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Bond duration, in general, measures the sensitivity of the full price including accrued interest to a change in interest rates. Macaulay duration is the weighted average of the time to receipt of coupon interest and principal payments, in which the weights are the shares of the full price corresponding to each payment.

This statistic is annualized by dividing by the periodicity number of coupon payments or compounding periods in a year. Modified duration provides a linear estimate of the percentage price change for a bond given a change in its yield-to-maturity. Approximate modified duration approaches modified duration as the change in the yield-to-maturity approaches zero.

Effective duration is very similar to approximate modified duration. Bonds with an embedded option do not have a meaningful internal rate of return because future cash flows are contingent on interest rates. Therefore, effective duration is the appropriate interest rate risk measure, not modified duration.

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The effective duration of a traditional option-free fixed-rate bond is its sensitivity to the benchmark yield curve, which can differ from its sensitivity to its own yield-to-maturity. Therefore, modified duration and effective duration on a traditional option-free fixed-rate bond are not necessarily equal.

When the coupon payment is made, the durations jump upward. Macaulay and modified durations are inversely related to the coupon rate and the yield-to-maturity. Time-to-maturity and Macaulay and modified durations are usually positively related. They are always positively related on bonds priced at par or at a premium above par value. They are usually positively related on bonds priced at a discount below par value.

This rate of return, known as the coupon rate, is set at issuance and Therefore, the formula for the holding period return yield of bonds is quite. a bond's yield to maturity (YTM) and its holding period return, and why current yield, running yield, nominal yield (coupon rate), and yield to.

The exception is on long-term, low-coupon bonds, on which it is possible to have a lower duration than on an otherwise comparable shorter-term bond. The reduction in the effective duration is greater when interest rates are low and the issuer is more likely to exercise the call option.

Money duration is a measure of the price change in terms of units of the currency in which the bond is denominated. Subtract from this figure any taxes and any fees or commissions. Cancel Download. At the center of everything we do is a strong commitment to independent research and sharing its profitable discoveries with investors. An easy way to think of YTM is to consider it the resulting interest rate the investor receives if he or she invests all of his or her cash flows coupons payments at a constant interest rate until the bond matures. Solution: We first need to calculate the semi-annual yield.

The reduction in the effective duration is greater when interest rates are high and the investor is more likely to exercise the put option. The duration of a bond portfolio can be calculated in two ways: 1 the weighted average of the time to receipt of aggregate cash flows and 2 the weighted average of the durations of individual bonds that compose the portfolio. The first method to calculate portfolio duration is based on the cash flow yield, which is the internal rate of return on the aggregate cash flows.

It cannot be used for bonds with embedded options or for floating-rate notes. The second method is simpler to use and quite accurate when the yield curve is relatively flat. Its main limitation is that it assumes a parallel shift in the yield curve in that the yields on all bonds in the portfolio change by the same amount. Money duration is a measure of the price change in terms of units of the currency in which the bond is denominated.

The price value of a basis point PVBP is an estimate of the change in the full price of a bond given a 1 bp change in the yield-to-maturity. Convexity is the secondary, or second-order, effect.

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It indicates the change in the modified duration as the yield-to-maturity changes. Money convexity is convexity times the full price of the bond. Combined with money duration, money convexity estimates the change in the full price of a bond in units of currency given a change in the yield-to-maturity.

Convexity is a positive attribute for a bond. Other things being equal, a more convex bond appreciates in price more than a less convex bond when yields fall and depreciates less when yields rise. Effective convexity is the second-order effect on a bond price given a change in the benchmark yield curve.

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It is similar to approximate convexity. The difference is that approximate convexity is based on a yield-to-maturity change and effective convexity is based on a benchmark yield curve change.

Callable bonds have negative effective convexity when interest rates are low. The increase in price when the benchmark yield is reduced is less in absolute value than the decrease in price when the benchmark yield is raised.

There is no limit to the gain if the stock price went up. The price of a call decreases when the exercise price increases. The investor is bearish on the stock, i. Because B is more volatile, its price should be higher. But its price is the same as A. That means that A's price is higher for some reason. Looking to compare online brokerages? Visit our Broker Center anytime. This article is part of The Motley Fool's Knowledge Center, which was created based on the collected wisdom of a fantastic community of investors.

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Thanks -- and Fool on! Motley Fool Staff. Updated: Nov 25, at PM.