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## How To Calculate Bond Yield

(2011-09-04 15:21:56)

### 杂谈

How To Calculate Bond Yield
Learning to calculate a bonds rate of return or yield starts with understanding the different rate indicators involved. Bond yields are based on the coupon rate, the price paid and the maturity length of the investment.

The 3 key interest indicators are: Nominal Yield, Current Yield, and Yield to Maturity.

Nominal

The Nominal rate or coupon rate is the fixed interest rate on the bond. This is the rate that the issuer pays to par value. It is fixed, it never changes and it is only paid to par. Par is the amount of bonds you own. This yield may or may not be your total net rate of return. If the bond was purchased at a premium (above par), then your overall yield to maturity will be lower than your stated coupon rate.

If a bond has a 7% nominal yield or coupon and was purchased at a premium of \$103 (\$1030), then your YTM will calculate lower because the 7% interest is only paid to the \$1000 par. The \$30 premium does not earn interest and is not redeemable at par. So, a 7% bond at a premium is not really "yielding" 7% in that example.

A bond purchased at a discount will have the reverse affect on yield. The Yield to maturity would be higher for a discount bond, based on the fact that you are still earning interest on par even if you paid under par. The overall YTM wil calculate higher for a bond.

Current

The current yield on a bond is calculated by dividing the nominal rate by the current market price. Doing this will have a similar result to the yield to maturity when bonds are bought at premiums or discounts. A premium bond will have a lower current yield compared to it's coupon rate and a discount bond will have a higher current yield than it's nominal rate.

Yield To Maturity

The most important rate of return indicator is a bond's yield to maturity. The YTM factors in everything to give the true overall yield to an investor.

It examines the nominal yield, current yield and years to maturity. The overall rate of return can be effected by the length of time the bond is held. If a 4 point premium was paid on an 8% bond, but the bond has a maturity of 15 years, that yield will be different than if the bond was only good for 2 years.

How to calculate yield to maturity:

This is done by using the key components of a bond: the coupon rate, the price and the years to maturity. A 5% bond priced at \$850 and maturing in 15 years would calculate as follows:

Yearly Coupon Interest = \$50 (5% paid to \$1000)
Total Discount = \$150 (\$100 par - cost of \$850)
Annual Discount = \$10 (\$150 total discount divided by 15 years)
Average price - \$925 (difference between \$850 and \$1000 par)

Add the \$10 annual discount to the coupon payment of \$50. This gives you \$60, which is divided by \$925 and that will give you the yield to maturity of this bond - 6.49%

Tax Equivalent Yield Calculator

The after tax yield or tax equivalent is used with Municipal Bonds mostly. Since the interest on municipal bonds are federally tax free, a tax equivalent yield is needed to compare municipals with other taxable investments that may be in front of an investor. An example we can calculate would be comparing a 6% municipal with an 8% corporate bond. The tax bracket for this example is 28%. You need to calculate the tax free yield on the municipal and then compare it to the 8% stated yield on the corporate bond.

Municipal yield divided by 100 minus the tax bracket will give you the after tax yield equivalent. 6% divided by 72 (100-28) will equal 8.33%, which is greater than the 8% corporate bond.

Callable YTC - Call Bonds

Fixed income securities or bonds that are callable may be priced to their yield to call. This date, if called is basically an early maturity for the bondholder. The one key difference is that notes or bonds that go to maturity always mature to par, so the yield is calculated with that in mind.

Callable securities could be called at different prices than par. The yield to call will be higher than the nominal yield if the bond is called at a price above the price paid by the investor originally. The YTC will be lower if the reverse is true. Similar to par non callable bonds, if a fixed income investment was bought at par and is called at par - the yield to call will equal the nominal rate.

Learning to calculate a bonds rate of return or yield starts with understanding the different rate indicators involved.学习计算与理解不同的利率指标涉及债券利率的回报或收益率开始。 Bond yields are based on the coupon rate, the price paid and the maturity length of the investment.债券收益率，票面利率的基础上，付出的代价和投资期限长度。

The 3 key interest indicators are: Nominal Yield , Current Yield , and Yield to Maturity . 3个关键的利率指标： 名义收益率 当前收益率 到期收益率

Nominal 标称

The Nominal rate or coupon rate is the fixed interest rate on the bond.名义利率或票面利率为固定利率债券。 This is the rate that the issuer pays to par value.这是利率，发行人支付面值。 It is fixed, it never changes and it is only paid to par.它是固定的，它永远不会改变，它是唯一的标准支付。 Par is the amount of bonds you own. PAR是你自己的债券金额。 This yield may or may not be your total net rate of return.这个收益率可能会或可能不会是你的总净回报率。 If the bond was purchased at a premium (above par), then your overall yield to maturity will be lower than your stated coupon rate.如果债券溢价（高于票面价值）购买的，那么你的整体到期收益率将低于您说的票面利率。

If a bond has a 7% nominal yield or coupon and was purchased at a premium of \$103 (\$1030), then your YTM will calculate lower because the 7% interest is only paid to the \$1000 par.如果债券的名义收益率7％或优惠券，在103元（1030美元）的溢价购买，那么您油尖旺将计算出较低的，因为只有7％的利息支付给1000美元的面值。 The \$30 premium does not earn interest and is not redeemable at par. 30美元的溢价不赚的利益，而不是按面值赎回。 So, a 7% bond at a premium is not really "yielding" 7% in that example.因此，在溢价7％的债券，是不是真正的“收益”，例如7％。

