Is return of German bonds good appropriate proxy for risk free rate?

For the estimation of the expected long-term risk-free rate we used the average rate of return on long-term (10-year) AAA-rated[1] government bonds in the Euro area in the period 1999 – December 2016, as we believe this period is appropriate in showing long-term trends. In this period the monthly rates of return on yearly basis were fluctuating from -0.16% to 5.70%, on average on the level of 3.36%. In our opinion, based on the trends in financial markets and the fluctuation of market interest rates, a 3.5% rate reflects the long-term required return on risk-free investments in the future expected by the market (see figure below). Additional justification for the estimated risk-free rate is below:

 

  • Situation after the market crisis and uncertainty on the financial markets lead to higher interest rates for businesses, partly as a result of temporary liquidity problems and the inability of long-term lending and borrowing, but at the same time to a decrease in reference interest rates, as central banks increase the quantity of money in circulation in order to provide additional liquidity and accelerate economic growth. Therefore, we believe that the current (low) return on long-term AAA-rated government bonds in the euro area doesn’t fully reflect the long-term risk-free rate.
  • Additionally, due to increasing risks of many long-term government bonds in the euro area investors flee to safer investments, which are AAA-rated government bonds, which is another reason for their low return and thus these bonds don’t fully reflect the risk-free rate. At the end of 2012 an additional reason for the decrease in returns in the U.S. was the risk of “tax gap”.
  • Additional reason for decreasing returns is in decreasing number of AAA-rated government bonds in the euro area. At the end of 2015, only the following countries had the highest rating: Germany, Netherlands, Finland and Luxemburg (credit rating of Austria has been lowered by Fitch ratings to AA+ as at 13.2.2015, credit rating of Finland has been lowered by Standard & Poor’s to AA+, which is usually followed by Fitch).
  • Duff & Phelps also recommends using the risk-free rate of return of 4% on the basis of their estimates of normalized earnings of 20-year U.S. government bonds (in connection to a 5% equity risk premium).
  • Since 2013 inflation rates in euro area have decreased significantly, posing an additional downward push on nominal risk free rates (see table below), as a consequence nominal rates were in 2015 on the levels of real risk free rates. In the observed period (1999-December 2016) thus the average of real risk free rates was estimated[2] on the level of 1.6% and average euro inflation on the level of 1.7%. In the long-term future we expect the real risk free rate to range between 1.5% and 2.0%.Long-term inflation rate, constantly forecasted by ECB on the levels between 1.8% and 2.0%, is in this report also estimated to range between 1.5% and 2.0% due to current situation on financial markets and the fact that ECB projections of inflation increase to 2.0% were not achieved in the last few years. Additionally, euro area long-term inflation rates expected by IMF are somewhat lower (in 2014 at 1.5%, in December 2016 at 1.8%).

Thus, by summing up estimated spread of expected long-term real risk free rate and expected long-term inflation rates, we estimated long-term (nominal) risk free rate in the range between 3.0% and 4.0%, with the average of 3.5%.

 

Estimation of expected long-term risk free rate

In line with the long-term nature of estimating the value of a business, we believe 3.5% to be the most appropriate long-term risk-free rate and we will therefore apply it in our estimation of required rate of return on equity using the CAPM model.

 

*Real risk free rate was calculated by using the latest available annual consumer price inflation rate as a proxy for expected inflation. Source: ECB Monthly Bulletin until December 2014, Economic Bulletin and Statistical Bulletin until December 2016.

*Real risk free rate was calculated by using the latest available annual

Expected Inflation

 

 

 

 

 

 

 

 

 

 

AAA Rated 10Y Bonds

Source: ECB Reports, ECB Monthly Bulletin until December 2014, Economic Bulletin and Statistical Bulletin until December 2016.

 

 

Fluctuation 10Y Bonds

Source: ECB Reports, ECB Monthly Bulletin until December 2014, Economic Bulletin and Statistical Bulletin until December 2016.

 

 

 

[1] ECB uses credit ratings of Fitch agency to determine AAA-rated government bonds.

[2] The computation of real interest rates based on nominal interest rates is subject to several practical and conceptual difficulties, as a reliable measure of expected inflation over the relevant horizon is normally not observable and can only be estimated. Furthermore, it is not obvious which price deflator is most relevant. The simplest approach to the computation of short and long-term real interest rates is to use the latest available annual consumer price inflation rate as a proxy for expected inflation (ECB Monthly Bulletin), which was also used in our estimate.