Interest Rates and Rates of Return

Learning Objective

• Core Competency: Explain the fundamental differences between interest rates and rates of return on financial instruments.

Foundations of Investment Returns and Holding Periods

• Holding Period Concept: When making an investment, the primary focus of an investor is the earnings accrued during a specific interval of time, formally designated as the holding period.

• Components of a Coupon Bond Return: For an investor who purchases a coupon bond and holds it for a duration of one year, the overall return on investment comprises two distinct elements:

  • Income Component: The coupon payment received during the period.

  • Capital Component: The change in the market price of the bond over the course of the period, which yields either a capital gain (if the market price increases) or a capital loss (if the market price decreases).

• Rate of Return ($R$): To standardize performance measurement across different investments, returns are typically calculated as a percentage of the initial amount invested, known as the rate of return ($R$).

Case Illustration: Rate of Return on a Corporate Bond

• Baseline Parameters:

  • Issuer: Ford

  • Purchase Price: $\$1,000$

  • Face Value (Par Value): $\$1,000$

  • Coupon Rate: $5\%$

  • Annual Coupon Payment: $\$50$

• Scenario A: Bond Price Appreciation (Capital Gain)

  • Year-End Bond Price: Increases from $\$1,000$ to $\$1,169.84$

  • Coupon Received: $\$50$

  • Capital Gain: $\$169.84$

  • Rate of Return Calculation:

$R = \frac{\text{Coupon} + \text{Capital gain}}{\text{Purchase price}} = \frac{\$50 + \$169.84}{\$1,000} = 0.220\text{, or } 22.0\%$

• Scenario B: Bond Price Depreciation (Capital Loss)

  • Year-End Bond Price: Falls from $\$1,000$ to $\$864.09$

  • Coupon Received: $\$50$

  • Capital Loss: $\$135.91$

  • Rate of Return Calculation:

$R = \frac{\$50 - \$135.91}{\$1,000} = -0.086\text{, or } -8.6\%$

General Formulation of the Rate of Return

• Analytical Breakdown: The rate of return over a one-year holding period can be generalized by breaking it down into two additive financial metrics:

  • Current Yield: The coupon payment divided by the initial purchase price of the bond.

  • Rate of Capital Gain (or Loss): The dollar amount change in the bond's price divided by the initial purchase price.

• Conceptual Identity:

$\text{Rate of return} = \text{Current yield} + \text{Rate of capital gain}$

• Mathematical Formula:

$R = \frac{\text{Coupon}}{\text{Initial price}} + \frac{\text{Change in price}}{\text{Initial price}}$

Critical Principles Governing Bond Rates of Return

• Base Price in Current Yield Calculation: When determining the overall rate of return over a specific period, the current yield must be calculated using the bond's price at the beginning of the year (initial price), rather than subsequent intermediate or end-of-year values.

• Incurrence of Capital Gains and Losses (Realized vs. Unrealized):

  • An investor incurs a capital gain or loss regardless of whether the bond is actively sold at the conclusion of the holding period.

  • Realized Return: Occurs when the bond is sold at the market price, locking in cash proceeds.

  • Unrealized (Paper) Return: Occurs when the investor continues to hold the bond despite price fluctuations.

  • In both situations, the bond's price has changed, representing a tangible economic change in total investment value that must be incorporated into the rate of return.

• Divergence of Return from Yield Metrics:

  • Neither current yield nor yield to maturity (YTM) serves as a consistently reliable indicator of the actual rate of return earned during a specific holding period.

  • Underlying Cause: Both current yield and yield to maturity fail to account for the impact of potential capital gains or losses triggered by market price volatility over the investor's holding timeframe.