Showing posts with label Government Bonds. Show all posts
Showing posts with label Government Bonds. Show all posts

Sunday, 12 November 2017

Singapore Savings Bonds – 2 Years On

It has been 2 years since the launch of the Singapore Savings Bonds (SSB) in Oct 2015. How have the SSB interest rates changed in the past 1 year and how have SSB performed compared to the more traditional Singapore government bonds, i.e. Singapore Government Securities (SGS)? The comparison for the 1st year (Oct 2015 to Sep 2016) is discussed in Singapore Savings Bonds – A Year On. This post continues the discussion for the 2nd year (Oct 2016 to Sep 2017).

The most important factor for both SGS and SSB is interest rates. In the 1st year, interest rates went down. However, in the 2nd year, interest rates went up, especially during the Nov to Dec 2016 period which saw US Federal Reserve raising interest rates again in Dec 2016 after a 1-year hiatus. Figs. 1 and 2 below show the 10-year interest rates for the 1st and 2nd year.

Fig. 1: 10-Year Interest Rate for Year 1

Fig. 2: 10-Year Interest Rate for Year 2

For the 2nd year, the highest 10-Year SSB interest rate achieved is 2.44%, for the tranche issued in Feb 2017. This is still lower than the all-time high of 2.78%, for the tranche issued in Nov 2015. The all-time low is 1.75%, for the tranche issued in Sep 2016. The current SSB interest rate is 2.07%.

If you have bought the 1st tranche of SSB in Oct 2015, the interest rate for the 2nd year would have stepped up from 0.96% to 1.09% in Oct 2016. The market price of SSB is a constant $100, as it is capital protected by the government. In comparison, the coupon (i.e. interest rate) for SGS is constant while the market price of SGS varies with prevailing interest rates, rising when interest rates fall, and falling when interest rates rise.

How does this 1st tranche of SSB compare with the corresponding 10-year SGS bond? Figs. 3 and 4 show the price performance of the SSB and 10Y SGS for the 1st and 2nd year.

Fig. 3: Price Performance of 10-Year SGS and SSB for Year 1

Fig. 4: Price Performance of 10-Year SGS and SSB for Year 2

In the 1st year, the 10Y SGS went up in price due to the fall in interest rates, resulting in a capital gain of 6.57%. On top of that, investors in 10Y SGS would have pocketed a coupon of 2.375%, which, based on the purchase price of $98.61 in end Sep 2015, is equivalent to a yield of 2.41%. The total gain for the SGS is 8.98%, compared to 0.96% for the SSB. The table below shows the comparison between SSB and SGS for the 1st year.


SSB SGS
Capital appreciation - 6.57%
Yield 0.96% 2.41%
Total 0.96% 8.98%

However, in the 2nd year, interest rates went up, especially during the Nov to Dec 2016 period, resulting in a capital loss of -2.53% for the SGS. The yield for the 2nd year, based on the price of $105.09 in end Sep 2016, is 2.26%. Thus, investors who hold the 10Y SGS for the 2nd year would have a net loss of -0.27%, compared to 1.09% for the SSB. The table below shows the comparison between SSB and SGS for the 2nd year.


SSB SGS
Capital appreciation - -2.53%
Yield 1.09% 2.26%
Total 1.09% -0.27%

Thus, when interest rates go up, it is better to hold SSB, as they are capital protected. However, when interest rates go down, it is better to hold SGS, as they can generate capital gains. By juggling between SGS and SSB, you can get the best of both worlds. The contrasting performance of SGS and SSB for the past 2 years shows that the discussion in Getting the Best of Both SSB & SGS is correct.


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Sunday, 30 October 2016

SSB Interest Rate Estimates – A Year On

Some readers might know that I run a parallel blog at (The) Boring Investor's Statistics that shows some of the investment statistics that I monitor on a regular basis. One of these statistics is a forecast of the interest rates of the Singapore Savings Bonds (SSBs) to be announced in the upcoming month. The interest rates for the SSB to be announced in the following month is based on the average yield (i.e. interest rates) of the Singapore Government Securities (SGS) benchmark bonds in the current month. As an example, the SSB to be announced in Nov (and issued on 1 Dec) is based on the average SGS yields in Oct. The SSB that is available for subscription in Oct, however, is based on the average SGS yields in Sep. Thus, by comparing the average SGS yields for Sep and Oct, you can assess whether you should apply for Oct's SSB (to be issued on 1 Nov) or wait for Nov's SSB.

