Depending on objectives, investors can estimate the return that they will earn on a bond by calculating either its yield to maturity or its expected return.
Conservative investors focus on the Y.
If interest rates fall, earning interest income over extended periods of time is more important than earning a quick capital gain.
Because these investors intend to hold most of the bonds that they buy to maturity, the Ytm is a reliable measure of the returns that they can expect over time--assuming, of course, the reinvestment assumptions embedded in the yield measure are reasonable.
Bond traders who want to profit from swings in market interest rates calculate the expected return to estimate the return they will earn on a bond.
Capital gains by purchasing and selling bonds over relatively short holding periods is their main concern, so the expected return is more important to them.
The promised or expected yield is a measure of return that investors can use to determine the relative attractiveness of fixed-income securities.
To evaluate the merits of bonds, we must look at their returns and risks.
The return that bonds give should be enough to compensate investors for the risks that they take.
The higher the risk, the higher the return the bond should generate.
One of the problems with the yield to maturity is that it assumes you can reinvested the bond's periodic coupon payments at the same rate over time.
Your actual return will be lower if you spend this interest income at a lower rate.
Ytm assumes the investor will hold the bond to maturity.
PArt FoUr I InvEstInG is in the Y.
If rates have moved up since you purchased the bond, the bond will sell at a discount and your return will be less than the Ytm.
The opposite will happen if interest rates go down.
The problem with yield to maturity is that it doesn't take into account the effects of reinvestment risk and price risk.
Take a look at a situation in which market interest rates have fallen and see how reinvestment and price risks behave relative to one another.
Bond prices will go up.
You could be tempted to cash out your holdings and take some gains.
The only way to take advantage of falling interest rates is to sell before maturity.
The good news is that rates are falling.
When interest rates fall, there are opportunities to invest at high rates.
You lose on the reinvestment side if you gain on the price side.
If you don't sell out, you will face decreased opportunities.
Each coupon payment must be reinvested at the same Ytm rate in order to earn the Ytm promised on your bonds.
As rates fall, it becomes more difficult to invest in the stream of coupon payments at that rate.
The opposite happens when market rates rise.
The price of the bond goes down, but your opportunities go up.
Bond investors need to know how significant the risks are for a particular bond.
The measure captures the extent to which the price of a bond will change depending on the interest rate environment.
It gives you a better idea of how likely you are to earn the return you expect by measuring the duration of a bond.
It will help you tailor your holdings to your expectations.
The concept of duration was first developed in 1938 by actuary Frederick Macaulay.
The amount of interest payments, the yield to maturity, and the term to maturity all affect the interest rate risk of a bond.
As interest rates change, term to maturity is important because it affects how much a bond's price will rise or fall.
Bonds with longer maturities fluctuate more than shorter ones.
While the amount of price risk embedded in a bond is related to the issue's term to maturity, the amount of reinvestment risk is related to the size of a bond's coupon.
There's more to invest in bonds that pay high coupons.
There is a conflict between price and reinvestment risk because they are related to interest rates.
Changes in interest rates will cause price risk and reinvestment risk to push and pull bonds in opposite directions.
An increase in rates will result in a drop in price.
Declining rates will increase prices but decrease opportunities.
At some point in the future, these two forces should offset each other.
The bond's duration is at that point in time.
To determine an issue's duration, these variables are combined.
Knowing a bond's duration helps capture the bond's under lying price volatility.
Since a bond's duration and volatility are related, it follows that the shorter the duration, the less volatility in bond prices.
The average maturity of a fixed-income security is the measure of duration.
An alternative definition of average maturity is that it captures the average timing of the bond's cash payments.
For a zero-coupon bond that only makes one cash payment on the final maturity date, the bond's duration is equal to its maturity.
Because coupon-paying bonds make periodic interest payments, the average timing of these payments is different from the actual maturity date.
A 10-year bond that pays a 5% coupon each year will give a small cash flow in the first year and a large cash flow in the last year.
The "average maturity" is a little less than 10 years because of the weight that duration puts on these intermediate payments.
