even using the last 'bad" quarter comparison to the same quarter the previous year), it is the prudent call to make, especially in the absence of news about new products in the near term.
2. Operating margin: I had projected a target  pre-tax operating margin of 30% in my December 31, 2012, valuation, about 5% below the prevailing margin of 35.30% from the last annual report (the 10K in September). The pre-tax operating margin has dropped to 30.92% in the trailing 12 months ending March 31, 2012, and was about 29%, just in the last quarter. Since margins are coming down faster than expected, I lowered my target margin to 25%. 
3. Cost of capital: The cost of capital that I had used in my December 2012 valuation was 12.49% reflecting my expectation that Apple would stay an all equity funded firm in the foreseeable future. The decision to use debt upends that process and adding $50 billion in debt to the capital structure, while buying back $50 billion in stock raises the debt ratio in the cost of capital calculation to about 13%, while lowering the cost of capital to about 11.29%. 

The net effect of these changes is that the value per share that I obtain for Apple is about $588, about 3.5% lower than the value of $609 that I estimated in early January. You can download the spreadsheet with my valuation of Apple. Again, make your own judgments and come to your own conclusions. If you are so inclined, go to the Google shared spreadsheet  and enter your estimates of value.

If you are concerned about whether borrowing $50 billion will put Apple in danger of being over levered, I did make an assessment of how much debt Apple could borrow, by looking at the effects of the added debt on the costs of equity, debt and capital, with the objective being a lower cost of capital. I try to be realistic in my estimates of cost of equity (adjusting it upwards as a company borrows more) and the cost of debt (by coming up with a prospective rating at each dollar debt level and cost of debt at each debt ratio). If Apple can maintain its existing operating income, its debt capacity is huge ($200 billion plus) but even allowing for a halving of their operating income, it has debt capacity in excess of $100 billion. As with the valuation spreadsheet, you are welcome to download my capital structure spreadsheet for Apple and play with they numbers.

Clear and present dangers
Given the price collapse over the last few months, it would be foolhardy not to stress test the numbers in this valuation. In the first set of tests, I went back to the discounted cash flow valuation and computed my break even numbers for growth, operating margins and cost of capital, changing each of these variables, holding all else constant. The table below lists the current numbers for Apple for these variables, my estimates and the break even that yields today's stock price ($420 on April 28, 2013).

Holding all else constant, Apple's revenues would have to decline 5% a year for the next 5 years to justify a value per share of $420. Similarly, the pre-tax operating margin would have to drop to 12% from 30% today, holding the other variables at base case levels, to get to the same price. As an investor in Apple, there seems to be plenty of buffer built in, at least at current stock prices.

Will Apple go the way of Dell and Microsoft?
As a technology firm, though, your concerns may be about the company hitting a cliff and essentially either losing value or becoming a value trap. In particular, you may be worried that Apple may follow in the footsteps of two technology giants that have had trouble delivering value to stockholders in the last decade. One is Dell Computers, where Michael Dell's attempts to rediscover growth have failed and the company is now facing a more levered, low growth future. The other is Microsoft, a less dire case, but a stock that hit its peak about a decade ago and has plateaued since. Can Apple be "Delled" or "Microsofted"?

To be Delled: What awaits a company when it's product/service becomes a commodity and it operates at a cost disadvantage. 
Dell was an success story in the growing PC business through much of the late 1990s and the early part of the last decade. As the market for PCs grew, Dell used its cost advantages over Compaq, IBM and HP to make itself the most profitable player in the market. What's changed? First, the market for PCs hit a growth wall, as consumers turned to tablets and other connected devices. Second, PCs became a commodity, just as Dell lost its cost advantage to Lenovo and other lower cost manufacturers. With Apple, the peril is that their biggest and most profitable business, smartphones, may be heading in that direction. Unlike Dell, though, Apple is more than a hardware manufacturer and it's success at premium pricing in the PC business is indicative of the pricing power that comes from creating the operating system that runs the hardware. I believe that the risk of Apple being Delled is small.

