Letter number 26 of July 2007


News : The equity risk premium

1. The principle

Trades in corporate stocks, like trades on all markets, are made at the market price, ie, a price that involves both a buyer and a seller.

This market price is arrived at and explained by several factors, the purest of which theoretically, and the most widely used, is the discounting of free cash flows generated by the investment at a rate that reflects the market risk of this investment. This rate is determined as the risk free interest rate plus a risk premium that is proportional to the market risk of the asset. This risk premium that takes the form of the product of the ß ratio of the investment (1) and the difference between the expected market return and the risk, and the risk free interest rate: r = rf + ß × (E (rm) – rf).

In the euro zone, the expected rate of return on the market in mid 2007 is around 8% (2). Accordingly, on the basis of a risk free interest rate of around 4.7% corresponding to the 10-year government bond rate, the risk premium for the European equities market is currently below 4.0%.

2. Two radically different methods for estimating the risk premium

Estimates of the equity market risk premium, ie, the difference between the market return and the risk free interest rate, are currently arrived at using two possible approaches:

• Either on the basis of forecast data (future free cash flows) and the current share price, from which we deduct, after a few calculations, the discount rate used, and thus the risk premium since the discount rate is equal for the whole of the market at the risk free interest rate plus the risk premium.  In this case, we refer to the anticipated or forward risk premium (3), because it is based on investors' current expectations, both anticipated and not anticipated, because it is the risk that is anticipated not the premium, which is current.

Or on the basis of historical data relating to rates of returns received by investors since over very, very long periods. On efficient markets, historical rates of return should be equal to future rates of return.  In this case we refer to the historical risk premium, based on the very pleasing principle that, over the very long term, we end up getting what we ask for.

3. Weaknesses of the historical premium

From a conceptual point of view, only the anticipated risk premium is acceptable for calculating a discount rate. The price of an asset today can only correspond to expected discounted cash flows that it should generate given the rate of return required by the investor today. So, the $ / € exchange rate is currently 1.35.  It is at this price that it is possible to buy or sell the dollar, not at 1.10, even though this is the average exchange rate over the X previous years.

The historical premium has, de facto, three drawbacks:

• Given the volatility of annual returns recorded (annual rates of + 20 % or – 20 % are not unheard of (4)), calculations have to be based on data over a very long period in order to reduce the standard deviation of observations and to arrive at a relevant average (5). Even over 75 years, the theoretical standard deviation of observations following a normal rule is 2.5%, which means that a premium of 5%, for example, has as much chance of being 2.5% as 5% or 7.5%.  So UBS (6) estimates that the risk premium for the USA, calculated by Ibbotson (7) since 1926, often cited and used (7.1% on arithmetical average and 5.2% on geometric average), would change by one point if it were calculated from 1925 or 1927.

• When markets are rising, as they have been since March 2003, the historic rate of return achieved increases and thus the risk premium calculated as an average including recent years in which performances were (very) good, rises, when, because the market is performing so well, rates of return required by shareholders fall.  Similarly, when markets are falling (2000 to 2003), rates of return achieved are negative and bring down the historic average which takes them into account.  At the same time, investors’ required returns rise (which explains a part or the whole of the fall).  This is completely inconsistent

• Calculations of historical returns ignore the case of firms that went bankrupt over the period studied as this method only looks at the performance of share prices of firms still in existence today.  However, the basis of a rate of return is the remuneration of the risk that a firm that goes bankrupt could generate only at a given moment.  So it’s hardly surprising that using this method, we arrive at a higher risk premium (around 7%) than with the prospective method (just under 4% currently) as it ignores the case of investments with a -100% return (bankruptcy). It’s a bit like including only those who have passed all of their A-levels in a survey to measure the average level of education of all 18 year-olds (8).
4. Historical inconsistent use of premiums

From a practical point of view, we see that those using the historical approach to the risk premium, often because they believe the current risk premium to be volatile, which is true, forget that the risk-free interest rate is even more volatile, as illustrated by figures for the French situation since 1980:

Accordingly, proponents of the historical approach could, on the basis of the same argument of volatility, be justified in calculating the average risk-free interest rate over a long period.  They don’t do so of course, because they probably realise the absurdity of the result based on a parameter, the risk-free interest rate, that is readily available to all and sundry in the daily newspaper.

In addition, it is inconsistent, as can, unfortunately, often be observed, to calculate the risk premium (E (rm) – rf) using a given risk-free interest rate and in the formula r = rf + ß × (E (rm) – rf), replacing rf with a different figure from that used to calculate the risk premium (because most of the time we don’t know what risk-free interest rate was used to calculate the risk premium).

