Plotting Yield Curves For UK Gilts And US Treasuries - Canadian Bond Yield Calculation

 This web site allows you to plot the yield curves for UK Gilts and US Treasuries for different periods.

1. List the three facts about the term structure of  interest rates Select a period and print a plot of an upward yield curve. Make comments using the theories you studied about the term structure of interest rates.

1. Select another period and print a plot of an inverted yield curve and make comments using the theories you studied about the term structure of interest rates.

1. Compare, generally, between the UK Gilt and the US treasury yield curves in question (a) and (b) above, citing the power of prediction of the theories of term structure of interest rates in predicting the 2008/2009 financial crisis.

1. A bond with $1,000 face value, 6% coupon, market interest rates of %7, and three years to maturity.

1. Calculate the duration of the bond
2. Assume that market interest rates increased to 9%, re-calculate the duration of the bond
3. Assume that the market interest rates dropped to 2%, re-calculate the duration of the bond
4. Comment generally on the relationships between the interest rates, coupons, and the duration

1. Albert, a financial advisor in greater Halifax area, has just emailed his clients giving them the following advice: “there is no doubt that long-term bonds are a great investment because their interest rates are over 20%.” Comment generally on Albert’s advice.

Canadian Bond Yield Calculation

1. Coupon Bond Rate   Go to a website of your choice and search for Canada Bonds. (I recommend Globe and Mail and Financial Post).. 

   Choose 4 different Canadian bonds with the following characteristics: 

• One Federal government bond trading at a premium with more than ten years to maturity
• One corporate bond trading at a discount with less than ten years to maturity
• One corporate bond trading at a premium with  more than ten years to maturity
• One Provincial government bond trading at a premium with less than ten years to maturity 

1. For each bond, calculate the current yield.

Current yield is the financial measure which is used when calculating the current bonds value among other investments providing a fixed interest. The above statement implies that the interest rate for a given period of time will not change until the expiry of the maturity period. The current yield can also be referred to as dividend yield or the bond yield depending on the usage context. In the course of calculating the current yield, one is trying to evaluate the amount a bond is worth at a given particular moment. The essence of calculating the current yield is that it gives the approximate return on the investment (ROI).

The formula for calculating the current yield is taking the annual income which might be the dividend, the coupon or the interest and dividing by the current price.

i.e Annual Income / Current Price

There are two steps in calculating the current yield which are

1. Calculating the annual interest payment which is arrived at by taking the investment face value and multiplying it by the interest rate.
2. Calculating the current yield by dividing interest payment by the current price.

In the above scenario, the current yield of Federal government bond trading at a premium with more than ten years to maturity

163.73* getting 13.0984

13.0984 divide by 163.73 getting 8%

Corporate bond trading at a discount with less than ten years to maturity is

136.97* getting 12.1629

• divide by 136.97getting 8.88%

One corporate bond trading at a premium with more than ten years to maturity is

124.65* getting 18.0

8.6 divide by 124.65 getting 6.5%

Alberta Provincial government bond trading at a premium with less than ten years to maturity

124.19* getting 5.58

5.58 divide by 124.19 getting 4.5%

1. Compare the current yield to the yield to maturity. For which bonds is current yield closer in value to the yield to maturity? Explain

From the above calculations of the current yield, there is a relationship that between the current yield and yield to maturity in that when the market price of a bond is above the parity, also called the premium bond, the current yield and the yield to maturity are usually lower than the coupon rate (reportonbusiness.com, 2018). On the hand, when a bond sells at a lower price than the parity, also known as the discount bond, the associated current yield and the yield to maturity are usually higher compared to the coupon rate. The only exception experienced is when a bond sells at an exact parity value which leads to three rates ending up being identical.

This web site allows you to plot the yield curves for UK Gilts and US Treasuries for different periods.

1. List the three facts about the term structure of  interest rates

The three facts about the term structure of interest rates include

1. In the short term bond, the yields are more volatile than the yields which are on long term bonds.
2. The interest rates for the different maturities usually tend to move together as time goes by as shown in the curves for UK Gilts and US Treasuries for different periods.

• Finally, it is observed that the long term yields seem to be much higher than the short term yields in that the yield curves often slopes upward.

1. Select a period and print a plot of an upward yield curve. Make comments using the theories you studied about the term structure of interest rates.

From the plotted yield curve for Aug 14, 2017 it has been observed that in the short term bond, the yields are more volatile than the yields which are on long term bonds. Also from the curves, it is event that that the interest rates for the different maturities are moving together as time goes by as shown in the curves for UK Gilts and US Treasuries for different periods (Yieldcurve.com. 2018). Finally, it is observed that the long term yields are much higher than the short term yields in that the yield curves are upward sloping.

1. Select another period and print a plot of an inverted yield curve and make comments using the theories you studied about the term structure of interest rates.

Relationship between Current Yield and Yield to Maturity

From the plotted yield curve for April 23, 2018 it has been observed that in the short term bond, the yields are less volatile than the yields which are on long term bonds. Also from the curves, it is event that that the interest rates for the different maturities are moving separately as time goes by as shown in the curves for UK Gilts and US Treasuries for different periods. Finally, it is observed that the long term yields are almost equal the short term yields in that the yield curves are trying to slope horizontally. 

1. Compare, generally, between the UK Gilt and the US treasury yield curves in question (a) and (b) above, citing the power of prediction of the theories of term structure of interest rates in predicting the 2008/2009 financial crisis.

From the UK Gilt and the US treasury yield curves in question (a) and (b) above, despite the fact that there is high volatility in the short run, it was observed that due to the financial crisis of 2008/2009 theory number (iii) in our case was not consistent ad was not followed; it is expected that as time goes by the curve should slope upward but in this case it is the opposite since the curse started sloping in the opposite direction. The prediction theories in this case seemed to be out done in a way since the expectation that there would be a gradual upward sloping was not case during this period when the financial crisis took place.

1. A bond with $1,000 face value, 6% coupon, market interest rates of %7, and three years to maturity.

1. Calculate the duration of the bond

The duration of the bond is the measure of the sensitivity of the bond to the changes of the interest rates. When the duration of the bond is high, also, the sensitivity to interest rates is expected to high or the volatility should also be higher and the opposite is true.

The period is calculated using

This results to

In the above rule n = 3, r = 6, i = 7 and F = 1000 that market interest rates increased to 9%, re-calculate the duration of the bond

In the above rule n = 3, r = 6, i = 9 and F = 1000

1. Assume that the market interest rates dropped to 2%, re-calculate the duration of the bond

In the above rule n = 3, r = 6, i = 2 and F = 1000

1. Comment generally on the relationships between the interest rates, coupons, and the duration

When the coupons does not change and the interest rate changes either upwards or downwards, the duration remains almost unchanged. This is because if the rates changes people tend to sell their bonds prior to the maturity date and may end up getting less than what they paid for their bond. Also, there is a tendency that bonds will lose value in case the interest rate rises.

1. Albert, a financial advisor in greater Halifax area, has just emailed his clients giving them the following advice: “there is no doubt that long-term bonds are a great investment because their interest rates are over 20%.” Comment generally on Albert’s advice. Do you agree him? Disagree? Or uncertain?

I agree with financial advisor, Albert, that the long term bonds are a great investment because their interest rates are over 20%. This is because the long term yields seem to be much higher than the short term yields in that the yield curves often slopes upward as a result of gaining stability in the market. Though there might be fluctuations on the interest rates and may start reducing in terms of the yields, there is a likelihood that the market will stabilize and start rising again. 

References

Yieldcurve.com. (2018). YieldCurve.com - the site dedicated to fixed income and the global debt capital markets. [online] Available