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How is Modified Duration calculated for a Zero Coupon Bond?
3 years zero coupon bond. face value $100 and present market value $75. What will be its Macualay Duration and Modified Duration?
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A zero coupon bond is a bond which pays no interim cashflow (i.e. coupons). We usually price on the basis of percentage of Face Value (i.e. $100). So if you expected 5% return…, semi annually, over the 3 years remaining on the life of a ZC Bond, the price would be; 100/(1+Yield/frequency)^(TermXfrequency) 100/(1+5%/2)^(3X2) = $86.23 So you'd pay $86.23 now and get $100 back in 3 years. If so, then your return would be 5% s.a.
The advantage of buying zero-coupon bonds is that when they reach maturity, the investor then receives the full face value of the bond. These bonds became popular in the 1980…'s even though they were first released in the 1960's.
They are sold at discount and mature to face value over time.
(4) risk-averse investors anticipating increases in interest rates
If you purchase a zero coupon bond today for 225 and it matures at 1000 in 11 years what rate of return will you earn on that bond to the nearest 10th of 1 percent?
Po =I (PVIFA kdn) + M(PVIF kdn) = $225 = $ 1,000 (PVIF) note 1 = 0 since this is a zero coupon bond. (PVIFkd, ) =0.317
Zero Coupon Municipal Bonds are special because, unlike other bonds, they have no periodic interest payments. Rather, the investor receives one payment at maturity. This payme…nt is equal to the amount invested, plus the interest earned, compounded semiannually.
Most bonds have two parts: the coupons and the corpus. The corpus represents the principal; the coupons the interest. Coupons have redemption dates printed on them; you turn i…n your coupon to receive the interest payment.
The bond sells at a discount from its face value--sometimes a BIG discount. At the date of maturity, the bond will give you the full face value.
bond coupon rates and yield rates have very similar effects and a very similar relationship to duration, lemme explain, by first explain durations effects in relation to… interest rates, then yields and finally you can surmise that relationship between yield rates will be the same as coupon rates Duration can be seen as the elasticity of the bond's price with respect to interest rates. When duration is 7, a 15 year bond will fall 7% in value if interest rates increase by 1%. In the data we've generated we can also determine the relationship between yields and duration by analyzing the change after a 50 basis point decrease in rates. The duration will rise as yields are lowered, and conversely a high coupon rate or high yield will result in lower durations. While a higher yield reduces the present value of all the bond's payments, it reduces the value of payments further in the future by a greater proportional amount. This amounts to a reduction in duration. Merck & Company's bond has the highest yield and therefore one would surmise that the duration for MRK should be lower than the other bonds, this is only true if all other variables are held equal (ceteris paribus). This is not the case. The bonds have wildly different coupons remaining. Eli Lilly's bond has a similar number of coupons remaining-suggesting a relatively good candidate for comparison-and a lower yield than MRK, leading one to expect LLY bond to have a higher duration than MRK. An astute financial student would discourage this comparison, citing that LLY exhibits the highest (7.125%) annual coupon rate, which would in turn reduce the duration. While comparisons between bonds will fail us due to their unique characteristics, it is easy to see the change when examining a single bond and the effect of a 50 basis point decrease in rates has on the bond's duration. Every single bond's duration rose, relative to itself before the basis change, as their yields were lowered. This helps prove our assumption of the inverse relationship between yield and duration.
A zero coupon bond pays no interest. Thus the market price for such a bond is always LESS than the maturity (face) value. The amount by which the bond is priced be…low its maturity value is known as the DISCOUNT. For example, a $100 zero coupon bond maturing in one year priced to yield 10% (in simple terms) would be sold to the investor for $90.91 on the date of issue. The investor would receive no payments from the borrower until maturity, at which time the investor receives the $100 face value. There's another form of zero-coupon bond Some brokerages will take a regular bond with coupons and "strip" it. They'll remove the coupons and sell the corpus of the bond separately from the coupons. A zero-coupon bond that was issued as such will normally have a really long maturity date--five to ten years isn't uncommon. You buy them as long-term investments...if you've got a child who will begin college when she's 19, you might want to buy ten-year zero-coupons that mature as the child enters each year of college.
the main difference between deep discount bond and zero coupon bond is that in case of zero coupon bond no int is payable periodically while in case of deep discount bond …int is payable periodically at very lower rate say 2% per annum
if a bond has finite maturity or limited maturity then we must consider not only the interest rate stream but also the maturity value (face value). regards Sajida Gul
In Barry Bonds
Zero coupon bonds are sold at a price well below face value. Thus, these bonds are appealing to the small investor because they can be bought far more cheaply than ordinary de…bt obligations. The discount is usually from 50 to 75 percent.
Go to your local discount broker, (Schwab, Ameritrade, E*trade, Scottrade) open an account and they will cash it in or liquidate it for you. There will be a fee associat…ed with the transaction. Shop around, prices vary. If they can't (or won't) do it, have them give you the name and address of the transfer agent. You can send it to them to liquidate as well. Good luck.
Five-Year Zero Coupon If the 2 5 years are exactly the same with the exception of having coupons (same lender, same claims, same everything) then yes you should b…e able to. The trick is finding the right yield curve and discounting everything back to the present value. The coupons can be treated as mini zero-coupon bonds in their own right.
A bond that does not pay interest until the point in time when it reaches maturity.
Zero coupon bonds issued by the US Treasury are issued at a discount to face value. An investor holding zero coupon bonds is paid the full face value when the zero coupon …bond matures. The difference between the purchase price and the maturity value is know as the original issue discount which represents the interest earned on the zero coupon bond. Although a zero coupon bond does not pay annual interest, an investor must pay taxes each year based on the imputed receipt of income. Since the investor is not receiving interest payments during the life of the bond, taxes would be paid on interest income not actually received until bond maturity. Due to the yearly tax liability on imputed interest, it makes sense for most investors to hold zero coupon bonds in a tax deferred retirement account. The interest earned on zero coupon bonds issued by the US Treasury are exempt from state and local taxes.