Finally, those with many years experience in calculating expected risk premiums know that when interest rates rise, as they have been doing for some time, the risk premium tends to fall.  And also, the required rate of return doesn’t rise as high as the performance of the risk-free interest rate might lead one to assume, as the risk premium absorbs part of the rate hike.  And vice versa in the event of a fall in interest rates.  All things considered, the rate of return required by the shareholder, calculated using an expected risk premium is less volatile than the rate of return calculated using a constant risk premium.

5. To conclude

The reader will be well aware by now that we would strongly advise against using historical risk premiums in a practical financial operation. They may however be useful with a view to historical studies.

As there are several available sources for the expected risk premium and as over the very short term (a few days to a few weeks) they can, for technical reasons, be very volatile (9), averages of these various sources can be calculated over a period of a few (three?) months (10). There is a risk that averages calculated over longer periods could be disconnected from the market.  So, for example, a figure arrived at in July 2006 (on the basis of estimations for the first half of 2006) is unlikely to be of much relevance in April 2007.  Since January 2006, the CAC 40, the Dow Jones and the S&P 500 have risen by between 16 and 19%, although earnings forecasts have not been revised by this amount.  Over the same period, the risk-free interest rate in Europe has risen by 80 points and in the USA by 45 points, resulting in a fall in the risk premium since this period of around 70 base points.

Finally, it is with regret that we note that new players in the field of finance, especially valuation experts, seem to think it necessary to hide behind studies of historical premiums for their valuations, just because they exist and because they can be submitted to a judge if ever they need to defend their figures before the courts.  As if for the past 40 years, others, already cited in this article, had not been putting a lot of intellectual rigour and research into this area.

No expert worth his or her salt should arrive at a premium of 5% in 2007 (ne varietur), based on the average of a sample of 30 studies:

• one of which is pre-1965
• some of which only cite other studies in the sample which are then given twice as much weight
• two of which cover the Danish market (probably because “there is something rotten in the state of historic risk premia!”) while the rest of the sources mainly cover the US market
• with the same study cited twice because of a change in financial sponsor
• referring to financial text books which only cite the work of researchers without carrying out their own research (we’re in a good position to know!), quoted in editions that are more than 15 years old, even though they’ve been updated by their authors on a regular basis!
(1) For more details on the ß, see chapter 21 of the Vernimmen.
(2) Source: Associés en Finance and Exane BNP Paribas.
(3) Or prospective. For more details see chapter 22 of the  Vernimmen.
(4) See chapter 21 of the Vernimmen.
(5) In their book, The Equity Risk Premium, Oxford University Press 2006, W. Goetzmann and R. Ibbotson attempted to calculate the risk premium over the period 1792 – 1925.  They arrive at a figure of 2.72%, which they warn should be taken with caution, given the difficulties of measuring the risk-free interest rate in the USA over this period, which saw the US government go bankrupt several times (before 1815).
(6) The Wacc user’s guide, March 2005.
(7) See chapter 21 of the Vernimmen.
(8) Specalists refer to the surviving biais. For more see “The equity risk premium.” B. Cornell, Wiley, 1999, page 61.
(9) Analysts’ revisions of their forecasts are always a behind new information and the impact on the share price.  This means that in the very short term, an adjustment of the change in share price will impact strongly on the risk premium since over the very short term, forecasts of cash flows remain unchanged.
(10) In this case, an average of risk-free interest rates over three months should also be considered.

Statistics : Corporate income tax rates in the world

Once again this year, KPMG’s annual study shows a decline in the average corporate income tax rate, to 24.2%, in the European Union.

In addition, Spain and the Netherlands significantly reduced their rates. For 2008, one can expect the same trend as Germany, Spain and the United-Kingdom have already announce they will cut their corporate income tax rates.

Research : Is comprehensive income useful?

In March 2006, the International Accounting Standards Board (IASB) published suggestions for a new way of presenting results.  The IASB suggests that the last line of the income statement should be referred to as “comprehensive income” (CI), and no longer as net income.  CI is defined as the periodic change in equity capital, excluding any dealings with shareholders, ie, payment of dividends and capital increases/decreases.  It includes, in addition to net income in its IFRS version, all unrealised foreign exchange gains and losses, asset re-valuations, cash flow hedging, changes in the fair value of financial instruments intended to be sold, and actuarial gains and losses (if any) relating to pension fund commitments. On this basis, net income will have become merely an intermediary balance on the statement of change in equity, with the difference between this net income and CI being referred to as “other comprehensive income” (OCI).