To be Microsofted: The destiny of a business that has a profitable, cash-cow product(s) but runs low on imagination/creativity.
 Riding the success of Windows and Office, Microsoft became the largest market cap company about a decade ago. Like Apple, it seemed unstoppable. So, what happened? From the market's perspective, the company seemed to run out of imagination and creativity and investors got tired of waiting for the next big hit and moved on. Note, though, that while the stock price and market capitalization have not moved much over the last ten years, the company has returned billions in cash to its stockholders. Could this value stagnation happen to Apple? Yes, but to me (and I have never been shy about my Apple bias), there are is a big difference between the companies. One is that I don't think that Microsoft lost its imagination and creative impulses a decade ago. I don't think it ever had any. While Windows nor Office were workmanlike and professional products, neither can ever be called elegant or creative (and I speak as a heavy user of Office products). Apple, on the other hand, has created iconic products through the decades, some less successful than others (remember the Newton), and I find it hard to believe that those creative juices just dried up last September.

Buy or Sell? Hold or Fold?

If Apple was being priced as a high growth stock, with sustained margins and on the expectations of "big" new hits in the future, I would be worried about the last earnings report. It is not. As you can see from the break even table in the last section, it is being priced as a low growth, declining margin company, with no great hits to come. I find it striking that the same investors who have priced the stock on this basis react to incremental news on these items (growth, margins, new products), as if they had not already priced it in.

As I see it, if I have Apple in my portfolio at $420 and the company continues to disappoint on every dimension (growth, margins, new products), I will have a boring stock that delivers billions in earnings and pays a solid dividend. However, if the company surprises by stopping margin leakage and increasing revenue growth in the smartphone market or by introducing the iWatch or the iTV, it will be icing on my investment cake. In a market, where my alternative investments are richly priced, Apple looks like a winner, to me. It stays in my portfolio, the price disappointments of the last few months notwithstanding.

My earlier posts on Apple

1. Apple: Thoughts on Bias, Value, Excess Cash & Dividends (March 1, 2012)
2. Apple: Know when to hold 'em, know when to fold 'em (April 3, 2012)
3. Emotions, Intrinsic value and Dividend Clienteles: The Apple postscript (April 6, 2012)
4. Apple's Crown Jewel: Valuing the iPhone Franchise (August 29, 2012)
5. Winning by Losing: The power of expectations (October 9, 2012)
6. The Year in Review: Apple's Universe (December 27, 2012)
7. Are you a value investor? Take the Apple test (January 27, 2013)
8. Market Mayhem: Lessons for Apple (January 31, 2013)
9. Back to Apple: Thoughts on value, price and the confidence gap (February 7, 2013)
10. Financial Alchemy: David Einhorn's value play for Apple (February 8, 2013)

The Golden Rule? Thoughts on gold as an investment

Paraphrasing Winston Churchill, gold is a "riddle, wrapped up in a mystery inside an enigma", at least as far as I am concerned. I don't understand what moves the gold price and I have never held gold in my portfolio. That does not mean, however, that I am not fascinated by the price of gold and immune from its movements. That was brought home last week, when the price of gold dropped by 9% on April 15, 2013, the biggest one day drop in thirty years. Not only did the prices of other precious metals (silver dropped 12%) and industrial metals drop, but stock prices took a tumble as well. While the attention has focused on the price drop in recent days, gold has had a good run over the last decade.

The nominal and inflation-adjusted prices of gold have soared in the last decade, and at the end of 2012, the nominal price was at an all time high of 1664 and the inflation-adjusted price was close to its previous high set at the end of the 1970s. The big question that has been debated in recent days is whether gold will continue to drop in the coming days. More generally, is gold is under or over priced? With my limited understanding of gold, I decided to give it a shot.

Does gold have an intrinsic or fundamental value?
The intrinsic value of an asset is a function of its expected cash flows, growth and risk. Since gold is a non cash-flow generating asset, I argued in this earlier blog post  that you cannot estimate an intrinsic value for gold. It is the same argument I would make about all collectibles: Picassos, baseball cards or Tiffany lamps included.  If one of the central tenets of value investing is that you should never invest in an asset without estimating its value, that would seem to rule out gold as an investment for a classic value investor. In fact, Warren Buffett has repeatedly argued against investing in gold because it's value cannot be estimated.
There is an alternate route that can be used to estimate the "fundamental" value of a commodity by gauging the demand for the commodity (based on its uses) and the supply. While that may work, at least in principle, for industrial commodities, it is tough to put into practice with precious metals in general, and gold, in particular, because the demand is not driven primarily by practical uses. 

