The Cyclically Adjusted Price Earnings (CAPE) or Shiller PE ratio is 28.5. Although this is down from January 2018 where it stood at 33.3, the only other time’s it has been this high was in January 2000 (followed by years of poor returns) and Black Tuesday (of Great Depression fame.)

The standard PE ratio of 21.1 is high too, but not perhaps to the same degree as the CAPE ratio. This indicates that current earnings and relatively higher (compared to their historical average) than the average of earnings over the last 10 years (compared to the historical average of that measure over time.) This is, after all, the point of the CAPE ratio – it recognises that earnings are cyclical and that a simple PE ratio isn’t that predictive. In other words, recent earnings are high by compared to the last ten years.

Still, none of this is really good news for future performance on the S&P. However, is the situation really as dire as it seems? What impact did the 2008/2009 earnings period have? Do the extremely low interest rates in the US have a part to play here?

Any time part of a measure includes several prior years, it is worth considering what happened in that ten period and if there are any specific base year effects. The only one I’ll mention here is that the cyclically adjusted earnings part still includes the catastrophically low earnings period around 2008/2009. In another 6 to 12 months most of this effect will have disappeared and the CAPE ratio will decline all on its own

My prospective Equity Risk Premium (ERP) estimation tool takes US 10 year nominal yields (1.6%) and real yields (0.2%), the current S&P500 dividend yield (2.0%) and expected real GDP growth of 2% to realise an ERP of 3.8%.

The GDP forecast is the crucially subjective estimate. With population growth of just 0.7% per annum, estimates for medium term GDP growth of between 2% and 3% imply fairly significant per capita growth so I’m more comfortable with 2% than 3%. The 0.8% decline in population growth over the last 50 years (from 1.5% in the 1960s) means some gut feel estimates of achievable GDP growth still reflect this higher growth period.

As a sensitivity on this uncertain input, 3% GDP growth implies an ERP of 4.8%.

The reasonable long term range for an ERP is either 2% to 4% or 3% to 5% depending on who you ask. (There are also those who mis-estimate this and end up with 8% to 10%, but I’ve blogged extensively before on the ERP estimation flaws that are required to get those estimates.)

Whichever range you work with, actual market implied ERPs of 3.8% to 4.8% do not look unusually low, and therefore do not suggest the US market is quite as expensive as some other measures suggest. What is missing here is a time series of market implied ERPs.

In summary, the US market is likely expensive, and there are enough risk factors around to concern an investor. However, I don’t think it’s quite as dire as some have indicated.

Many researchers are comfortable with a range for Equity Risk Premiums of between 3% and 5%. Many corporate finance practitioners use a range from 5% to 8% or even higher. My nearly eight-year-old blog post on mis-estimating the ERP covered these differences in detail.

This post is a little different. Forget about what theory says, what are the implications of using a high risk discount rate (RDR) when calculating embedded values and then trying to maximise value.

Solvency II and SAM suggest a 6% (excess over risk-free) cost of non hedgeable capital. Most South African insurers calculating real-world embedded values use risk-free + 3.5% as their RDR.

Some insurers want to use an RDR closer to 15% or even 20%. The problem here is one of conviction. If the cost of capital was truly felt to be 20%, then capital optimisation, value optimisation and therefore reinsurance decisions should be made with this in mind.

It will almost always be the case that reinsurance will have an implied cost of less than 20%. Thus, the consistent action would be to grab as much reinsurance as possible, at least up the point where the reinsurer was concerned about skin in the game.

I don’t see this happening in practice.

Some insurer will argue that they don’t want to give away all their profits to a reinsurer. This fundamentally misunderstands how reinsurance is priced and the impact of return and profit commissions to facilitate reasonable commercial terms.

Similarly, the pursuit of greater investment returns usually results in more risk and more capital required. At a 20% return on capital requirement, pretty much no avoidable market risk should be retained. Yet I still see insurers opting to take on more credit risk (even at current depressed credit spreads) in pursuit of a little extra yield.

We can have a debate about the range of reasonable RDRs to use. But there is a credibility problem if this rate isn’t also used to decide on reinsurance and investment strategies.

In particular, he mentioned a specific assumption set he had seen including:

• ERP of 6.8%
• company specific risk premium of 4%

He also commented on how haphazard the use of risk premiums can be and referenced a few sources I’ve used myself.