A bond purchased at a discount will have the reverse affect on yield.以折扣价购买了债券，将有反向影响产量。 The Yield to maturity would be higher for a discount bond, based on the fact that you are still earning interest on par even if you paid under par.折扣债券到期收益率将更高，根据事实，你仍然看齐赚取利息，即使你支付低于标准杆。 The overall YTM wil calculate higher for a bond.油尖旺WIL整体计算的债券高。

Current 当前

The current yield on a bond is calculated by dividing the nominal rate by the current market price.目前债券收益率除以名义利率由目前的市场价格计算。 Doing this will have a similar result to the yield to maturity when bonds are bought at premiums or discounts.这样做，将有一个到期收益率，债券溢价或折价购买时类似的结果。 A premium bond will have a lower current yield compared to it's coupon rate and a discount bond will have a higher current yield than it's nominal rate.一个溢价债券将有一个比较，它的票面利率和折扣债券将有较高的产量比目前的名义利率较低的当前收益率。

Yield To Maturity 到期收益率

The most important rate of return indicator is a bond's yield to maturity.最重要的利率回报的指标是债券的到期收益率。 The YTM factors in everything to give the true overall yield to an investor.油尖旺一切因素，给真正的总收率投资者。

It examines the nominal yield, current yield and years to maturity.它考察的名义收益率，目前的产量和年至到期日。 The overall rate of return can be effected by the length of time the bond is held.债券举行的时间长度可以影响整体收益率。 If a 4 point premium was paid on an 8% bond, but the bond has a maturity of 15 years, that yield will be different than if the bond was only good for 2 years.如果4点的溢价支付8％的债券，但债券到期日为15年，产量将不同的债券相比，仅2年。

How to calculate yield to maturity:如何计算到期收益率：

This is done by using the key components of a bond: the coupon rate, the price and the years to maturity.这样做是通过债券的主要组成部分：票面利率，价格和年至到期日。 A 5% bond priced at \$850 and maturing in 15 years would calculate as follows:售价850美元的5％的债券，并在15年到期，计算如下：

Yearly Coupon Interest = \$50 (5% paid to \$1000)每年的票面利率= 50美元（5％支付\$ 1000）
Total Discount = \$150 (\$100 par - cost of \$850)总折扣成本= \$ 150（\$ 100面值 - ，\$ 850）
Annual Discount = \$10 (\$150 total discount divided by 15 years)年贴现率= 10元（合共150元折扣除以15年）
Average price - \$925 (difference between \$850 and \$1000 par)平均价 - \$ 925（\$ 850和\$ 1000面值之间的差异）

Add the \$10 annual discount to the coupon payment of \$50.新增每年10元的折扣券支付50元。 This gives you \$60, which is divided by \$925 and that will give you the yield to maturity of this bond - 6.49%这给你60元，除以925美元，这将使你该债券到期收益率 - 6.49％

Tax Equivalent Yield Calculator 税收等效产量计算器

The after tax yield or tax equivalent is used with Municipal Bonds mostly.税后收益率或税相当于是与市政债券大多使用。 Since the interest on municipal bonds are federally tax free, a tax equivalent yield is needed to compare municipals with other taxable investments that may be in front of an investor.由于联邦免税的市政债券的利息税相当于产量是需要与其他应税投资，可能会在投资者面前的直辖市。 An example we can calculate would be comparing a 6% municipal with an 8% corporate bond.一个例子，我们可以计算会比较6％与8％的企业债券的市政。 The tax bracket for this example is 28%.在这个例子中的税率为28％。 You need to calculate the tax free yield on the municipal and then compare it to the 8% stated yield on the corporate bond.你需要计算的税收市级和8％的人表示对企业债券的收益率比较自由产量。

Municipal yield divided by 100 minus the tax bracket will give you the after tax yield equivalent.市产量除以100减去税率会给你的税后收益率相当于。 6% divided by 72 (100-28) will equal 8.33%, which is greater than the 8% corporate bond. 6％除以72（100-28）将相等于8.33％，这是大于8％的企业债券。

Callable YTC - Call Bonds 赎回云锡-呼叫债券

Fixed income securities or bonds that are callable may be priced to their yield to call .固定收益证券或债券，可赎回的价格可能调用产量。 This date, if called is basically an early maturity for the bondholder.这个日期，如果调用基本上是一个早熟的债券持有人。 The one key difference is that notes or bonds that go to maturity always mature to par, so the yield is calculated with that in mind.一个关键的区别是，到成熟总是成熟的标准，票据或债券，因此产量计算考虑到这一点。

Callable securities could be called at different prices than par.可赎回的证券可称为在不同的价格比标准杆。 The yield to call will be higher than the nominal yield if the bond is called at a price above the price paid by the investor originally.调用的产量将高于名义收益率，如果债券价格高于最初由投资者支付的价格。 The YTC will be lower if the reverse is true.云锡将降低，如果情况正好相反。 Similar to par non callable bonds, if a fixed income investment was bought at par and is called at par - the yield to call will equal the nominal rate.类似非面值的可赎回债券按面值购买，如果有固定收入的投资，是按面值称为 - 调用将等于名义利率的收益率。

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