Interest Rates and Yield Curves

What are interest rates?

Passively

• A measure of the value of money, ie. the price of money

• A pure expression of the “time value of money”

• A measure of risk in business and the economy

Actively

• A tool for controlling economic activity through the supply of money

Money Supply

• 𝑴 × 𝑽 = 𝑷 × 𝒀

  • M = quantity (supply) of money

    V = velocity of money

    P = average prices of goods/services

    Y = real output of goods/services

Money neutrality

An increase in money supply will cause the average prices of goods and services to rise

Money Demand

• Transaction-Related

• Precautionary

• Speculative

What is the basis for determining interest rates?

• Other opportunities - Risk-free rate

• Devaluation of money over time - Inflation risk premium

• Level of trust in your partners - Default risk premium

• Level of trust in economic environment - Market risk premium

• Ability to convert the investment into cash - Liquidity premium

Coupon Rate

• Laid out in the bond paper

• May be fixed, or pegged to some other rate (floating rate) such as inflation, policy rates, etc.

• Determines the periodic cashflow of a bond

Interest Rate (Market)

• Determined by the supply and demand for money/bonds in the market

• Changes as markets adjust expectations and pricing

• Used to discount the cashflows of a bond (for trade)

Yield to Maturity

• The internal rate of return of a bond if held until maturity

  • The discount rate to be applied to its cashflows such that present value will be equal to the purchase price of the bond

• For newly purchased bonds, the YTM will usually be equal to the market interest rate

• When the price of a bond equals its par value (face value), then YTM will equal the coupon rate

Spot Rates

• The YTM of a zero-coupon bond

• Useful for calculation the present value of a series of cashflows with similar risk characteristics as the spot rates

• Applies a different discount rate for each cash flow, rather than a single “average” rate (the YTM)

Flight to Lower Risk

• Uncertainty in the market and economic downturns encourage investors to choose lower risk assets like bonds

• However, this should result in falling yields

Inflation Risk Premium

• As oil prices rise, inflation rises dramatically (almost everything uses oil)

• Investors want more compensation for increasing prices, hence demand higher rates

The Yield Curve

• A benchmark for bond rates and pricing throughout the market

• A strong indicator of economic trends and expectations

• A reflection of government policies (monetary and otherwise)

Money Neutrality

The theory that an increase in money supply leads to increased prices (inflation)

Equilibrium Interest Rate

The equilibrium rate where the demand for money equals the supply of money

Real Risk-Free Rate

The theoretical interest rate of a bond with no risks

Nominal Risk-Free Rate

The real risk-free rate plus expected inflation (ie. an inflation risk premium)

• In reality, the RFR also includes market and liquidity risk premia

Risk Premia

The additional required returns for a risky bond (on top of the risk-free rate)

• Inflation risk

• Default risk

• Market risk

• Liquidity risk

Inflation risk

Volatility of prices

Default risk

Possible failure to receive expected cashflow

Market risk

Changes in economic factors like interest rates or gov’t policy

Liquidity risk

Inability to convert the security into cash

Interest Rate

A policy rate or market driven rate that affects the pricing of bonds

Coupon Rate

Defines amount of money paid out by a bond regularly

Yield to Maturity

The expected return (yield) of a fixed income instrument if held to maturity

Spot Rate

The YTM of a zero-coupon bond

Yield Curve

Usually the set of spot rates for bonds with varied maturities but otherwise similar characteristics