# Letter number 26 of July 2007

- TOPIC
- STATISTICS
- RESEARCH
- QUESTIONS & COMMENTS

## News : The equity risk premium

**1. The principle**

**(1)**and the difference between the expected market return and the risk, and the risk free interest rate: r = rf + ß × (E (rm) – rf).

**(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**

• 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.

**3. Weaknesses of the historical premium**

**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.

*de facto*, three drawbacks:

**(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.

**(8)**.

**4. Historical inconsistent use of premiums**

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**

**(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.

*ne varietur*), based on the average of a sample of 30 studies:

**(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

## Research : Is comprehensive income useful?

**(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.

**(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?

*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.

**(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.