If this reform is adopted, it will be evidence that international accounting standards are shifting towards the principle of full fair value. The way the results are presented will highlight the change in the entity’s value more than the flows generated by the business. Accounting and finance academics at the University of Paris Dauphine (1) have looked into whether this notion could help to measure the financial performance of firms. They look at the respective contributions of operating income, net income and CI to the market value of firms. The usefulness of information contained in CI is limited in the five countries studied (the UK, Germany, France, Italy and Spain) compared with net income. On the other hand, OCI seems to add useful information to the valuation of share prices to that already contained in net income.

The authors also show that for firms that have already been publishing CI in anticipation of the reform, this figure does become more explanatory over time, especially in Germany.  For example, at the close of 2004, over 60% of German companies published their CI, compared with less than 10% in other European countries.

Using CI encourages the perception of accounting as a portfolio management tool, rather than a tool for managing a company.  The goal is to represent the whole of the value created for the shareholder over the period. This figure does however include a number of gains that have not yet been realised. According to the authors, this could be a source of possible manipulation of the figures when assessing the fair value of all of the unrealised gains and losses. Additionally, these figures are not always checked by management as they depend on market fluctuations.  Accordingly, the disciplinary power of CI remains to be demonstrated.

Professionals themselves appear to be divided on the issue, fearing that the reporting of value will end up replacing the reporting of performance, and that the distinction between income actually realised in cash and unrealised income will become increasingly difficult to make. Another cause for concern is the independence of the valuation. It would seem to be common sense to avoid giving the firm’s management the dual role of provider of information and (self)valuer, a job usually done by financial analysts.  After all, what thinking person would trust a film review written by the film’s director?

(1) On the relevance of reporting comprehensive income under IAS / IFRS : Insight from major european capital markets by Laurent Batsch, Jean-François Casta, Steve Lin and Olivier Ramond.

Q&A : What are Economic and regulatory capital?

Regulatory capital is the amount of tangible capital (ie, following deduction of goodwill) that the banking regulators (the Central Banks) require banks to maintain, given the nature of the banking activity. Under the provisions of Basle I, banks are required to set aside capital amounting to at least 4% of their average weighted assets (referred to, following various deductions, as tier 1 capital) and total capital including the above and hybrid securities (tier 2 and tier 3) (1) of at least 8% of their weighted assets. Regulatory capital is intended to represent the share of a bank to the required global equity in the banking industry given the systematic risk entailed in banking.

Basle II, which applies from 2008 (for banks that have chosen to sign up early) and which is a regulatory requirement, brings regulatory capital closer to economic capital, by no longer calculating regulatory capital as a percentage of the bank's assets but by weighting them differently according to their risk profile. 

Economic capital corresponds to the difference between losses that a bank could incur in extreme cases and the losses it could incur in the ordinary course of business, during normal periods.  “Average” losses are generally covered by the interest margin.  Larger losses are covered by economic capital. The lower the bank’s equity capital compared with the economic capital requirement, the less able it will be to absorb extraordinary losses and the more fragile it will be. In the same way that we don't build dykes along rivers just to cope with normal flow, but to protect ourselves during the sort of floods that happen once every 100 years, economic capital is often fixed by the bank's management in order to cover around 99.5%, or even 99.97% of cases. In the latter case, which generally corresponds to an AA rating, the bank has a 0.03%, probability of going bankrupt, or to go back to the river analogy, once in every 3,333 years, a river will burst its banks and flow over the dyke.

However, economic capital is not only a measure of the bank's risk as an absolute.  It is also used to measure internally the adjusted return on the risk of a business line, a product, a client or a transaction, on the basis of the required economic capital calculated at each of these levels.

As we have seen, the amount of economic capital determines the level of risk that the bank’s shareholders and creditors run, in the same way that in a firm, the amount of equity capital compared with capital employed determines the level of shareholder risk. In a bank, economic capital is managed under the global constraints of regulatory capital because history has shown that when a bank goes under, the repercussions on the economy are far more serious than in the case of an ordinary firm going bankrupt, which is why the state authorities, through the banking regulators, maintain tighter control over the running of banks than of other firms.
That said, there’s nothing to stop anyone from applying the economic capital method, the determination of which is mainly based on the calculation of value at risk (VAR) (2), to non financial groups in order to better assess the nature of the risk taken, the level of returns to be expected and the level of economic capital to be set aside in the company’s financial structure.  Ground-breaking work in this field has been carried out by Jacques Tierny.

With thanks to Eric Boutitié

(1) See the Vernimmen.com Newsletter n°15, April 2006.
(2) For more details on VAR, see chapter 50 of the Vernimmen.