A fixed-income security, such as a bond, provides three different types of returns, and a yield measure used by the investor should consider all these three sources of return. These are: the coupon payment received, capital gains/losses, and reinvestment income. Let’s look at each of these sources of income in detail. Coupon Payments When an […]

# Yield Measures, Spot Rates, and Forward Rates

## How to Calculate Yield to Maturity

Yield to Maturity (YTM) is the most commonly used and comprehensive measure of risk. In fact, if someone talks about just ‘Yield’ they are most likely referring to Yield to Maturity. In simple terms, YTM is the discount rate that makes the present value of the future bond payments (coupons and par) equal to the […]

## How to Calculate Current Yield

The current yield of a bond measures the interest income that an investor gets from the bond. It’s represented using the following formula: Current Yield = Annual Coupon Interest/Bond Price Where, Annual coupon interest is the total coupon payment received by the bond annually Bond price is the market price of the bond Let’s take […]

## Bond Equivalent Yield Convention

In the bond market the convention is to annualize the semi-annual yield by simply doubling it. So, if the semi-annual yield is 3%, the annual yield is calculated simply as 3% x 2 = 6%. The annual yield so calculated is called the bond-equivalent yield (BEY). This convention doesn’t follow the time value of money […]

## Yield to Maturity (YTM) Approximation Formula

Calculating yield to maturity can sometimes be a tedious process because we need to do trial and error to arrive at the exact yield. In this article we provide an approximation formula to calculate YTM that you can use for quick calculation. The following formula assumes semi-annual coupon payments. Where: F = Face Value = […]

## YTM and Reinvestment Risk

Yield to maturity calculates the total return an investor would earn by holding the bond till maturity. This includes both the coupon income and the capital gains from the bond. It also considers reinvestment income, however, with the assumption that coupon payments can be invested at the same rate as YTM. This means that you […]

## Factors Affecting Reinvestment Risk

As we learned in the previous article, coupon paying bonds have reinvestment risk because the investor is expected to invest the cash flows from the bond at the same rate as yield-to-maturity (YTM) to be able to realize the YTM if he holds the bond till maturity. There are two key characteristics of a bond […]

## Calculate Bond-Equivalent Yield of Annual-Pay Bonds

In the US, most bonds are generally semi-annual coupon paying bonds, so we calculate the semi-annual yield and then calculate the bond-equivalent yield (annualized) by simply doubling the semi-annual yield. This is done when the bonds have semi-annual coupon payments. However, not all bonds pay semi-annual coupon, especially there are many non-US bonds that pay […]

## How to Calculate Yield to Call of a Bond

For callable bonds that are likely to be called before their maturity, it is more useful to calculate yield to call instead of yield to maturity. The formula and steps to calculate yield to call are exactly the same as how we calculate yield to maturity, i.e., you calculate the discount rate that makes the […]

## Cash Flow Yield

For some debt products such as mortgage-backed securities, we calculate cash flow yield instead of yield to maturity. This is because investors in mortgage-backed securities receive their cash flow from the cash flow of the underlying collateral pool and this cash flow is not fixed. In the underlying collateral pool, the home owners make the […]