El blog que hace la economía accesible a casi todos # Cost of equity estimation for Russell 2000

We estimate a 7.3% of Cost of Equity for Russell 2000

This publication continues with the valuation of Russell 2000 and in this case focused on the explanation of the estimations of another important factor: the cost of equity (Ke). It is calculated using the following formula:

Cost of equity = Risk free rate of return + Beta × (market rate of return – risk free rate of return).

The Risk free rate of return can be estimated by adding the expected inflation rate to the real risk free rate of return. We estimate the inflation in line with the Federal Reserve objective. As Chart 7 shows below, it is not far from the historic tendency that has been 2.16% in the last twenty years. Our trading algorithm considers inflation rates centered on 2% with a standard deviation of 0.1%. Chart 7

There are a lot of discussions related to real risk free rate. Our estimation is 1%, which is in line with Bank of England’s and other projections of remarkable economic academics. But in any case, we are giving them a wide margin of error implicit in a standard deviation of 1%. Explanations about the reliability of this estimation are not included in the scope of this article. For further information, please consult the following websites:

Secular drivers of the global real interest rate – Bank of England

The equilibrium real funds rate: Past, present and future

Below, Chart 8 shows the historical evolution of the 10 Year USD Bond. Chart 9 also shows the histogram of the values of the expected risk free rate of return that our trading algorithm takes into account in order to calculate the value of Russell 2000, and also the asset allocation. Chart 8 Chart 9

The other, and even more important, factor that affects the cost of equity of Russell valuation is the risk premium that is the minimum amount of money that the expected return on a risky asset must exceed on the known return on a risk-free asset in order to encourage an individual to hold the risky asset rather than the risk-free asset. Its formula is:

Risk Premium = expected market rate of return – expected risk free rate of return.

Although it is important to notice that the correct calculation should be based on expectations, it is also worth mentioning that the historical dates are one of our main references. In this sense, it is worth analysing what the historical market return has been compared with the risk free rate of return. Below you can see:

 Arithmetic Average Risk Premium Standard Error 1928-2017 6,38% 2,24% 1968-2017 4,24% 2,70% 2008-2017 5,98% 8,70%

Chart 10

 Geometric Average Risk Premium 1928-2017 4,77% 1968-2017 3,29% 2008-2017 4,56%

Chart 11

Stern NYU

In addition, we have calculated the risk premium using different methods. Chart 12 describes the calculations:

Chart 12

Taking into account that the former consideration of our expectation for risk premium is 3.9% with a standard deviation of 2.1%. Chart 13

The last factor that we need to calculate for the Cost of Equity (Ke) of Russell 2000 starting with Risk Premium of S&P 500, is the Beta correlation coefficient between the two indexes. As Chart 14 shows, our central estimation for Beta of Russell 2000 referenced to S&P500 is 1.1 Chart 14

Now we have all the factors to calculate the Cost of Equity of Russell 2000:

Ke=3%+1.098*3.9%= 7.28%