Risk free rate

Risk free rate is an important factor in the CAPM model, first introduced by William Sharp. Risk free rate, should by its definition as the name suggest offer the return, which is not subject to any risk and is thus guaranteed return for an investor.

Proxy for risk free rate was historically equal to rates of government bonds of countries with the best credit rating (assed by rating agencies like S&P, Moody’s or Fitch). Investors used 90-day Treasury bill rate, as a proxy for risk free rate as it contains no credit risk and the maturity is so short that there is no liquidity or market risk. The five-year or ten-year Treasury also has no credit risk, but if interest rates rise, the market value could decline, that is why some argue that only short Treasury bills should be used as a proxy for risk free rate. When selecting the proxy for a risk free rate one should also select the instruments denominated in the same currency, because if that is not the case one faces exchange rate risk (if political risk is not the same for counties with the same currency, a great example of that is the European Union, it can be assumed in the CAPM model as a separate factor, but that is a topic for another article).

New phenomena are the negative interest rates, which are now present in European Union (counters with the highest credit rating – Germany, The Netherlands, Finland and even Austria and France), Switzerland and Japan. Proxy for a risk free rate is/will became a subject around which many arguments will open as it seem, that without taking on credit risk investors can expect to pay the borrowers to take their money.

Risk free rate for the purpose of valuation

For the purpose of valuation long-term projections for the company are usually prepared and in line with the long-term aim of estimating the value of a business, proxy for a long-term risk free should also be used.

As stated in the paragraph in, which is describing negative interest rates current situation and uncertainty on the financial markets lead to unexpected conditions on the market. Change in interest rates for businesses has changed, partly as a result of temporary liquidity problems and the inability of long-term lending and borrowing, and at the same time 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 government bonds in the euro area AAA-rated doesn’t fully reflect the long-term risk-free rate.

Another argument that long-term risk-free rate is not fully reflected in current long-term government bonds is the fact that many long-term government bonds investors fled to safer investments, which are government bonds with a credit rating of AAA, which is another reason (reflecting the simple supply and demand parity) that they have low return and thus don’t fully reflect the risk-free rate. What should be taken into account with the previous government about investors seeking AAA rated bonds is the fact that number of countries with that rating is declining, putting more pressure on yields of those countries.

Estimation of risk free rate

For the estimation of the expected long-term risk-free rate we use the average rate of return on long-term (10-year) AAA-rated government bonds in the Euro Area in the period 1999 – Current market data (depending on the date of valuation) 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 0.26% to 5.70%, on average on the level of 3.55%. In our opinion, based on the trends in financial markets and the fluctuation of market interest rates, 3.5% rate reflects the long-term required return on risk-free investments in the future expected by the market.

Inflation also plays a role in determining the risk free rate. After the end of 2013 inflation declined significantly putting negative pressure on nominal interest rates. In the period from 1999 until December 2015 average real interest in the Euro Area was equal to 1.7% and average inflation was equal to 1.8%. It is expected that real interest rates and inflation will move in the similar ranges as in the past putting the expected nominal risk free rate in the range between 3.0% and 4.0%, with an average of 3.5%.

In line with the long-term aim of estimating the value of a business, we believe 3.5% to be the most appropriate long-term required return on risk-free investments and should be applied when using the CAPM model for the purpose of business valuation.

Nominal and real return of AAA bonds
Fluctuation of 10y EU, USA, Japan bonds

Source: Reports of ECB, ECB Economic Bulletin

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