The ERP of 6.8% does seem high. However, it really isn’t possible to comment on the specifics of the company specific risk premium without knowing the company.

Although I haven’t updated my research on this in a few years, in my own work I still generally stick with a range of 3% to 5% for an ERP, before considering company specific factors, liquidity, and so on. Historically / empirically estimated ERPs shouldn’t change frequently since the time series used is long. Another few years on a 20 year estimation period shouldn’t have much impact.

Why some practitioners persist in using too-high ERP estimates

This delves into the area of philosophy, but here are my top reasons (a post from 2011 also covers this):

• Naive analysis of the historical returns in the US over very successful periods for the US economy and stock market easily give high ERP estimates
• comparison of equity returns against short dated T bills rather than longer term T bonds.  (This is less terrible if you apply the premium to short dated rates, but still problematic for several reasons.  It is totally wrong if you apply the rate to bond yields.)
• Confusing of ERP with the total risk premium for a specific share (and more on that later in this post)
• Declining ERPs over time has boosted historical realised ERPs compared to forward looking estimates.

Quick updated estimate of market implied ERP

The use a market implied ERP is still useful as a forward looking measure, especially where a valuation relative to current listed market instruments is important (and it usually is). However, it’s not like this isn’t a subjective process either.

Using this old spreadsheet ERP estimation tool, I used the following quick assumptions:

• Dividend yield of 2.8% (from the All Share)
• Real risk-free yield (R210 yield, which matures in about ten years time) of 2.5%
• Break Even Inflation of 6.1% (based on nominal ten year bond yields of 8.6% and the 2.5% real risk free yield)
• Assumed real GDP growth of 1.8% per annum (based on a combination of sources including our reserve bank, world bank and others) showing 1% growth in the immediate future possibly getting up to 2% over time.  (None of this is pretty, and none of this will really materially increase GDP per capita).

This gives a market implied ERP of just 2.2%. Although this feels quite low, it shouldn’t be surprising given that we all recognise the economic fundamentals feel weak but our stock market is priced at record nominal levels.

Other estimates of market implied ERP

The reader sent me to this website, which shows market implied ERPs. It’s a useful resource. Here is the current view up to 30 September.

They end up with a higher ERP of 2.6%, which actually gives me comfort in my quick estimate of 2.2%, especially when I see that in August their estimate was only 2.4%, which is even closer.

The problem with the JSE as the market for South African companies

Tencent. In a word, that is.And other multinationals and entities with significant exposures outside of South Africa. I believe one of the reasons these ERPs are looking so low is that growth prospects outside of South Africa are better than inside South Africa, so the stock market prices look “too high” compared to South African country prospects, resulting in a too-low ERP.

The problem with “risk free” in emerging markets

Risk free is a term that makes less and less sense the more one thinks about it.  Is Greece government debt risk-free? Is South African government debt risk-free? What about the credit and liquidity characteristics?

Differences between these even within a country, say between the chosen nominal and real bonds used to estimate certain parameters can influence the estimates.

Although the credit spreads should in theory be removed in the estimation of ERP, it is hard to shake the concern that there might be second order implications that are not quite so simple.

So what about other countries then?

From that same site (I’m not going to do a whole range of other countries myself):

• UK 5.8%
• US 3.6%
• Australia  4.4%
• Canada 4.8%
• Switzerland 5.8%
• Germany 6.4%
• France 6.1%
• China 3.8%
• Brazil 2.0%
• India 2.3%

I don’t know enough about Brazil or India to know where there are specific issues for those markets, whether the methodology here falls down, or whether this is part of an emerging market trend.

But overall, these ERPs fall mostly within a comfortable range of 3% to 5% , with some stretching a little outside that on either side.

Company specific parameters

Standard CAPM models assume company specific factors are irrelevant because that risk can be diversified away and therefore should earn no reward. This is broadly true for a diversified investor investing in listed, liquid stocks. Empirically it is absolutely not true for privately held shares, illiquid shares, investments where control may be gained or given up and a host of other possible scenarios.

Estimating a reliable Beta to apply in the CAPM model is about as difficult as anything else covered here, so even then the ERP is not the end of the story.

