A risk-free rate estimates the interest rate that investors expect to earn if an investment has no risk. Investment in the US T-bills, notes, and bonds are widely considered risk-free in that the repayment is ensured by the United States’ ability to raise taxes (Damodaran, 2013). 10-year treasury bonds are commonly used to estimate the risk-free rate and directly influence the interest rates paid on mortgages and other forms of debts available in the market. The bond pays a fixed rate of interest as opposed to the 3-months Treasury bill, which a zero-coupon bond that pays a par value at the end of the investment period. When calculating the risk premium, the risk-free rate is subtracted from the expected market return (Damodaran, 2013). For example, when a company has a long-term stable growth and without excess income, the risk premium can be estimated by subtracting the risk-free rate from the earning yield index of a company’s stock (Damodaran, 2013). Consequently, there exists a relationship between an equity risk premium and a risk-free rate.
The most appropriate estimate for a risk-free estimate should closely correlate with the estimated equity risk premium. Damodaran (2013) evaluated the relationship between implied risk premium and the 10-year Treasury bond rate using historical data between 1961 and 2012. The research findings established a positive relationship between the implied risk premium and the 10-year US Treasury bond rate. Other than the risk-free rate, implied risk premium proved a strong correlation with the inflation rate experienced in the US (Damodaran, 2013). The 10-year US Treasury bond rate better captures the inflation rate as compared to the short-term 3-month Treasury bill rate. The 10-year bond rate projects the future and awards the investors at an interest rate that accounts for the market inflation rates. If inflation is higher than the 3-month Treasury bill rate, investors are losing money due to the effects of inflation in eroding value.
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Both geometric and arithmetic means estimate the average return using different formulas. The arithmetic mean is the sum of all returns divided by the number of years. Contrary, the geometric mean for n years is the root of the product of all the returns. The arithmetic mean is more appropriate when the data entries are not correlated over time, while the geometric mean assumes a correlation between the data values (Damodaran, 2013). The geometric mean is considered a better estimate of the average stock return, given that empirical studies suggest a negative correlation of stock return over time (Damodaran, 2013). The geometric mean produces an average return lower than the arithmetic means but accounts for the compounded effect of the estimated discount rates (Damodaran, 2013). Contrary to the capital asset pricing model that may estimate the expected return of a single year, the geometric mean is an effective tool for evaluating the expected return over a long time.
The estimations for expected market return focus utilized data for the past 86 years. The choice is based on the acceptability and wide use of Ibbotson Associates’ estimates of stock return data and risk-free rates between 1926 and 2012 (Damodaran, 2013). The data reflects the characteristics of the US stock market over a more extended time, including the periods between the 1920s and 30s when the market portrayed unpredictable behavior. Analysis shows that the estimated returns may vary significantly depending on the periods factored in the analysis. For example, the geometric mean of a 10-year US bond is 4.20% of 1926-2012, 2.93% for the period1963-2012, and 1.72% for the period 2003-2012. The 86 year period between 1926 and 2012 captures the long-term characteristics of the US stock market and is hence a better estimate.
References
Damodaran, A. (2013). Equity risk premiums (ERP): Determinants, estimation, and implications–The 2013 edition. Managing and measuring risk: Emerging global standards and regulations after the financial crisis , 343-455.