What drives gold prices?
If gold does not have an intrinsic value, what is it that drives its value? There are at least three factors historically that have influenced the price of gold.

1. Inflation: If as is commonly argued, gold is an alternative to paper currency, you can argue that the price of gold will be determined by how much trust individuals have in paper currency. Thus, it is widely believed that if the value of paper currency is debased by inflation, gold will gain in value. To see if the widely held view of gold as a hedge against inflation has a basis, I looked at changes in gold prices and the inflation rate each year from 1963-2012. 

The co-movement of gold and inflation is particularly strong in the 1970s, a decade where the US economy was plagued by high inflation and the correlation between gold prices and the inflation rate is brought home, when you regress returns on gold against the inflation rate for the entire period:

Annual % Change in Gold price = -0.08 + 4.37 (Inflation rate)

R squared = 19.9%

While this regression does back the conventional view of gold as an inflation hedge, there are two potential weak spots. The first is that the R-squared is only 20%, suggesting that factors other than inflation have a significant effect on gold prices. The second is that removing the 1970s essentially removes much of the significance from this regression. In fact, while the large move in gold prices in the 1970s can be explained by unexpectedly high inflation during the decade, the rise of oil prices between 2001 and 2012 cannot be attributed to inflation. In fact, taking a closer look at the data, it is clear that gold is more a hedge against extreme (and unexpected) movements in inflation and does not really provide much protection against smaller inflation changes.

2. Fear of crisis: Through the centuries, gold has been the “asset” of last resort for investors fleeing a crisis. Thus, as investor fears ebb and flow, gold prices should go up and down. To test this effect, we used two forward-looking measures of investor fears – the default spread on a Baa rated bond and the implied equity risk premium (which is a forward looking premium, computed based upon stock prices and expected cash flows). As investor fears increase, you should expect to see these premiums in both the equity and the bond market increase. 

While the relationship is harder to decipher than the one with inflation, higher equity risk premiums correlate with higher gold prices. Again, regressing annual returns on gold against these two measures separately, we get:

Annual % Change in Gold Price = -0.25 + 8.91 (ERP)

R squared = 10.3%

Annual % Change in Gold Price = 0.10 + 0.25 (Baa Rate - T.Bond Rate)

R squared = 0%

These regressions suggest little or no relationship between bond default spreads and gold prices, but a positive relationship, albeit one with substantial noise, between gold prices and equity risk premiums. Thus, gold prices seem to move more with fear in the equity markets than with concerns in the bond market. Every 1% increase in the equity risk premium translates into an increase of 8.91% in gold prices.

3. Real interest rates: One of the costs of holding gold is that while you hold it, you lose the return you could have made investing it in a financial asset. The magnitude of this opportunity cost is captured by the real interest rate, with higher real interest rates translating into much higher opportunity costs and thus lower prices for gold. The real interest rate can be measured directly used the inflation indexed treasury bond (TIPs) rate or indirectly by netting out the expected inflation from a nominal risk free (or close to risk free) rate.

Note that the TIPs rate is available only for the last decade and that the real interest rate is computed as the difference between the ten-year US treasury bond rate in that year and the realized inflation rate (rather than the expected inflation rate). Regressing changes in gold prices against the real interest rate yields the following:

Annual % Change in Gold price = 0.27 - 6.94 (T.Bond Rate - Inflation Rate)

R Squared = 36.6%

High real interest rates are negative for gold prices and low real interest rates, or negative real interest rates as is the case today, push gold prices higher.

A Relative Valuation of Gold
Knowing that gold prices move with inflation, equity risk premiums and real interest rates is useful but it still does not help us answer the fundamental question of whether gold prices today are too high or low. Can you do a relative valuation of gold? I don’t know but I am going to try.

A. Against the inflation index
The most comprehensive paper that I have seen on the relationship between gold prices and inflation  is available here, with a follow up here. In these papers, the price of gold is related to the CPI index and a ratio of gold prices to the CPI index is computed. I try to replicate their findings and I use the US Department of Labor CPI index for all items (and all urban consumers) set to a base of 100 in 1982-84, but with data going back to 1947. The level of the index at the end of 2012 was 231.137. Dividing the gold price of $1664/oz on December 31, 2012, by the CPI index level yields a value of 7.20. To get a measure of whether that number is high or low, we computed it every year going back to 1963: 

At the year-end price in December 2012, gold prices were at an all time high, relative to the CPI. Updating the gold price to 1382.2/oz, the price on April 17, yields a Gold/CPI ratio of 5.98.

