We need the market risk premium to arrive at the cost of equity when using the CAPM model. Finance professionals estimate market risk premium by looking at historical returns. Is that appropriate? Is that accurate? Does it serve the purpose?
Estimating a market risk premium is challenging due to the following:
Backward-looking: Since investing is about the future, we want to be looking at forward risk premiums. However, there is no one by God who can predict the future and get a correct estimate of the forward risk premium.
Disagreement on time frames: Even when we agree that we can look to the past to arrive at an estimate of the market risk premium, there is significant disagreement on the time frame to be used: Do we use a 1, 5, 10, 20, 30, 50, 100-year average.
Disagreement on frequency: Even when we agree that we can look to the past to arrive at an estimate of the market risk premium, there is significant disagreement on the frequency to be used: Do we use daily, weekly, or monthly, quarterly or annual prices to estimate the returns.
Disagreement on methodology: Even when we agree that we can look to the past to arrive at an estimate of the market risk premium, there is significant disagreement on the method to be used: Do we use geometric average or arithmetic average?
Which market is to be considered: Should we use the US market or the London market or another one?
High variance: Even if we agree on a method, we will see that there is a high degree of variance in the historical risk premiums. This indicates a high coefficient of variation.