There is, however, a small issue. Applications for SSBs close on the 4th last business day of the month. In the case of Oct's SSB, it closed on 26 Oct. Thus, if you are thinking of whether to apply for Oct's SSB or wait for Nov's SSB on 26 Oct, you only have the SGS yields from 1 Oct to 26 Oct to compare against the yields for the entire month of Sep. If the yields from 27 Oct to 31 Oct were to change drastically from the yields from 1 Oct to 26 Oct, your forecasts for Nov's SSB interest rates would be incorrect. 
 
For my (The) Boring Investor's Statistics blog, I usually blog on weekends only, hence, the forecast is carried out and posted even earlier, on the weekend prior to the close of application. This means that the post can sometimes be as many as 8 business days from the end of the month. The forecast error can be larger. As an example, for Oct, the application closed on 26 Oct, but my forecast was posted last Sun on 23 Oct. This means that I have 3 fewer days of data to carry out my forecast.
 
I usually provide 2 forecasts, one based on the SGS yields up to the date of forecast (known as the equal-weighted forecast), and another assuming the yields for the remaining days of the month to be the same as that on the last available date (known as the end-weighted forecast, because the yield on the last available date has a weight of 3-8 times more than all other days). After providing the forecasts for over a year, how accurate have my forecasts been? Fig. 1 below shows the forecast errors for both methods.

Fig. 1: SSB Interest Rate Forecast Errors

The figure above shows that the average errors for the end-weighted forecasts are smaller than that of the equal-weighted forecasts for all time periods except for the 10-year interest rates. However, on closer inspection, the equal-weighted forecast errors are of higher magnitude and are sometimes postive and sometimes negative, resulting in a smaller error when averaged. When compared using standard deviation, which considers only the absolute value of the errors, the end-weighted forecasts have smaller variance than the equal-weighted forecasts for all time periods. Thus, end-weighted forecasts provide better estimates of the SSB interest rates.

Fig. 2 below shows the forecast SSB interest rates superimposed on the SGS yields for the previous month. When SGS yields are relatively constant for the month, both forecasts yield very good results. However, when SGS yields are either rising or falling, the errors become larger. The equal-weighted forecasts have larger errors than the end-weighted forecasts because they do not take into consideration the direction of the SGS yields. End-weighted forecasts are more accurate as they give more weight to the SGS yields near the end of the month as described above.

Fig. 2: Accuracy of SSB Interest Rate Forecasts

Finally, the most valuable lessons that I learnt from forecasting SSB interest rates over the past 1 year is this: the future cannot be predicted. Although I could enhance my forecast methodology and perhaps provide good estimates of SSB interest rates, the best I could forecast is only 1 month in advance. I cannot forecast the SSB interest rates beyond 1 month. When the first tranche of SSB was announced in Sep 2015 with a 10-year interest rate of 2.63%, I forecasted that the next tranche of SSB would have a higher interest rate and decided not to apply for it. When the second tranche was announced with a 10-year interest rate of 2.78%, I was proven right! At that time, there was even an outcry among the SSB investors who had applied for the first tranche as their SSBs were now less valuable. Little did I expect that the SSB interest rates for all subsequent tranches would drop below that of the first tranche! The 10-year interest rate for the current tranche is only 1.79%, which is much lower than the 2.63% for the first tranche. Investors who bought into the first tranche of SSBs got a good deal after all. Smart alecs like me can only watch the SSB interest rates going lower.

If you are interested in forecasts of the SSB interest rates, you can refer to SSB Interest Rate Estimates at my (The) Boring Investor's Statistics blog. Just bear in mind the lesson I learnt above, which is that the future cannot be predicted.


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Sunday, 23 October 2016

Singapore Savings Bonds – A Year On

It has been a year since the launch of the first Singapore Savings Bonds (SSB) in Oct 2015. How have the interest rates of SSBs changed in this 1 year and how have they performed relative to the more conventional government bonds, namely, the Singapore Government Securities (SGS)?

Fig. 1 below shows the 10-year interest rates of SSBs (red line). The interest rates are computed as the average of the benchmark 10-Year SGS interest rates (blue line) over the previous month. (Note: There is always a confusion over the "month" of the SSB. The SSB announced in Oct is issued in Nov and based on the average rates of the 10-Year SGS benchmark bond in Sep.). As you can see from Fig. 1, interest rates have been on a downward trend, reflecting the eagerness of central banks around the world to lower interest rates, to even negative levels in some countries.

