# 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

For further details about the calculation please consult:

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

Method | Calculation Formula | Data Sources | Observation & Comments | Value | Standard Deviation |

Historical market return of S&P500 compared with the risk free rate of return. | Historic average of return of S&P500 –return of 10Yr Treasury Bond | 1966- 2017 | · Using geometric averages as an alternative to arithmetic, the results would be 3.3% instead of 4.2%.
· The Standard Deviation is calculated considering even negative values which are not reliable in the long term. That is one of the reasons for our lower standard deviation estimation. |
4,20% | 2,7% |

Expected market return and risk free | Dividend/Price + g dividend – risk free rate | · Future growth evolution in line with the tendency growth of GDP 2000 – 2017. · To calculate the expected dividend yield, we use the formula Dividend Yield = 1- g/ROE and our estimation for ROE is 13%· Risk free at 3% . |
· This is the most correct method from an academic point of view as it is solely based on the expectations of the real shareholder return: the dividends and difference between the buying and selling prices.· Sometimes, as is the case for S&P500, the retribution of the shareholders is shared between dividends and other types of remuneration (mainly buyback programmes). In order to simplify the calculation, we consider all the remuneration of the shareholder as dividends but the results are the same as considering only the real cash dividends and then increasing the g of the dividends provoked by the share buybacks.· Dividend Yield is 3,2% compared with 2% in 2017 and the retribution to the shareholders by buybacks that was 2.4%
· Growth g = 3,6%, 1.6% in real terms plus 2% inflation. · The standard deviation is much higher than the other two methods mainly because it is affected by the variability of ROE. |
3,81% | 3.4% |

Base of PE | Expected E/P – risk free rate | · Dates 2007-2017 | · This method is commonly used by investors but it is not correct from academic point of view. It identifies the return to shareholder with the inverse of PE which is not correct. Although to mention it here as a reference or expectation does not consider it.
· Our reference are the average of the historic P/E from 2007 to 2017 · The average value of the last decade is 3.3% that is close to the values calculated by other methods. · The standard deviation calculated by this method is extraordinarily low, especially considering the market situation in 2008 and 2009. |
3.3% | 1,4% |

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%