Bond Volatility
Bond volatility refers to the degree of variation in the price of a bond over time. It is a measure of the uncertainty or risk associated with the bond's value. Higher bond volatility indicates greater price fluctuations, which can impact the bond's performance and the overall risk of a bond portfolio.
5 Key excerpts on "Bond Volatility"
eBook - ePubIntroduction to Fixed Income Analytics
Relative Value Analysis, Risk Measures and Valuation
- Frank J. Fabozzi, Steven V. Mann(Authors)
- 2010(Publication Date)
- Wiley(Publisher)
...Duration is such a measure and we will discuss it as well as a supplementary measure called convexity later in the chapter. We describe the basic price volatility characteristics of bonds in the next section. It should come as no surprise that there are limitations of using one or two measures to describe the interest rate exposure of a position or portfolio. Nevertheless, these measures provide us with some important intuition about assessing interest rate risk. EXHIBIT 12.5 Illustration of Full Valuation Approach to Assess the Interest Rate Risk of a Bond Portfolio for Four Scenarios Assuming a Parallel Shift in the Yield Curve Two bond portfolio (both bonds are option-free) EXHIBIT 12.6 Illustration of Full Valuation Approach to Assess the Interest Rate Risk of a Bond Portfolio for Four Scenarios Assuming a Nonparallel Shift in the Yield Curve Two bond portfolio (both bonds are option-free) PRICE VOLATILITY CHARACTERISTICS OF BONDS There are four characteristics of a bond that affect its price volatility: (1) term to maturity, (2) coupon rate, (3) the level of yields, and (4) the presence of embedded options. In this section, we examine each of these price volatility characteristics. Price Volatility Characteristics of Option-Free Bonds Let’s begin by focusing on option-free bonds (i.e., bonds that do not have embedded options). A fundamental characteristic of an option-free bond is that the price of the bond changes in the opposite direction from a change in the bond’s required yield. Exhibit 12.7 illustrates this property for four hypothetical bonds assuming a par value of $100. When the price/yield relationship for any hypothetical option-free bond is graphed, it exhibits the basic shape shown in Exhibit 12.8. Notice that as the required yield decreases, the price of an option-free bond increases. Conversely, as the required yield decreases, the price of an option-free bond increases. In other words, the price/yield relationship is negatively sloped...
eBook - ePub- Frank J. Fabozzi, Frank J. Fabozzi(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
...The Concept and Measures of Interest Rate Volatility ALEXANDER LEVIN, PhD Director, Financial Engineering, Andrew Davidson & Co., Inc. Abstract: The knowledge of interest rates and cash flows represents the basis for valuation of fixed income financial instruments. In reality, not only are future interest rates random, but the future cash flows of many securitized investments are also uncertain, as they depend (are “contingent”) on interest rates. Valuation of rate options and embedded option bonds, including MBS and ABS, requires sophisticated models of this randomness. In this entry, we introduce the concepts of market volatility and discuss how it is measured. The dynamics of rates are subject to market forces, mean reversion, and combinations of diffusions and jumps. BASIC DEFINITIONS AND FIRST FINDINGS We can't tell in advance what interest rates will be. Investors may be either enriched or bankrupted from sudden changes in interest rates. Financial institutions devote considerable resources to risk management and hedging. Yet, if future interest rates were deterministic, there would be no need to hedge. Coping with uncertainty is a central feature of investment markets. The pricing of options and embedded-options instruments utilizes a statistical concept to describe the magnitude of potential interest rates changes. The key notion is the volatility of interest rates. While this term conjures up images of instability, flares of activity, and unpredict-ability, it is actually a very specific description of the range of possible outcomes. More precisely, volatility can be defined as the standard deviation of a rate's annualized daily increments. Table 1 provides an example for yields on the 10-year Treasury measured over 10 consecutive business days...