The median value is 2.55 for the 1963-2012 time period and 2.91 for the 1971-2012 period. Thus, based purely on the comparison of the current measure of the Gold/CPI ratio to the historical medians does miss the fact that  equity risk premiums are high and real interest rate are negative today, both of which should make gold more attractive as an investment. Consequently, I regressed the Gold/CPI index against equity risk premiums and real interest rates and while real interest rates seem to have little effect on the Gold/CPI ratio, there is strong evidence that it moves with the ERP, increasing (decreasing) as the ERP increases (decreases):

1963-2012 Time Period:

Gold Price/ CPI = -1.75 + 115.4 (ERP)

R Squared = 52.9%

1971-2012 Time Period

Gold Price/ CPI = -0.88 + 100.2 (ERP)

R Squared = 49.1%

The implied equity risk premium for the S&P 500 at the start of April 2013 was 5.79%, and plugging that value into the gold/CPI regression yields the following:

Gold/CPI (given ERP = 5.79% on 4/1/13) = -0.88 + 100.2 (.0579) = 4.92

While gold remains over priced, relative to historic norms, it looks far less over priced once we account for today's risk premiums.

B. Against other precious metals
There is another way that you can frame the relative value of gold and that is against other precious metals. For instance, you can price gold, relative to silver, and make a judgment on whether it is cheap or expensive (on a relative basis). At the end of December 2012, the gold price was $1664/oz and the silver price was $30.35/oz,, yielding a ratio of 54.84 for gold to silver prices (1664/30.35). To get a measure of where this number stands in a historical context, we looked at the ratio of gold prices to silver prices from 1963 to 2012: 

The median value of 51.22 over the 1963-2012 period would suggest that gold is not over priced, relative to silver. In fact, silver has dropped in price more than gold has this year and using the April 17, 2012 prices for gold (1382.2) and silver (23.31), we get a ratio of 59.30. Given that gold and silver move together more often than they move in opposite directions, I am not sure that this relationship can be mined to address the question of whether gold is fairly priced today, but it can still be the basis for trading across precious metals.

Gold as insurance
It can be argued that pricing gold relative to silver or against the inflation index misses the primary rationale for investors holding gold, i.e., as insurance against uncommon but potentially catastrophic risks to their assets, from hyper inflation to war and terrorism. Viewed from that perspective, gold operates as insurance for an investor whose assets are primarily financial and thus exposed to these catastrophic risks. Put in less abstract terms, if you add gold to your portfolio, it is not to make money, per se, but to buy protection against “black swan” events that could swamp your other investments. If you view gold as a hedge/insurance against event risk, there are two implications:

1. You should not expect to gold to generate high annual returns over long periods. In fact, notwithstanding boom periods  (the 1970s and the last decade) gold has, for the most part, generated low returns over long periods, relative to other risky investments. 
2. It also follows that the price of gold should reflect the cost of buying the insurance, which in turn will be driven by the uncertainty you feel about the future and the likelihood of catastrophic events. Thus, the multiple crises over the last decade (banking, war, terrorism) explain both the surge in gold prices over the last decade and the correlation with equity risk premiums.

It is worth noting that gold is not the only insurance against black swan events. There eare other ways, using other real assets (collectibles, real estate, other commodities) or financial derivatives (including puts on indices) that can deliver the same hedging results, perhaps at a lower cost.

The bottom line
I have always been uncomfortable talking about the value of gold as an asset and its place in my portfolio. Writing this post has been cathartic, since it has allowed me to recognize the two sources of my discomfort. First, I am most comfortable with cash flow generating investments, where I can estimate an intrinsic value, and my valuation tool kit is limited when it comes to valuing gold. Second, I don't share the fervor that some investors  have for gold, who seem to view it as much in emotional terms as in financial ones.