When valuing a private company, one needs to look at how private companies are valued.

That’s not as vapid as it may sound. Valuation should be concerned with market consistency. This is why we speak about “market implied ERP” in the first place. So, if most other private company valuations (and transactions) factor in company specific factors such as:

• liquidity
• control
• small stock effects
• key person risks
• concentrated customer risks
• leverage (especially if not factored into the Beta).

then a valuation that aims to be consistent with other valuations should factor these in too.

That list isn’t complete and many of the items overlap.  Each one also needs to be carefully weighed against:

• is this not already factored into the ERP?
• is this not already factored into the Beta if one is used
• is this not already factored into the estimation of cash flows

That last one is key.  In fact, it is often the reverse that is true.  Known risks are not reflected in a true probability weighted best estimate manner in the future cash flows. Thus, without some risk adjustment in the discount rate, the value will be overstated.

Scenarios and cash flows as alternative ways to allow for risk

If multiple scenarios are used in the valuation, with attached probabilities, it may be that these risks are adequately considered in the cash flows and do not need an additional adjustment in the discount rate.  Key person risk or customer concentration risk can be reflected in a scenario with a 10% or 20% probability of seriously negative consequences of losing that rainmaker or specialist knowledge, or of losing a single customer along with 50% of revenues.

For larger businesses, with more diversified revenue streams, larger numbers of customers and fewer key person risks (or better ways of mitigating them), these risks tend can be reflected naturally in the cash flows since past experience will likely include some instances of the risk. (This links to another post on ENID.)

Consistent with the market

A useful resource here is PwC’s valuation methodology survey.

Final thought – is a company specific risk premium of 4% too high?

While it is hard to say without knowing the specifics of the company, it doesn’t strike me as obviously too high for a moderate sized, unlisted company.

A recent article in The Actuary magazine addressed whether “de-risking in members’ best interests?“  I say “recent” even though it’s from August because I am a little behind on my The Actuary reading.

In the article, the authors demonstrate that by modelling the impact of covenant risk, optimal investment portfolios for Defined Benefit (DB) pensions actually have more risky assets than if this covenant risk is ignored.

The covenant they refer to is the obligation of the sponsor to make good deficits within the pension fund. Covenant risk then is the risk that the sponsor is unable (typically through its own insolvency) to make good on this promise.

On the surface it should seem counterintuitive that by modelling an additional risk to pensioners, the answer is to invest in riskier assets, thus increasing risk.

The explanation proffered by the authors is that the higher expected returns from riskier assets allow the fund to potentially build up surplus, thus reducing the risks of covenant failure.

I can follow that logic, particularly in the case where the dependence between DB fund insolvency and sponsor default is week. It doesn’t mean it’s a useful result.

The optimisation considered only one side of the equation – what is in members’ best interests. It ignores the other side of the problem – the financial impact (expectation and variability around that) for the sponsor’s financial position.

To take it to the extreme, if every sponsor just liquidated all its assets and transferred them to the DB fund, that would be a pretty good outcome for fund members. Not so much for the sponsor.

Without having seen the detailed model results, what I expect is happening is that the increased allocation towards risky assets is increasing expected returns (as it should) but also increasing the risk to the sponsor of having to put in additional funds. Any time this is done and the sponsor doesn’t default, there is no downside for fund members. The only risk to fund members is the combination of being underfunded and sponsor default.

The risk to the sponsor of increased frequency of injections required has been well established for decades. Depending on what you are willing to assume about risk premiums for risky assets and the assumed risk appetite, the higher expected return might outweigh the increased risk. This is not a point to be glossed over let alone left entirely untouched.

It also raises an awkward question about what they’ve modelled in terms of the covenant in the “no covenant risk” scenario. Surely if one models the covenant and not risk to the covenant, all benefits should always be paid to the members, regardless of asset mix?

I’m not at all convinced that these results are reliable. But either way, the fact that they are optimising and showing results for only one side of a two sided problem makes the approach utterly flawed.

It’s worth reading in its entirety for the insights. I don’t agree with everything there, and I certainly don’t agree with the widely held view (not among the authors) that the universe of countries included in the survey is supposed to be somehow representative of the world.

