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# Category: Level I Fixed Income

## Yield Spreads

A yield spread is an amount of interest that is added to another interest rate (or rates) to achieve some specific goal. For example, a yield spread might be added to the yield to maturity (YTM) of a risk-free bond to arrive at the YTM for a given risky bond of the same maturity. Or…

## Risks in Fixed Income Investing

There are quite a few risks inherent in investing in fixed income securities / portfolios. Amongst them are these that I’ll discuss in this article: Interest rate risk Yield curve risk Call/prepayment risk Reinvestment risk Credit risk Liquidity risk Currency exchange rate risk Inflation risk Volatility risk Event risk Sovereign risk I’ll cover each of…

## Convexity

As we’ve seen in the article on duration, the duration of a bond (whether Macaulay duration, modified duration, or effective duration) is not constant; amongst the factors that cause (all types of) duration to change is the bond’s yield to maturity (YTM). Because duration changes with YTM, using only a bond’s (or bond portfolio’s) modified…

## Calculating Spot Rates (from Forward Rates)

A spot interest rate is a discount rate that takes a single payment at one point in the future and discounts it back to today; a forward rate is a discount rate that takes a single payment at one point in the future and discounts it to another (nearer) time in the future; they each…

## Yield Measures (Fixed Income)

There are a number of types of yield measures for bonds; you need to know how they are calculated, the assumptions that underlie them, and their strengths and weaknesses. The measures of interest are: Nominal yield Current yield Yield to maturity Yield to call Yield to refunding Yield to put Yield to worst Cash flow…

## Bond Equivalent Yield (BEY)

Because a large number of coupon-paying bonds make their coupon payments semiannually (e.g., US Treasury Notes and Bonds, and many corporate bonds), and each coupon payment is ½ of the annual coupon (i.e., each coupon is calculated as 0.5 × annual coupon rate × par), the default yield convention for bonds is that the annual…

## Macaulay Duration, Modified Duration, and Effective Duration

In this article I’ll cover three quantities that go by the name of “duration”: Macaulay duration Modified duration Effective duration I’ll explain how each type of duration is calculated, the characteristics of each type of duration, the similarities and differences amongst the types of duration, and how they are used in practice. Types of Duration…

## Calculating Forward Rates (from Spot Rates)

A forward interest rate is a discount rate that takes a single payment at one point in the future and discounts it to another (nearer) time in the future; they have their own special notation. For example, if we’re measuring time in years, the discount rate that would take a payment 6 years from now…