As a complete novice in assessing the value of gold, here is how I see its value. As a stand-alone investment, I would not buy gold, given its history (of delivering low returns in the long term) and given how it is priced today. As insurance, though,  I think it makes sense to add to your portfolio, even at today's prices. You don't have to be a conspiracy theorist or paranoid about central banks to have legitimate fears that prices in financial markets, built upon uncommonly low interest rates, may collapse. I know that the price of gold as insurance is higher than it has been in the past, but the risks that you are insuring against are also much higher than they have been historically.

Update: If you are interested in exploring the data on your own, you can download the raw data on gold prices, silver prices, CPI, interest rates, ERP and other variables. 

A Sweet Spot for US Equities: Opportunity and Dangers

The US equity markets are on a roll. Today, the S&P 500 hit an all time high, just weeks after the Dow also broke its record. While it has been less than five years since the crisis of 2008 and the epic collapse of equities in the last quarter of that year, the returns earned by those who stayed the course, even relative to pre-crisis price levels, is a testimonial to the dangers of staying out of equity markets for extended periods.  As with every other market surge, this one has brought with it the usual questions: Have stocks gone up too far, too fast? Are we due for a correction? Should we stay in the market or take profits? I could cop out and use the excuse that I am not a market timer, but that would be a lie. All investor are market timers, with the differences being one of degree. So, the honest truth is that I have a view about markets but that it does not dominate my investment decision process.

Since it is so easy to be swayed by story telling, when talking about equity markets, I try to bring the same tools to assessing markets that I do for individual stocks. The intrinsic value of equities, in the aggregate, is determined by four variables:

1. Cash returned to equity investors: Ultimately, we buy stocks to get cash flows in return, with those cash flows evolving over the last three decades from almost entirely dividends to a mix of dividends and stock buybacks. Holding all else constant, the more cash that is returned to investors in the near term, the more you will be willing to pay for stocks. 
2. Expected growth: The bonus of investing in equity, as opposed to fixed income, is that you get to share in the growth that occurs in earnings and cash flows in future periods. Other things held equal, the higher the expected growth in earnings and expected cash flows, the higher stock prices should be. 
3. Risk free rate: The risk free rate operates as more than base from which you build expected returns as investors. It also represents what you would earn from investing in a guaranteed (or at least as close as you can get to guaranteed) investment instead of stocks. Consequently, stock prices should increase as the risk free rate decreases, if you hold all else fixed. 
4. Risk premium: Equities are risky and investors will demand a “premium” for investing in stocks. This premium will be shaped by investor perceptions of the macro economic risk that they face from investing in stocks. If the equity risk premium is the receptacle for all of the fears and hopes that equity investors have about the future, the lower that premium, the more they will be willing to pay for stocks. 

Note that while it is easy to focus on each of these variables and draw conclusions about the impact on stock prices, they tend to move at the same time and often pull in different directions. For instance, stronger economic growth will push up earnings growth but interest rates will usually go up as well. In a similar vein, paying out more in cash flows to investors in the current period will often mean less being invested into businesses and lower growth in the future. It is the trade off that determines whether stock prices will go up or down as a consequence. On each of these variables, the US equity market is looking at "good" numbers right now: the cash returned to investors by US companies has rebounded strongly from post-crisis lows, earnings growth is reasonable, the risk free rate is at a historic low and the equity risk premium, while not quite at pre-crisis levels, has declined significantly over the last year. To explore both where we are and the potential dangers that we face as investors, let’s take a look at each variable.

1. Cash flows
a. Background: Until the early 1980s, the primary source of cash flows to equity investors in the United States was dividends. As I noted in this post from a while back, US companies have increasingly turned to returning cash in the form of buybacks. While there are some strict value investors who believe that dividends are qualitatively better than buybacks, because they are less volatile, the aggregate amount returned by US companies in buybacks is too large to be ignored. 