Fig. 1: SSB 10-Year Interest Rates

The highest 10-year interest rate achieved for SSBs was for the second tranche of SSBs issued in Nov 2015. The interest rate was 2.78%. The 10-year interest rate touched a low of 1.75% for the tranche issued in Sep 2016. The interest rate for the current tranche is not much higher, at 1.79%.

If you had bought the first 2 tranches of SSBs issued in Oct and Nov 2015, you would be happy with your purchase, since interest rates for all subsequent tranches have been below these rates. 

However, the performance of the more conventional 10-Year SGS bond was even better. Fig. 2 below shows the price performance of the 10-Year SGS bond since the issue of the first SSB.

Fig. 2: Price Performance of 10-Year SGS and SSB

On 1 Oct 2015, when the first tranche of SSB was issued, the 10-Year SGS benchmark bond traded at $98.61 for every $100 of bond principal. Due to the fall in interest rates, prices of bonds have been on the rise. A year later, on 30 Sep 2016, the same bond traded at $105.09. Investors who bought the SGS bond would have gained a capital appreciation of 6.6%. On top of that, investors would have received another 2.375% in coupons (i.e. interest) for holding the bond. Since investors bought the bond at less than the principal of $100, the coupons translate to an interest yield of 2.41% ($2.375 / $98.61). In contrast, SSBs are capital-guaranteed, which means that their value stays at $100 regardless of whether interest rates are going up or down. Over the same period, investors in the Oct 2015 SSB would have received 0.96% in interest, being the 1-year interest rate of the SSB. In total, investors in SSB and SGS would have received the following returns over the 1-year period.


SSB SGS
Capital appreciation - 6.57%
Interest 0.96% 2.41%
Total 0.96% 8.98%

Thus, the 10-Year SGS bond has outperformed the Oct 2015 SSB by as much as 8.02% over the 1-year period. The main reason is that interest rates have dropped from 2.54% in Oct 2015 to 1.74% in Sep 2016. 

Hence, if interest rates are rising, it is better to stay with SSBs as they are capital-guaranteed. However, if interest rates are falling, SGS are a better choice as they will gain in price. By juggling between SSB and SGS, you can gain from changes in interest rates. This is exactly the conclusion discussed a year ago in Getting the Best of Both SSB & SGS.


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Sunday, 20 September 2015

Sneak Preview of SSB Interest Rates

Nobody likes to lose money, so wouldn't it be nice if you could place your bets after the results are known? Well, the Singapore Savings Bonds (SSB) almost just allow you to do that. The interest rates for SSB are computed based on the average yields (i.e. interest rates) for the previous month's Singapore Government Securities (SGS). The applications for SSB will close on the 4th last business day of the month. So, by monitoring the SGS yields for the current month, you could estimate what would be the SSB interest rates for the next month. If the estimated interest rates for the next month are higher than that for the current month, it is advantageous to skip the current month's SSB and apply for the next month's SSB instead. Let us take a look at how this works.

The current month's SSB interest rates are shown below. They are based on the average yields of the previous month's SGS, which are also shown below. The SGS yields can be found at the SGS website. As you can see, the SSB interest rates are very close to the average yields of the 1-year, 2-year, 5-year and 10-year SGS bonds.


1-Year 2-Year 5-Year 10-Year
SSB Rates for Sep 0.96% 1.02% 2.01% 2.63%
Avg SGS Yield for Aug 0.96% 1.03% 2.03% 2.63%

For Sep, SGS yields have been rising and the average yields (up till 18 Sep) are shown below. Compared to the average SGS yields for Aug, the yields have risen across the board by 0.10% to 0.20%. If there is no significant change to the SGS yields from now till the end of the month, you can expect the SSB interest rates for Oct to be higher than that for Sep by the same margin.


1-Year 2-Year 5-Year 10-Year
SSB Rates for Sep 0.96% 1.02% 2.01% 2.63%
Avg SGS Yield for Aug 0.96% 1.03% 2.03% 2.63%
Avg SGS Yield for Sep (Todate) 1.12% 1.12% 2.22% 2.83%
Difference (Todate) 0.16% 0.10% 0.19% 0.20%

However, on 18 Sep, US Federal Reserve announced an important decision not to raise interest rates. This caused the SGS yields for that day to drop by as much as 0.1% or 10 basis points, which is considered significant. Since nobody can forecast how SGS yields will move from now till the end of the month, let us assume that the SGS yields for the next 7 working days would be the same as the yields for the latest available date, i.e. 18 Sep. Making this assumption, the estimated average SGS yields for Sep are shown below.


