Help this question!! The US government issures a 1-year bond?
Answers:
You can actually calculate the numbers assuming the market interest rate is the risk free rate:
If the face value is $5000, that means you get paid $5000 in a year (assuming no credit risk on the government bond). So, simply discounting (with the assumption we are using annual rates with annual compounding), the price of the bond is:
5000/1.2 = $4,166.67
If the price drops by 5%, you have:
0.95 * 4,166.67 = $3958.33
Recomputing the yield (again assuming an annual rate using annualized compounding):
Yield = $5000/$3958.33 - 1
Yield = 26.316%
This makes sense because price and yield are inversely related. As price decreases, yield increases.
You must be working on your series 7 exam.:)
As the price drops the current yield will go up. A zero is sold at a discount to face value, so let say the original price was 4200 for a 1 year 5k bond. If the price drops by 5% then you would only have to pay $3990 for the 5k bond. However, this might be a trick question as govt bonds aren't "insured" in the typical sense. They are backed by the us government, but typically are not insured by a third party.
zero coupon means you receive no interest payments so principle appreciation is how your interest rate is calculated. Since it is only one year, you won't need a compound interest table, but the general formula still holds:
Future Value = Present Value (1 + interest rate)^(# of years)
Future value is $5000 since they will pay you that when the bond matures in a year. The number of years is 1. Now, since the "market rate" (the rate of risk free return) is 20%, this means the bond price has to be discounted from face value to give investors the 20% return they require. All zero coupon bonds sell originally for less than face value, but the exact number can be found by plugging the numbers into the formula:
$5000 = PV (1.2)^1
$5000/1.2 = $4166.66 -----> this is the market price the bond sells for. The answer can be checked easily. In THIS CASE, since the duration is only one year, the yield to maturity here is calculated by taking the difference between the issuing price of $4166.66 and the face value of $5000, which equals $833.34, and dividing by the issuing price, $4166.66. So $833.34/$4166.66 = 20%. This is also the current yield in this case.
If this price falls by 5% (which would be $4166.66 * .05 = $208.33, giving the bond a price of $4166.66 - 208.33 = $3958.33) the yield would increase, because it will appreciate in value more (by $5000 - $3958.33 = $1041.67) Yield to maturity would increase from 20% to $1041.67/$3958.33 = 26.32%. As you can see, bond prices and yields move in opposite directions. Remember to use the formula above (or work with a compound interest table) if the duration of the bond is longer than one year to find the answers to these kind of questions.
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