The countries chosen have an absolutely clear bias in their selection. They are successful economies with successful financial markets. They are included by virtue of their long-term success and capital growth and returns for investors.

The authors know this, but many readers don’t.  The returns per this survey are an overly rosy view of possible future returns.

Market Risk Premium used in 56 countries in 2011: a survey with 6,014 answers

• Interesting not least because it is a survey of required Equity Risk Premiums (or Market Risk Premiums) rather than expected. The rates are higher than I use, although this is also useful information when attempting to perform a “benchmark” valuation. I still struggle to see how these high estimates tie in with prospective estimates of overall economic growth and market performance, which is an important sense-check on any ERP estimate.

The Equity Premium in 150 Textbooks

• The results show a range from 3% to 10%, and that 51 books use different equity premia in various pages. The 5-year moving average has declined from 8.4% in 1990 to 5.7% in 2008 and 2009. This declining trend has been observed over even longer periods and is one of the common reasons for mis-estimating the ERP. 

Equity Premium: Historical, Expected, Required and Implied

• This work provides a fairly in-depth analysis of the differences between the various definitions of ERP and a comprehensive survey of major sources for estimates of these. In general, the estimates of the Expected ERP over T-bonds (rather than short-dated T-bills) are in line with the range I use of 3% to 5% with several showing values to the lower end of this range.

The authors of Triumph of the Optimists have joined forces with Credit Suisse to publish the Credit Suisse Global Investment Returns Yearbook 2010 (pdf) which is a brief update of their brilliant research.  You should definitely read the original book.

The updated research shows a very familiar picture to that of the book.  Here are a few important outcomes:

• Realised excess returns of equities over bonds have been negative for most countries for the last decade.

Clearly, using realised excess returns (or historical ERPs) over a short period as a measure of future ERP is a bad idea.  I’m fairly sure the future ERP is positive.

• For the World, the US, the UK, Australia, Belgium, Canada, Denmark, France, Germany, Ireland and South Africa (a few countries I chose to look at before I realised the trend is near-universal) have had declining historical ERPs over the last 110 years. Some have had a few bumps in between, but the overwhelming trend has been downward.  The last decade’s poor performance has obviously helped establish this trend, but it was pretty well established for most of these countries even without the last decade.

Using unadjusted historical ERPs over long periods is a dangerous idea because trends in the data make it a poor estimate of future experience.

• Over the last 110 years, the average realised ERP in the World has been 3.7% (over bonds).

ERPs of 7% or 8% or higher are way too high to be realistic even compared to the historical record which probably overstates future ERPs

• The historical ERP of South Africa over the last 110 years has been 5.4% over bonds. This includes a 25 year period from 1960 to 1984 where the ERP was approximately (I unapologetically hacked the authors’ pristine numbers to estimate this) 11%.

Even allowing for this exceptionally good period (associated with gold boom years) an ERP for South Africa of 7% or 8% is just too high. We should further be cautious of using a single country’s historical experience given the wide standard errors around these estimates given the variability of the data. South Africa, along with Australia, have the highest and second highest real equity returns per year over the 110 year period. Unless we expect this miracle to continue, we should expect more average growth (mean-reversion in this context is alive and well(.

• The mean-reversion effect in equity returns is small if it exists at all (this from the 2009 report).

One should not expect to make strong returns in years following poor returns. The time to recover from significant falls, in real terms, can be decades (see Japan) or easily longer than 5 years (several examples).

Overall, the appropriate ERP for South Africa is probably still somewhere between 3% and 5%, with plenty of evidence to support estimates towards the lower end of that range.

If you use a basic prospective ERP estimate tool with the JSE All Share’s current dividend yield of 2.17%, you need to be expected real GDP growth of 7% in future. Any takers?

Typically viewed as risky investments, the junk bonds boom of the 80s showed that there is more to junk than just a risky investment.

Locally, our pension funds and other retirement savings money should be more heavily invested in junk bonds. I’m surprised more people aren’t talking about this. It might be due to the limited availability of junk in the SA market. On the other hand, if demand picked up, I’m sure we could see more original-issue junk bonds as yields drop and become more attractive financing vehicles.