1-Year 2-Year 5-Year 10-Year
SSB Rates for Sep 0.96% 1.02% 2.01% 2.63%
Avg SGS Yield for Aug 0.96% 1.03% 2.03% 2.63%
Avg SGS Yield for Sep (Todate) 1.12% 1.12% 2.22% 2.83%
Avg SGS Yield for Sep (Estimated) 1.17% 1.13% 2.20% 2.79%
Difference (Todate) 0.16% 0.10% 0.19% 0.20%
Difference (Estimated) 0.21% 0.11% 0.17% 0.17%

The average SGS yields are estimated to continue moving up for the 1-year and 2-year bonds but down for the 5-year and 10-year bonds. Still, the SGS yields are estimated to be higher across the board by 0.11% to 0.21% for Sep than Aug. You can expect the SSB interest rates for Oct to be higher than that for Sep by the same margin.

Among the various SGS yields, the most important one is the 10-year SGS yield, because that determines the annualised return for the entire 10-year lifespan of the SSB. The higher, the better.

However, if 2 SSBs were to have the same 10-year interest rate but different 5-year interest rates, how would you choose? It depends on the individual investor's preference. A higher 5-year interest rate would mean that you can collect higher interest payouts earlier, even though over the entire 10-year lifespan of the SSB, you get the same annualied interest rate. However, because higher interest is paid out early in the SSB lifespan, the interest-on-interest compounding effect is lower. Consider 2 extreme cases in which one SSB pays out a constant 2.63% every year versus another one which pays out only in the 10th year. For the constant-payout SSB, the total interest you will get over the 10-year lifespan for every $100 invested is $26.30. For the bullet-payout SSB, the total interest you will get at the 10th year is $29.64, or $3.34 higher than the constant-payout SSB.

So, if the current month's SGS yields are higher than the current month's SSB interest rates, it is best to skip the current month's SSB and wait for the next month's SSB. However, what happens if the reverse occurs, i.e. next month's SSB interest rates are likely to be lower the current month's SSB interest rates? You can actually choose to invest in the current month's SSB and observe the future trend of SGS yields. Unlike fixed deposits and stocks where you can only get the interest/ dividend on the maturity of the fixed deposit or ex-dividend date of the stock, bonds pay accrued interest for the duration that you are holding the bond. Using the 1-year interest rate of 0.96% for the current month's SSB, you will get accrued interest of 0.08% for each month you are holding the bond. So while you are holding onto the SSB and waiting for the interest rates to rise, you are being paid for waiting. However, please take note that there is an application and redemption fee of $2 per transaction which will cut into the interest earned.

To conclude, things are seldom in favour of investors. But with SSB, things are tilted quite overwhelmingly in favour of investors! Not only are you allowed to place your bets after the results are known, you also have a SGS put option to guard against interest rate rises, as discussed in Getting the Best of Both SSB & SGS.


Sunday, 30 August 2015

Getting the Best of Both SSB & SGS

You probably have heard a lot about the Singapore Savings Bonds (SSB) and have formulated your investment strategy for it. Even my colleague who did not study finance can tell me that she will churn her SSB for newer ones if interest rate rises. Having studied finance and traded Singapore Government Securities (SGS) before, I should do one better than hers.

Before going into my investment strategy for SSB and SGS, let us understand what are the characteristics of SSB and SGS. SGS is the traditional government bond which is backed by the government. Like any other bonds, its price will rise if interest rate falls and fall if interest rate rises. SSB, on the other hand, is capital-guaranteed by the government. Regardless of the direction of interest rate, its price will never rise or fall. In fact, you cannot trade SSB in a secondary market. You can only sell it back to the government at the original price.

Thus, when interest rate rises, churning your current, lower-coupon (i.e. interest) SSB for newer ones with higher coupons to keep up with the higher inflation rate can be a good investment strategy. SGS, on the other hand, would be a poor investment as its price will fall in such an environment. However, when interest rate falls, instead of keeping your SSB until maturity, it is a good strategy to switch out of SSB into SGS to take advantage of the capital appreciation potential of SGS. When interest rate has fallen low enough, you can then switch back from SGS to SSB for the capital-guarantee feature of SSB.