eBook - ePubBond Duration and Immunization
Early Developments and Recent Contributions
- Gabriel Hawawini, Gabriel Hawawini(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
...[p. 55] However, the high market rates of interest in recent years have given greater practical importance to the inverse relationship between term to maturity and change in bond price. In a recent book directed at portfolio managers, Sidney Homer and Martin Leibowitz demonstrate this phenomenon numerically for hypothetical bonds. They show that when market interest yields are reduced by 25 percent from 9.5 percent to 7.1 percent, “… 20-year 1’s, 2’s, 3’s, and 4’s (coupons) are more volatile than 30-year 9’s” (p. 52). The authors find no easy answer for the “puzzling” behavior and conclude that “… the volatility of any conventional high-grade bond results from the interaction of three factors: maturity, coupon, and the starting level of yields” (p. 51). The apparent inability of analysts to explain this unusual bond price pattern reflects an incomplete understanding of the mathematics of bond prices. While price volatility is related to the time structure of a bond, it is not mathematically related to term to maturity in any simple way. Rather, it is proportionately related to the duration of the bond. 2 The general theorem may be stated: For a given basis point change in market yield, percentage changes in bond prices vary proportionately with duration and are greater, the greater the duration of the bond. The validity of this statement for all bonds is demonstrated below. It will also be demonstrated that this proposition underlies Malkiel’s third theorem and that this theorem, like his second theorem, represents a special case that applies only to coupon bonds that sell at or above their par value, and to zero coupon bonds. Duration is a concept first introduced by Frederick Macaulay to provide more complete summary information about the time structure of a bond than term to maturity. 3 Maturity provides information only about the date of final payment. However, nonzero coupon bonds generate regularly scheduled payments before maturity...
eBook - ePubEquity Valuation, Risk, and Investment
A Practitioner's Roadmap
- Peter C. Stimes(Author)
- 2011(Publication Date)
- Wiley(Publisher)
...It has been long observed empirically that yield volatility of fixed-income securities increases as duration shortens. Long-maturity Treasury bond yields, as an example, might vary between 4.5% and 5.5% during a period when three-month bills vary between 1.0% and 5.5%. Since the equity market composite can be thought of as having a very high duration with respect to inflation-adjusted discount rates, according to equation (3.26), there is every reason to think that the inverse relationship between yield volatility and duration carries over from debt markets to equity markets. For another thing, since both volatility definitions are of the percentage changes in real discount rates and since the common equity discount rates are higher than those of fixed-income securities, a higher volatility number for fixed-income securities is necessary to keep absolute basis point changes in fixed income securities in the neighborhood of changes in equity discount rates. 11 Changes in observed stock market volatility, both in aggregate composites and for individual companies, are likely to be influenced mostly by changes in discount factor volatility. After all, cash-flow volatility, determined by underlying micro- and macroeconomic structures, can be presumed to be fairly stable over time. Likewise, leverage ratios change, but fairly gradually, and therefore change observed common equity volatility only gradually. The changes in volatility occasioned by changes in discount rates will have some investment implications with regard to security selection and asset allocation. These implications are explored in Chapters 9 and 10. In passing, note that those changes in volatility attributable to implied changes in discount factor volatility are likely to present option strategy opportunities. These opportunities would arise since our approach is consistent with the idea of mean reversion in discount rate volatility...
eBook - ePubKeene on the Market
Trade to Win Using Unusual Options Activity, Volatility, and Earnings
- Andrew Keene(Author)
- 2013(Publication Date)
- Wiley(Publisher)
...CHAPTER 13 What Is Volatility and How Does It Affect Options? A ny financial dictionary defines volatility as “a measure for variation of price of a financial instrument over a period of time.” A trader can look at historical volatility through many different timeframes: 10 days, 100 days, 1 year, or even 5 years. I'd like to take this definition one step further by saying that implied volatility, when looked at through the lens of options prices, is a measure of how much the market is expecting the underlying stock to move in either direction within a certain timeframe. In this chapter I discuss how historical and implied volatility affect options prices. ■ Basics of Volatility and Options Trading Volatility is a very important part of options trading, so it is essential to cover it in depth. This is because small changes in the implied volatility can significantly impact the option's price. Volatility is a key component to understand because a trader can make or lose money on an options trade even if the stock does not move. Here is the interview question that a seasoned trader would ask a potential trader: XYZ is trading $100 and I am long the XYZ $100 straddle for $10. If one week passes and the stock has not moved at all in that week, how much would the straddle would be worth? Is it possible that I could have made money on my trade? Most would say “No, the straddle should have decayed in value. That is true, but if the implied volatility had gone from 20 to 40 on a possible drug announcement, the price of the straddle would have doubled from $10 to $20 as well. So, implied volatility is the hardest element of the pricing model to grasp, because it changes so much on a minute-to-minute basis as well as on a daily basis. Let's look at the two types of volatility used in options pricing: historical and implied. ■ Historical Volatility Historical volatility is a measure of volatility expressed as an average over a given time period...