Over the last decade, buybacks have been more volatile than dividends but the bulk of the cash flows returned to stockholders has come in buybacks.
b. Level: In the most recent twelve months for which data is available (through December 2012), the companies in the S&P 500 bought back almost $400 billion worth of stock, much more than the $270 billion that they paid out in dividends. In terms of index units and as a percent of the level of the index, the aggregate cash flows have recovered fully from their post-2008 swoon.
c. Sustainability: While it is good that cash flows are bouncing back, we should worry about whether companies were over reaching and paying out too much in 2012, perhaps in advance of the fiscal cliff at the end of 2012, in which case you should expect to see a drop off in cash flows in the near term. There are three reasons to believe that this is not the case. First, as Birinyi Associates notes in this blog post, the pace of buybacks is increasing in 2013, not dropping off, with the buybacks authorized in February 2013 at an all-time high. Second, the cash returned in 2012 may have been a historic high in dollar value terms, but as a percent of the index, it is close to the average yield over the last decade. Third, the aggregate cash balances at the S&P 500 company amounted to 10.66% of firm value at the end of 2012, suggesting that companies have cash on hand to sustain and perhaps even increase cash returned to stockholders. While a portion of this cash is trapped, it is possible that corporate tax reform, if it happens, will release this cash for distribution to stockholders.

2. Expected growth
a. Background: For dividends and buybacks to continue to grow in the future, there has to be growth in earnings. While that growth can be estimated by looking at history or by tracking analyst forecasts of earnings for the individual companies, it has to be earned by companies, reinvesting their earnings back into operations and generating a healthy return on equity on those investments.
Intrinsic growth rate = Equity Reinvestment Rate * Return on equity
Thus, while history can sometimes yield skewed values (up or down) on growth and analysts can become overly optimistic or pessimistic, the intrinsic growth rate will be grounded in reality.
b. Level: To look at earnings growth in the S&P 500, lets begin by looking at history. In the table below, we report on earnings growth rates over 5 years, 10 years, 20 years and 50 years in index earnings.

	Arithmetic average	Geometric Average
Last 5 years	6.46%	4.42%
Last 10 years	9.66%	8.33%
Last 20 years	9.60%	8.28%
Last 50 years	8.30%	6.90%

Over the last 5 years, the compounded average annual growth rate in aggregate earnings for the S&P 500 has been 4.42%. As the most widely followed index in the world, analyst estimates of growth in earnings are widely available both for individual companies in the S&P 500 index and for aggregate earnings in the index. Using the former to construct a bottom-up estimate of growth yields 10.57% as the expected growth rate in March 2013. Since there is evidence that analyst estimates of growth are biased upwards at the company level, we also looked at the “top down” estimates of growth that analysts are forecasting for aggregate earnings in March 2013, obtaining a lower growth rate of 5.33% a year for the next 5 years.
c. Sustainability: Are analysts over estimating earnings growth? One way to check is to compute the intrinsic growth rate by computing the equity reinvestment rate and return on equity for the index. To compute the equity reinvestment rate, we use the aggregate cash returned to investors (75.31) in 2012 and the earnings on the S&P 500 (102.47) in 2012:
Equity Reinvestment Rate = 1 - 75.31/102.47 = 26.51%
To compute the return on equity on the index, we divide the aggregate earnings on the index in 2012 by the aggregate book value of equity on the index (613.14) at the start of 2012:
Return on equity = 102.47/613.14 = 16.71%
The product of the two yields a sustainable growth rate:
Sustainable growth rate = .2651 * .1671 = .0443 or 4.43%
While this number is lower than the top-down analyst estimate of growth, it is within shouting distance of the estimate. There is, of course, a concern that some investors and analysts have voiced about the operating earnings number reported for the S&P 500, arguing that it is over stated. If it is, then the equity reinvestment rate and ROE are both over stated, and the expected growth rate will be lower.

3. Equity Risk Premium (ERP)
a. Background: Put simply, the equity risk premium is the market price of equity risk. It is determined on the one hand by perceptions of the macro risk that surround investors, with greater risks going with a higher ERP, and on the other hand by the collective risk aversion of investors, with more risk aversion translating into a larger ERP. A larger ERP implies that investors will pay lower prices for the same set of equity cash flows. The conventional wisdom that this number is stable in mature markets was shaken by the banking crisis of 2008, as premiums in the US and European equity markets experienced unprecedented volatility.
b. Level: There are two ways in which ERP can be estimated. One is to look at a long period of history and to estimate the premium that stocks would have generated, over an above the treasury bond rate, over that period. This “historical” premium approach yields 4.20% as the ERP for US stocks in 2013, using data from 1928-2012. The other is to estimate an “implied” premium, by backing out an internal rate of return from current stock prices and expected cash flows. This approach yields much more volatile equity risk premiums over time, as can be seen in the graph below: 

The implied ERP at the start of 2013 was 5.78%, lower than the ERP at the start of 2012, but still at the high end of the historical range.
c. Sustainability: I have been estimating the monthly ERP for the S&P 500 since September 2008, and as can be seen in the figure below, the premium of 5.43% at the start of March 2013 represents a significant decline from a year ago. Note, though, that it is still much higher than the premium that prevailed in September 2008, just prior to the crisis. In fact, the average implied ERP over the last decade has been 4.71%, lower than the current implied ERP.