To understand what kind of figures are we talking about, let us consider a 10-year SGS whose coupon rate is 3% and an equivalent SSB. The coupons from SSB will step-up in such a way that if you hold it for 10 years until maturity, the effective annual coupon rate is equivalent to 3%. On the other hand, SGS will pay a coupon of 3% from the first year onwards for the next 10 years.

Ignoring the effects of decreasing maturity of the SSB/ SGS with the pasage of time, if interest rate (known as Yield-to-Maturity) for a 10-year SGS were to rise to 4%, the price of the SSB would still be $100 (bond prices are quoted in face value of $100, so I will use the same convention here), whereas the SGS would fall to $91.82, a fall of 8%. Conversely, if interest rate were to fall to 2%, the price of the SSB would still be $100, while the SGS would rise to $109.02, a rise of 9%. Thus, if interest rate were to swing between 2% and 4%, the price of SGS would swing by $17.20. If this sounds interesting to you, you may wish to know that you are not limited to a 10-year tenure for SGS. The longest-maturity SGS is 30 years. The corresponding price range for a 30-year SGS for interest rate between 2% to 4% is $82.62 to $122.48, or a swing of $39.86. Not only that, the SGS will pay the full 3% coupon every year, whereas you will get the full 3% coupon from SSB only if you hold it for 10 years. 

Generally, how I view a SGS with a 3% coupon trading at an interest rate of 2% is, you will only get an effective 2% coupon from this point in time onwards (because the price will fall from $109.02 to $100 as it approaches maturity). The remaining 1% (i.e. 3% coupon minus 2% interest rate) is "paid upfront" in the form of capital appreciation. Selling the SGS at $109.02 effectively locks in the 1% coupon for the remaining maturity of the SGS.

How do you know if interest rates are going up or down? I do not know. But every month, I will keep track of where interest rates are relative to historical values. You can find it at my statistics blog, which is reproduced below for July's statistics.

Cumulative Interest Rate Distribution (Jul 15)

The figure above shows that the interest rate for the 10-year SGS (brown line) is finely poised around the 50th percentile mark, which means that historical interest rate for that SGS has been above the current interest rate 50% of the time and below it 50% of the time. Do take note that the 20-year and 30-year SGS were introduced in Feb 2007 and Mar 2012 respectively. Hence, the historical interest rate range that they can trade in might not be representative.

To conclude, SSB or SGS alone might not be a good investment asset for all interest rate environments, but together, they can make a very interesting investment asset!


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Wednesday, 19 September 2012

Government Bonds – The Tools

Now that you are equipped with the basic knowledge of trading SGS bonds, the next question to ask is when to buy or sell. To answer this question, you need to know the current yield relative to the historical range. A useful tool is to plot the cumulative distribution of the historical yields and the current yield. See the graph below.


The lines represent the cumulative distribution of the historical yields of all benchmark bonds while the triangles represent the current yield. Using the 3-month bill as an example, the average yield is about 1.5% historically while the current yield is less than 0.25%. As you can see, the current yields for practically all bonds are languishing at new historical lows except for the relatively new 30-year bonds. As bond prices move in opposite direction from interest rates, interest rates are likely to rise in the next few years and bond prices likely to drop (by a factor of Change in Interest Rate x Duration). Hence, significant potential losses exist for long-term bonds.

A second useful tool is to compare the spread between long-term and short-term bonds. Usually, a spread exists between these bonds, as longer-term bonds would need to offer higher yields to compensate investors for inflation in future. However, during certain periods, the spread could significantly widen or narrow beyond its usual range. This can give rise to potential trades in either long-term or short-term bonds. See the graph below.


In this graph, the blue line represents the yield of the shortest bill while the pink line represents the yield of the longest bond available (which could be the 15-year, 20-year or 30-year bond available at that time). The yellow line represents the spread between these 2 yields. As you can see, there is a range of between 1% and 3.5% in which the spread usually fluctuates. However, in Sep 2006, the spread was negative. A review of the long- and short-term yields reveal that this was a result of the short-term yield rising to meet the long-term yield. Such an anomaly is unlikely to continue for long and the strategy would be to bet that the short-term yield would decline to its usual range. Hence, the strategy would be to buy short-term bonds. Recall that the Change in Bond Price is approximately equal to Change in Interest Rate x Duration, you would want to pick the bond whose yield is as close to the short-term yield as possible while at the same time have as long duration as possible. This is actually a trade-off as the longer the duration (and maturity), the further away its yield will be from the short-term yield.

