The debt securities issued in the market can have many features; one such feature is an embedded option such as a call option. The call option gives the issuer the right to but the bond back from the investor at prespecified terms after a certain period. Similarly, there could be a put feature in the […]

# Fixed Income Securities

## Impact of Yield Level on Bond’s Price Sensitivity

In the previous article we learned about how maturity, coupon, and embedded options impact interest rate risk in bonds. Apart from this, the price sensitivity of a bond to interest rate change is also affected by the level of yield (interest rate). Note that other factors remaining the same, the different bonds trade at different […]

## Bond Features Affecting Interest Rate Risk

We know that a bond’s price is inversely related to the yield. How sensitive a bond price is to yield depends on the various features of the bond such as its maturity, coupon rate, and any embedded options in the bond. Let’s look at how these factors influence the impact of interest rate changes on […]

## Understanding Inverse Price/Yield Relationship in Bonds

The investors in bonds face interest rate risk because the price of the bond is inversely proportional to the changes in interest rates. So, if interest rates rise, the bond’s price will fall and if interest rates fall, bond’s price will rise. But why this inverse relationship? Let’s understand this with the help of an […]

## Key Risks Associated with Investing in Bonds

Bonds are a lucrative investment class for investors and portfolio managers. However, just like any other investment, investing in bonds also has many risks associated with it. This article lists the key risks: Interest Rate Risk: Bond prices are inversely related to interest rates. When interest rates rise, bond prices fall and vice versa. Call […]

## Sensitivity Analysis (Duration and Convexity)

The sensitivity analysis of fixed-income instruments refers to how the price moves in relation to each of sensitivity estimates such as price, duration and convexity. The relationships are mainly represented by the following three equations: Equation 3 obviously implies that the effect on price is positive once convexity is positive. This normally holds true to […]

## Sensitivity Measures for a Portfolio

In financial markets assets are managed at a portfolio level which in other words means a large number of securities are managed in a group. It would be very inconvenient to consider movements in each position that composes the portfolio individually. A more practical and efficient solution would be to measure and manage the sensitivities […]

## Economic Interpretation of Sensitivity Measures

Duration can be interpreted as the average time receipt of each cash flow weighted by its present value. This applied to all cash flows is called Macaulay duration. The duration of a coupon paying bond can be written as: This equation can also be re-written as follows: Each weight is the present value of each […]

## Sensitivity Measures for Fixed Income Investments

The derivatives associated with fixed income instruments have special terminology for them. The negative of the first derivative is called the Dollar Duration (DD). Where is called the modified duration. Thus dollar duration is: The price is the dirty price of the bond including any accrued interest. The dollar value of the basis point measures […]

## Taylor Series Expansion

In financial markets participants would like to measure the effect of changes in the price of the bond due to changes in yield. This enables better risk management of financial assets as the impact of asset values is determinable. Recomputing the value of the bond using the changed yield comes across as an obvious solution. […]