[I have an  long, not-very-fun update that I do on equity risk premiums that you can download and peruse, if you are so inclined. It includes everything that I know about ERP]

4. Risk free rate
a. Background: As sovereigns increasingly face default risk, it is an open question whether any investment is risk free in today’s environment. However, for an investor in US dollars, the return you can expect to make on a long term treasury bond not only represents a base from which all other expected returns are computed but is an opportunity cost of investing in something risk free instead of stocks.
b. Level: By any measure, risk free rates are at historic lows in much of the developed world. On March 26, 2013, the ten-year US Treasury bond rate was at 1.91%, well below where it stood prior to the last quarter of 2008 and well below rates that prevailed a decade earlier. 

The average for the ten year bond rate for the last decade was 3.59% and lengthening the time period pushes the average up to 4.62% (last 20 years) and 6.58% (last 50 years)
c. Sustainability: Is the treasury bond rate destined to rise and if it does, will it bring down stocks? To answer this question, we have to look at what has kept rates low for such an extended period. While the answer to some is that it is the Fed’s doing, I, for one, don’t attribute that much power to Ben Bernanke. The Fed has played a role, but it has succeeded (if you can call it success) only because inflation has been benign and real economic growth has been abysmal for this period. There are at least four scenarios that I see for the future direction of interest rates, with differing implications for stocks. 

Scenario	Treasury bond rate	Outlook for stocks
More of the same (anemic economic growth, low inflation)	Stays low	Neutral
Stronger economic growth, low inflation	Rises to reflect higher real growth	If economic growth translates into earnings growth, neutral. If not, mildly negative.
Low economic growth, high inflation	Rises to reflect higher inflation	Negative. Higher required returns on stocks, no offsetting positive.
Higher economic growth, low inflation, Fed Magic	Stays low	Positive

If you believe that the Fed can keep a lid on interest rates, as economic growth returns, the outlook is positive for stocks. I think that the most likely scenario is that the interest rates will rise as the economy improved, and the outlook for stocks will depend in large part on whether earnings growth picks up enough to offset the interest rate effect.

Valuation of the S&P 500 Index

To see the interplay of these numbers and the resulting consequences for stocks, I valued the S&P 500, as of March 26, 2013, using the following inputs: 

Based upon my assumptions, the market’s current winning ways can be justified. Replacing the current implied equity risk premium with the average premium over the last decade (4.71%) yields a level of almost 1800 for the index, and using the analyst-estimated growth rate will make it even higher. Higher risk free rates have a negative, albeit muted, effect on value, if accompanied by higher growth rates, but do have a much more negative impact, if growth rates remain unchanged. You may have very different views on the market drivers and if you are interested, you can input your numbers into the attached spreadsheet to get an assessment of value for the S&P 500 index.

Bottom line

When stocks hit new highs, the natural impulse is to look for signs of over valuation, but there are good reasons why US stock prices are elevated: cash flows are high, growth looks good, the macro risks seem to have faded (at least some what) and the alternatives are delivering lousy returns. In the near term, stocks remain vulnerable to two possibilities. One is that another macro crisis will pop up (Italy, Spain, Portugal or a non-EU black sheet) that will cause equity risk premiums to jump back to the 6%+ levels that we have seen so often in the last 5 years. The other is a sudden surge in interest rates, unaccompanied by better earnings or higher earnings growth. Since all risky asset classes (corporate bonds, real estate etc.) will be also adversely affected by either of these developments, I don't see much point to shifting from equities to other risky assets to protect myself against these risks. I could, of course, choose to stay in cash, but as the last 5 years have indicated, waiting for the "right time" to invest can leave you on the sidelines for too long. So, I am going to stop worrying about the overall market and go back to finding under valued companies.