Consider another example in Jun 2008 when the spread reached the higher range of 3.5%. Here, the rise in spread was contributed both by a rise in long-term yield and a fall in short-term yield. Again, this high spread could not be sustained for long and either a fall in either long-term yield (which is profitable if you buy the bond) or a rise in short-term yield (which is loss-making if you buy the bond) or both would be likely. However, from the historical trend of long-term yields, the long-term yield at that time was not at the high-end of its range and it was possible that the long-term yield could move higher and result in a loss for bond holders. Similar, the short-term yield was at the low-end of its range and could potentially rebound. This transaction, while likely, is not a "sure" thing compared to the earlier example. As it turned out, the long-term yield fell while the short-term yield roughly held steady. Holders of long-term bonds would have made a profit.

The above are 2 useful tools for investment in SGS bonds. Hope they can assist you in investing in SGS bonds!


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Sunday, 16 September 2012

Government Bonds – A Primer

Equities are not the only investment class. Most retail investors usually neglect bonds, as they are not listed on the stock exchange and are not as volatile or exciting as shares. Moreover, trading in government bonds (known as Singapore Government Securities or SGS) requires one to visit the local banks that serve as traders in the secondary SGS bond market. The bank officers are usually clueless about the trading process and often need to consult their Treasury colleagues at the headquarters. Nevertheless, SGS bonds can be a useful asset class in any investment portfolio.

Before beginning, there are several important basic knowledge to be learnt for bond trading. Firstly, bond prices are quoted in values of $100. So, a bond that is priced at $108 means that you buy $100 worth of bonds at $108.

Secondly, the bond prices quoted are clean prices, meaning it does not include the interest accrued. The price that you actually pay is the dirty price, which is the clean price ($108 for the example above) plus any accrued interest at the date of settlement. Let's work through this with one of the SGS bonds, NZ10100F, which has a coupon (i.e. interest) rate of 2.875% and matures on 1 Sep 2030. Its current quoted price is $109.48. Its accrued interest since the last coupon payment (on 1 Sep 2012) is $0.10, representing the coupon of 2.875% for 13 days since 1 Sep 2012. So, if you wish to buy this bond, you'll need to pay the clean price of $109.48 + accrued interest of $0.10 or $109.58. The further away from the last coupon payment date, the higher is the accrued interest. Nevertheless, you will actually get back the accrued interest from the next coupon payment, which will be for the period from 1 Sep 2012 till 31 Mar 2013. Of course, when you sell the bond, the buyer will also have to pay you the accrued interest for the days that you have held on to the bond since the last coupon payment.

So, after paying $109.58 for the bond, what do you get back in return? You'll get a semi-annual coupon of 2.875% (or $1.4375 per $100 bond) until it matures on 1 Sep 2030, upon which you will also get back the principal of $100. Overall, what is the net return? This is known as the Yield-to-Maturity (YTM), which can be computed either with Excel or more simply, a bond tool, one of which can be found on the SGS website. See below for a screenshot.



Also on the SGS website are the daily closing prices of all SGS bonds (https://secure.sgs.gov.sg/fdanet/SgsBenchmarkIssuePrices.aspx#), which is the primary means of checking the price of SGS bonds.

Thirdly, bond prices move in opposite directions from interest rates. When interest rates drop, bond prices rise and conversely, when interest rates rise, bond prices drop. This is because as the prevailing interest rates rise, the fixed coupon from the bond is no longer as attractive and the bond must drop in price to compensate for the relatively less attractive coupon. The amount bond prices move relative to interest rates is dependent on the duration of the bond. The longer the bond is from maturity, the higher the duration and the more the price will move in response to interest rate changes. For small changes in interest rates, the relationship can be approximated by the following formula: Change in Bond Price = Change in Interest Rate x Duration of Bond. Thus, for a 20-year bond with a duration of approximately 16 years, a 0.1% rise in interest rates will result in a 1.6% drop in price. The exact duration of a bond needs to be computed using Excel, but can be approximated by 0.8 x its remaining maturity if it still has more than 10 years remaining and by 0.9 x its remaining maturity if it still has more than 5 years remaining. For bonds that are maturing in less than 5 years, the duration is approximately equal to its remaining maturity.

With the above basic information, you should be ready to start trading in bonds.


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