The concept was developed by the actuary.
Although duration is often computed using semiannual compounding, Equation 11.8 uses annual coupons and annual compounding to keep the discussion and calculations as simple as possible.
The formula looks more formidable than it actually is.
The duration is not hard to calculate if you follow the basic steps.
The discount rate can be used on the bond.
The fraction of the bond's total value accounted for by each indi vidual payment is the weight.
The weights must sum to 1.0 because a bond's value is the sum of its cash payments.
For each year in the life of the bond, repeat steps 1 through 3 and add up the values computed in step 3.
In row 1 of Table 11.1, we can see that a bond makes a $75 coupon payment in the first year, and then discounts that to the matter by its cover.
The current market price of the bond is $970.20.
In column 4 we divide the present value in column 3 by the current price to yield a total of 0.07252.
The weight is given to the cash payment made in the first year.
The bonds add to 1.0 even though they sum the weights in column 4.
The duration of this bond is less than it's maturity as interest rates go up or down.
In addition, keep in mind that the duration on any bond will change over time as the YTM and term to prices of these bonds would all change, so keep in mind 50 to 100 basis points.
The concept of duration is more than just indi vidual bonds.
It can be applied to whole portfolios of fixed-income securities.
It is easy to calculate the duration of a portfolio.
The individual securities in the portfolio and their weights are all we need.
The weighted average of the durations of individual ties in the portfolio is the duration of a portfolio.
An approximate measure of duration is provided by this weighted-average approach.
It is a close approximation and is widely used in practice.
The current market price is themount invested.
If the government bonds are quoted at 90 and the investor has $300,000 in them, then 0.90 is how much the bonds will cost.
The bond portfolio has an average duration of over 10 years.
If you want to change the duration of the portfolio, you can either shift the weight of the portfolio to longer- or shorter duration bonds, or add new bonds to the portfolio with the desired duration characteristics.
A bond's price volatility is a function of its term to maturity and its coupon.
There is no correlation between bond maturities and bond price volatilities.
As long as the market doesn't experience wide swings in interest rates, there is a close relationship between bond duration and price volatility.
If the yield swings are small, a bond's duration can be used as a predictor of its price volatility.
Bond prices change as interest rates change.
Bond prices go up when interest rates go down.
Bond prices fall when interest rates go up.
As interest rates change, the duration measure predicts that bond prices will move in a linear fashion.
When interest rates fall, bond prices will rise a bit faster than the dura tion measure would predict, and when interest rates rise, bond prices will fall at a slightly slower rate than the duration measure would predict.
The duration measure helps investors understand how bond prices will respond to changes in market rates if they are not too large.
We can find modified duration by taking the Macaulay duration and dividing it by the bond's yield to maturity.
In this case, the bond was priced to yield 8%, so we use a yield to maturity of 12%.
The modified duration value is calculated by taking the inverse relation between bond prices and interest rates and dividing it by the price of the bond.
A 50-basis-point increase in market interest rates will result in a 4% drop in the price of this 15-year bond.
Information like this is useful to bond investors.
The duration measures we've studied so far don't always work well for bonds that may be called or converted before they mature.
The duration measures we've been using assume that the bond's future cash flows are paid as originally scheduled through maturity, but that may not be the case with callable or convertible bonds.
The effective duration is an alternative duration measure used for these types of bonds.
Suppose you want to know the effective duration of a bond that pays a coupon semiannually.
The yield on the bond is 7%.
Suppose the bond's yield goes up.
The price goes up to $938.62 in that case.
We can use Equation 11.11 to calculate the bond's duration.
If interest rates rise or fall by a full percentage point, the price of the bond would fall.
If interest rates move by more or less than 1.0%, you can use effective duration in place of modified duration in Equation 11.10 to find the percent change in the price of a bond.
One modification may be necessary when calculating the effective duration of a callable bond.
Proceed as before.
You can use duration analysis to make decisions about bonds.
You can use modified duration or effective duration to measure the potential price volatility of an issue.
The structuring of bond portfolios is an equally important use of duration.