There are always marks for considering tax

Why should pension funds be invested in junk? Tax. Approved retirement savings vehicles in South Africa don’t pay income tax. Thus, the value of securities that would attract significant tax is higher for these investors than for the market as a whole. If risk and return are balanced for the market as a whole, the extra return available to retirement vehicles through not paying tax is a bonus over and above that appropriate for the risk.

Conversely, pension funds should stay far away from tax-efficient instruments such as preference shares. The prices of these instruments have already been bid up by tax-paying investors.

Investment attractiveness from an untaxed investors perspective

Property isn’t bad from a tax perspective, since it provides taxable rental income, inflation-like growth in rental streams and an additional return given the large investment size and illiquidity of the investment.

Equities are awful for a retirement investors from a tax perspective. Tax exempt dividends and lower-taxed capital gains make up the return. Yes, this is still a source of good long-term returns and a way to earn the Equity Risk Premium over time. But more of the excess returns required by pension funds should be generated by junk bonds.

Junk Bonds provide a high return (all of it taxable in the hands of a tax-paying investor) from credit risk and illiquidity risk.

Some junk is pink, but it’s not all rosy

Pension funds should have less equity, less government bonds, more more more junk bonds. We need to work to find more and better ways of building this market so pension funds can make use of it. (Regulation 28 limits the extent of foreign exposure, another possible way to increase junk bonds investments). The added diversification of adding a different type of risk category to the investment portfolio means we will likely be able to maintain the overall level of risk (or even decrease it) while boosting returns due to the tax premium.

I’m not discounting the default risk inherent in junk bonds, and that this isn’t ideal for a pension fund. It’s a real pity pension funds can’t short the equity of the underlying companies (in moderation) to provide some protection against deterioration of illiquid junk bonds they start migrating down the credit ratings from BB towards ultimate default.

So, how does one not lose money with the Make a Million competition?

Don’t enter.

You are overwhelmingly like to lose money if you enter this competition. I’ve said this before, and I’ve been right before. I’m right again.

There’s also the little idea that the  structure of the Make a Million competition increases risks of  financial meltdown

Let’s look at some hard statistics to show what I mean.

Telling statistics (what they don’t show)

In the MaM presentation, the organisers include some interesting statistics about number of trades, trading activity and many other metrics.

They don’t show average returns or performance.

So let’s look at some of the numbers:

Raw return data (excluding prize money) based on 2009 MaM competition.

Suddenly the competition doesn’t look so great, does it?  (This isn’t the first time, here is my analysis of the Comedy and Tragedy that was the 2008 Make a Million competition.)

Here’s a little explanation of each of the items in the table:

Average Return

This is the return than you can expect to make on average. Yes, that’s a loss of over 10% of your investment. For all the talk about trading opportunities by the MaM organisers and sponsors, the trading result of this competition (ignoring prizes) is that more money is lost than is made.

Expected Loss

This is the total Rand amount you will lose on average (again ignoring prizes) by entering the competition. Quite a steep price. (The prize money makes the competition profitable on average, but only in a very skewed manner that only helps one person.  More on this in a bit)

Median Return

This is the return that half the entrants earned less than, and half the entrants earned more than. Half the participants lost more than 15% of their investment.

Mode Return

This is less intuitive to understand. The most common result for a entrant was to lose 9% of their starting stake.

Probability of breaking even, earning less than 10% or doubling money

Hopefully these are reasonably self-explanatory. What’s clear is that there is a high probability of doing badly, and a low probability of doing well.

Probability of winning

Ultimately your probability of winning serious money is still very low.

Great returns and manageable risk?

The MaM roadshow presentation concludes that there exist opportunities for great returns and manageable risk. I’m not sure what definition they’re using for “great returns” or “manageable risk” but in my book the returns are low and the risk is high. Look at the figures in the table above and explain how that can be interpreted any differently.

Is there any good news at all?

In fairness, there is a million rand prize available for the winner. This doesn’t change the probability of winning, the probability of earning 10%, the probability of doubling your money, the probability of losing any particular amount, but does add extra winnings to the best performer, which increases the average return considerably to 8.5% over the period. So yes, if you win, you will win. Remember the 0.2% probability of winning. In odds, that is about 500:1 against.

Winning strategies

There are some strategies than can help you win Make a Million.  They’re not really legal or ethical but you might want to know the sort of thing your competitors may be up to.