risk-free rate

Examples of risk-free rate in the following topics:

• The Relationship Between Risk and Return and the Security Market Line

  • Investment assets are typically characterized as having two performance risks: systematic (or market risk) and non-systematic risk.
  • In finance, the capital asset pricing model (CAPM) is used to determine the required rate of return of an asset, taking into account an asset's sensitivity to non-diversifiable or systematic risk.
  • The expected return of an asset is equal to the risk free rate plus the excess return of the market above the risk-free rate, adjusted for the asset's overall sensitivity to market fluctuations or its beta.
  • Mathematically, the capital asset pricing model can be written as: E(Ri) = Rf + β(E(Rm) - Rf), where R is the return, E(R) is the expected return, i denotes any asset, f is the risk-free asset, and m is the market.
  • The intercept is the nominal risk-free rate available for the market, while the slope is the market premium, E(Rm)− Rf.

• The Cost of Debt

  • The credit risk for a certain class of a company's debt requires a premium on return of 5%.
  • The risk free rate is 5% and the corporate tax rate is 20%.
  • In practice, the interest rate paid by the company can be modelled as the risk-free rate plus a risk component, taking into account credit risk; which is the amount of risk incurred by taking on more leverage in capital structure .
  • Thus, for profitable firms, debt is discounted by the tax rate .
  • Cost of debt equals the interest rate of the debt (composed of the risk-free rate and a credit risk premium) times one, minus the corporate tax rate.

• Defining the Security Market Line

  • The security market line displays the expected rate of return of a security as a function of systematic, non-diversifiable risk.
  • The Y-intercept of the SML is equal to the risk-free interest rate.
  • Recall that the risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss.
  • When used in portfolio management, the SML represents the investment's opportunity cost -- i.e., investing in a combination of the market portfolio and the risk-free asset.
  • The y-intercept of this line is the risk-free rate (the ROI of an investment with beta value of 0), and the slope is the premium that the market charges for risk.

• The Capital Asset Pricing Model

  • The capital asset pricing model helps investors assess the required rate of return on a given asset by measuring sensitivity to risk.
  • This model focuses on measuring a given asset's sensitivity to systematic risk (also referred to as market risk) in relation to the expected return compared to that of a theoretical risk-free asset.
  • All this really means is that the CAPM tries to measure the risk the market will offer the asset compared to the risk-free rate, and make sure the expected return will offset that risk.
  • On the left side of the equation below, you have an assessment of the overall risk relative to a risk-free asset.
  • On the right side, you have the overall return (similarly relative to a risk-free asset).

• Expected Risk and Risk Premium

  • Systemic risk is the risk associated with an entire financial system or entire market.
  • The term risk premium refers to the amount by which an asset's expected rate of return exceeds the risk free rate.
  • The difference between the return of an asset in question and that of a risk-free asset -- for instance, a US Treasury bill -- can be interpreted as a measure of the excess return required by an investor on the risky asset.
  • The risk premium, along with the risk-free rate and the asset's Beta, is used as an input in popular asset valuation techniques, such as the Capital Asset Pricing Model.
  • Beta is a measure that relates the rate of return of an asset, ra, with the rate of return of a benchmark, rb.

• The Cost of Common Equity

  • -- Expected return for a security equals the risk-free return for the market plus the beta for the security times its risk premium.
  • The CAPM shows that the cost of equity is equal to the risk free rate plus a premium expected for risk.
  • In the dividend growth model, dividends paid to common shareholders along with the overall expected growth rate are used to calculate a cost for the common stock.
  • The risk premium is the additional rate that must be paid to common shareholders above what is paid to bond holders, given the amount of risk carried by the equity.
  • Expected return for a security equals the risk-free return for the market plus the beta for the security times its risk premium.

• The "Bond Yield Plus Risk Premium" Approach

  • Simply put, the yield on a bond is the rate of return received from the investment.
  • This is also referred to as the internal rate of return (IRR).
  • The equity risk premium is essentially the return that stocks are expected to receive in excess of the risk-free interest rate.
  • It can be very difficult to get an accurate estimate of the risk premium on an equity, having a duration of roughly 50 years, using a risk-free rate of such short duration as a 10-year Treasury bond.
  • A hypothetical graph showing yield to maturities (or internal rates of return) for corresponding present values.

• Measuring Country Risk

  • International investors, buying foreign bonds, can experience a currency exchange rate risk, an interest-rate risk, a borrower default, and/or a country risk.
  • Consequently, the interest rate is comprised of the risk-free interest rate and risk premium.
  • Risk-free interest rate reflects the market interest rate with a zero default rate.
  • Investors believe the U.S. government debt is risk-free because the U.S. government can increase taxes or print money to repay the bonds.
  • If a country possesses a low score, then analysts and economists would add a large risk premium to the risk-free interest rate.

• Drivers of Market Interest Rates

  • Market interest rates are mostly driven by inflationary expectations, alternative investments, risk of investment, and liquidity preference.
  • In a free market there will be a positive interest rate.
  • The greater the risk is, the higher the market interest rate will get.
  • However, economists generally agree that the interest rates yielded by any investment take into account: the risk-free cost of capital, inflationary expectations, the level of risk in the investment, and the costs of the transaction.
  • where in is the nominal interest rate on a given investment, ir is the risk-free return to capital, pe = inflationary expectations, i*n = the nominal interest rate on a short-term risk-free liquid bond (such as U.S.

• Default Risk and Bond Price

  • For instance, the U.S. government has little risk of default, and investors call U.S. securities default-risk-free instruments.
  • Economists call the difference between the interest rate on the U.S. government bonds and corporate bonds the default risk premium.Investors add default risk premium to a risk-free investment, so they can invest in "risky" bonds because they earn a greater return.
  • Rating companies such as Standard & Poor's Corporation and Moody's Investor Service assess the default risk for corporations.
  • Thus, the demand for corporate bonds falls while the demand for government bonds rise because the investors consider the government bonds default-free.
  • Taking the difference between the government bond and corporate bond interest rates, we can calculate the risk premium.