If you thought interest rates would go up, you could reduce the portfolio by selling bonds with longer maturities and buying bonds with shorter maturities.
Shorter-duration bonds do not decline in value the same way as longer-duration bonds.
The opposite strategy would be appropriate if you felt interest rates were going to decline.
In their day-to-day operations, active, short-term investors use duration analysis.
Longer-term investors use it in their investment decisions.
Some investors hold portfolios of bonds for the purpose of beating the market, but rather to accumulate a specified level of wealth by the end of the investment horizon.
You can derive a specified rate of return from bond investments over a given investment interval regardless of market interest rates over the course of the holding period.
You can "immunize" your portfolio from changes in market interest rates over a given investment horizon.
In order to understand how and why bond portfolio immunization is possible, you need to remember that there are two distinct and opposite changes in bond valuation when market interest rates change.
An increase in rates has a positive effect on the reinvestment of coupons.
The price and reinvestment effects work against each other when interest rates change.
When the average duration of the portfolio is the same as the investment horizon, the counteracting effects will not affect your position.
The property is already embedded in the duration measure, so it shouldn't come as much of a surprise.
It should also apply to the weighted-average duration of a whole bond portfolio if that relationship applies to a single bond.
A bond portfolio is immunized when there is offsetting price and reinvestment effects.
When the weighted-average duration of the bond portfolio is exactly the same as your invest ment horizon, your wealth is unaffected by interest rate changes.
A 10-year, 8% coupon bond with a duration of 8 years is an example of a bond immunization.
We assume that you want your invest ment horizon to be 8 years.
The 8% coupon bond is assumed to have originally been purchased at par.
At the end of the fifth year, market interest rates for bonds of this quality will drop from 8% to 6%.
Because you had an invest ment horizon of 8 years and want to lock in an interest rate return of 8%, you will accumulate cash totaling $1,850.93.
The immunization strategy netted you a total of $1,850.33, but it was just 60 cents short of your goal.
The market price for the bond increased when the market interest rates dropped to six percent, despite the fact that reinvestment opportunities declined in years 5, 6, and 7.
Capital gains were offset by the loss in reinvested income.
This result shows the power of bond immunization and the flexibility of bond duration.
Even though the table uses a single bond for illustration, the same results can be obtained from a bond portfolio that is main tained at the proper weighted-average duration.
Portfolio rebalancing is required to maintain a fully immunized portfolio.
The duration of a portfolio changes when interest rates change.
Effective immunization requires that the portfolio have a duration value equal in length to the remaining investment horizon.
In the absence of interest rate changes, a bond's duration declines more slowly than its term to maturity.
Changes in portfolio composition will be dictated by the passage of time.
The duration of the portfolio will match the remaining time in the investment horizon.
The most notable of which are associated with portfolio rebalancing, port folio immunization strategies can be extremely effective, but immunization is not a passive strategy and is not without potential problems.
Bond investors usually follow one of three investment programs.
There are people who live off the income.
They are conservative investors who want to maximize their current income.
Second, there are bond traders.
Their investment objective is to maximize cap ital gains.
There are long-term investors.
They want to maximize total return from both current income and capital gains over a long period of time.
You need to adopt a strategy that is compatible with your goals in order to achieve the objectives of these programs.
Money managers use a variety of techniques to manage their multimillion dollar bond portfolios.
There are different strategies that use interest rate forecasting and yield spread analysis.
Most of the strategies require a large computer port.
We can look at some of the more basic strategies to get an idea of the different ways in which fixed-income securities can be used.
The bond immunization strategies are passive in nature.
These tools are used by investors to lock in rates of return that they deem acceptable, even though they are not attempting to beat the market.
A lack of input regarding investor expectations of changes in interest rates and bond prices is what characterizes passive investment strategies.
The strategies do not generate significant transaction costs.
The most passive investment strategy is a buy-and-hold strategy.
The investor needs to replace bonds that have deteriorated credit ratings, have matured, or have been called.
Although buy-and-hold investors restrict their ability to earn above average returns, they also minimize the losses that transaction costs represent.